ferromagnetically contacted single-wall carbon nanotubesjjensen/publ/thesis-ii.pdf · 2009. 6....

Ferromagnetically ContactedSingle-Wall Carbon Nanotubes

Ane Jensen

Ph.d. Thesis

Department of PhysicsTechnical University of Denmark

andNano-Science Center, Ørsted Lab.

NBI fAPG, University of CopenhagenSeptember 2003

Ferromagnetically ContactedSingle-Wall Carbon Nanotubes

Abstract

Ferromagnetic leads of metallic Fe and semiconducting Ga1−xMnxAs, areapplied on single-wall carbon nanotubes (SWNTs), with the purpose ofstudy spin-polarized transport under the unique conditions offered by thenanotubes. The electron transport in SWNTs is one-dimensional and bal-listic. This may imply the formation of a Luttinger liquid, where the elec-tron spin and charge degrees of freedom are decoupled. Usually, the tubesform tunnel contacts to the leads and behave as quantum dots at low tem-peratures. In such devices characteristic phenomena related to the elec-tronic spin, e.g. shell-fillings and Kondo resonances have previously beendemonstrated to occur. The present experiments show that the impact ofthe ferromagnetic leads is a hysteretic magnetoresistance at low tempera-tures. The hysteresis is found to increase strongly when the temperatureis reduced to the millikelvin regime. The experiments show a surprisinglylarge diversity in sign and magnitude of the hysteretic magnetoresistance.

Simple models of spin-polarized transport are discussed, and qualitativeagreements between their predictions and the experiments are obtained.However, the models fail to explain the observations that both signs ofthe hysteretic magnetoresistance may occur, and that the relative changesapproach 100% in some of the devices. The experiments, presented inthe thesis, show clear effects due to spin-polarized tunnelling through theinterface between a ferromagnetic lead and a single-wall nanotube. Thetheoretical understanding of spin-polarized tunnelling is still incomplete,and a detailed understanding of the present observations has to await fur-ther experimental and theoretical developments.

i

Enkeltvægs kulstof-nanorørmed ferromagnetiske kontakter

Resumme

Komponenter af enkeltvægs kulstof-nanorør med ferromagnetiske elek-troder af henholdsvis metallisk Fe og halvledende Ga1−xMnxAs er stude-ret, med henblik pa at udforske spinpolariseret transport gennem de unikkenanorør. Elektrontransporten i nanorør er endimensional og ballistisk. Deendimensionelle forhold kan betyde at der dannes en Luttinger væsketil-stand, som blandt andet forarsager en separation af elektronernes ladnings-og spin-tilstande. Som regel dannes der tunnelkontakter mellem nanorørog elektroder, hvorved nanorørene ved lave temperaturer vil opføre sigsom kvanteprikker. Egenskaber relateret til elektronernes spin, sa somspin-skaller og Kondo resonanser er tidligere observeret i sadanne kompo-nenter. De aktuelle eksperimenter viser, at nanorør med ferromagnetiskeelektroder udviser stor hysteretisk magnetomodstand ved lave tempera-turer. Størrelsen af den hysteretiske opførsel vokser kraftigt nar tempera-turen reduceres til millikelvin omradet. Malingerne viser et overraskendestort udfaldsrum, med hensyn til fortegn og størrelse, af den hysteretiskemagnetoresistans.

Simple modeller for spinpolariseret transport bliver diskuteret. Deres for-udsigelser og eksperimenterne stemmer kvalitativt overens. Modellerne erdog ikke i stand til at forklare observationerne af begge fortegn af den hys-teretiske magnetoresistans samt relative ændringer pa op til omtrent 100%i nogle komponenter. Eksperimenterne, som bliver præsenteret i denneafhandling, udviser klare effekter af spinploariseret tunnelering over kon-taktfladen mellem en ferromagnetisk elektrode og et enkeltvægs kulstof-nanorør. Den teoretiske forstaelse af spinpolariseret tunnelering er endnubegrænset. En detaljeret forklaring af de foreliggende observationer maafvente fremtidige eksperimentelle og teoretiske landvindinger.

iii

Foreword

This thesis is a presentation of the work I have performed during mythree years PhD study. The PhD study was carried out at the TechnicalUniversity of Denmark at Department of Physics in the PhD programmeMathematics, Physics and Informatics, with a scholarship grant from theTechnical University of Denmark. The thesis presents experimental workon ferromagnetically contacted single-wall carbon nanotubes, which wasmainly carried out at the Nano-Science Center, Ørsted Laboratory, NielsBohr Institute for Astronomy, Physics and Geophysics (NBIfAPG), Uni-versity of Copenhagen. Prior to my PhD study I spent four months as atrainee at NTT Basic Research Laboratories, Japan in the group of HideakiTakayanagi and Junsaku Nitta. My traineeship at NTT and the work onmy master thesis, provided me with an introduction to the field of spin-tronics, which has been a great help to me during my PhD study.

The main supervisor on my project has beenProfessor Steen Mørup Department of Physics, Technical University ofDenmark.Co-supervisors:Associate Professor Jørn Bindslev Hansen Nano-Science Center, ØrstedLaboratory, NBIfAPG, University of Copenhagen and Department of Phy-sics, Technical University of DenmarkAssociate Professor Poul Erik Lindelof Nano-Science Center, Ørsted Lab-oratory, NBIfAPG, University of CopenhagenAssociate Professor Claus Schelde Jacobsen Department of Physics, Tech-nical University of Denmark.

Acknowledgement

The experimental techniques for the fabrication of single-wall carbon nan-otube devices were developed at the Ørsted Laboratory by Jesper Nygardand Jørn Borggreen in cooperation with Per Ruggard Poulsen and DavidH. Cobden (Washington). Some of the measurements, and the measure-ment setups, were made in collaboration with Jesper Nygard and JonasRahlf Hauptman. Janusz Sadowski was in charge of the molecular-beamepitaxy (MBE) growth of GaAs/AlAs and Ga1−xMnxAs in the MBE ma-chines at the Ørsted Laboratory and in Lund. Professor Pavel Streda fromthe Institute of Physics, Academy of Sciences of the Czech Republic hasbeen very helpful with the interpretation of the experiments.

I would like to thank Jesper Nygard, Jørn Borggreen, and Jonas RahlfHauptman for their collaboration and help with the experimental work

v

and for numerous fruitful discussions.

Brian Skov Sørensen and Søren Erfurt Andresen have been the best roommates and supported me with helpful assistance and positive remarks.

The forum of our nanotube journal club, held by Thomas Sand Jespersen,Jonas Rahlf Hauptman, Kristoffer Haldrup, Jesper Nygard, Kasper Grove-Rasmussen, Henrik Ingerslev, and Poul Erik Lindelof, has been an excel-lent place for discussions and the learning about the strange world of nan-otubes.

I also wish to thank all members of the group of Nano Physics at the ØrstedLaboratory for providing me with a pleasant place to work at.

I have been very happy to participate in the NEDO-workshop on spintron-ics. I thank Junsaku Nitta and Jørn Bindslev Hansen and the rest of theparticipants in the workshop for many interesting and inspiring symposiaand the accompanying stimulating discussions.

I have benefitted much from the participation in the study group on nano-magnetism organized by Steen Mørup.

Thanks to Cathrine Frandsen for help on MFM.

Inge Rasmussen and Johannes Skov have provided valuable work in orderto ensure the metallization chamber to be in good shape. Thanks for yoursupport during my PhD study.

Big thanks to Nader Payami in the processing laboratory and the peopleat the workshop for their help with any practical problems.

Finally, thanks to Niels W. Andersen and Jens Jensen for their help duringthe final work of the thesis writing.

Ane Jensen, September 22, 2003

vi

Contents

1 Introduction 1

1.1 Spin-tronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Mesoscopic Transport in Carbon Nanotubes . . . . . . . . . . 6

2 Experimental Techniques 13

2.1 Device Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Preparation of Single Wall Carbon Nanotubes . . . . . . . . . 13

2.1.2 Fabrication of Devices with SWNTs . . . . . . . . . . . . . . 16

2.2 Setup for Transport Measurements . . . . . . . . . . . . . . . . . . . 22

3 Characterization of the Ga1−xMnxAs Films 25

3.1 Hall-Bar Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Discussion of the Results . . . . . . . . . . . . . . . . . . . . 26

3.2 GaMnAs Leads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Experimental Results 33

4.1 Experiments on Fe Contacted Nanotubes . . . . . . . . . . . . . . . . 33

4.1.1 Fe Leads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

vii

4.1.2 Devices of Fe Contacted Tubes . . . . . . . . . . . . . . . . . 34

4.2 Experiments on Ga1−xMnxAs Contacted Nanotubes . . . . . . . . . . 40

4.2.1 Devices of GaMnAs Contacted Tubes . . . . . . . . . . . . . 41

5 Interpretation and Discussion 49

5.1 Nanotube Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 The Effects of the Ferromagnetic Leads . . . . . . . . . . . . . . . . 52

5.2.1 Observations of Hysteretic Magnetoresistance . . . . . . . . . 52

5.2.2 Models of Spin-Polarized Transport . . . . . . . . . . . . . . 54

5.2.3 Discussion of the Spin-Polarized Transport . . . . . . . . . . 59

6 Conclusion 61

Appendix

A Measurements on Fe contacted nanotubes 67

A.1 Fe-T-Fe#1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.2 Fe-T-Fe#3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.3 Fe-T-Fe#4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

B Measurements on GaMnAs/Au contacted nanotubes 71

B.1 GaMnAs-T-Au#2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

B.2 GaMnAs-T-Au#3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

C A Simple Model of the Contact between Lead and SWNT 73

D Two Spin-Channel Conductance 77

viii

Chapter 1

Introduction

An introduction to measurements on ferromagnetically contacted single-wall carbonnanotubes naturally falls into two parts. I will start by presenting the field of spinelectronics, or in short spin-tronics, and subsequently give an introduction to carbonnanotubes, focusing on properties related to transport and spin.

1.1 Spin-tronics

The class of electronics based on the electron spin, commonly referred to as spin-tronics, has emerged rapidly. Spin-tronics rely on the ability to transport and manipu-late spin. It has been argued, that spin-based electronics may have several advantagesover traditional charge electronics. First of all, the adding of spin-dependent effectsto standard electronics generates new devices with new functionalities. Furthermore,spin-tronics devices are believed to have low power consumption and high switchingspeed compared to electronics. For reviews of the topic see references [1, 2].

In ferromagnetic metals (FMs) an imbalance between up and down spin electrons ispresent in the narrow d-bands, in order to minimize the exchange energy. This im-balance is the origin of the magnetization of the metal. The spin-dependent elec-tronic states generate a polarization of the current carrying electrons, implying a spin-polarized current. The polarization P of the current depends on to which extent theunpolarized s- and the polarized d-bands cross the Fermi energy, and it is expressed by

P =Jmin − Jma j

Jmin + Jma j=

Nmin(EF)−Nma j(EF)

Nmin(EF)+Nma j(EF)(1.1)

1

2 1. Introduction

Where Jmin(ma j) is the current of minority (majority) spin electrons, and Nmin(ma j)(EF)is the density of states at the Fermi energy for electrons with minority (majority) spin.

The most efficient way to detect the current polarization in FMs is by measuring thetunnel current between the FM and a superconductor. This was demonstrated byTedrow and Merservey [3], who made use of the fact that spin-polarized electronscan tunnel from a FM into a non-magnetic material. The situation is shown schemat-ically in figure 1.1a. The density of states in a superconductor has sharp maxima justaround the superconducting gap. In a magnetic field, the Zeeman splitting causes thesharp maximum in the density of states to separate into two, one for each spin state.These sharp spin states are effective probes of the spin-dependent states in the FM.Superconducting tunnel contacts for the detection of the polarization are still widelyused today, and are even more efficient in the Andreev reflection regime [4, 5]. Theexperimental values for current polarization in the transition metals (Fe, Ni, and Co)lie within the range of 35−45% [3, 4, 5].

An important improvement in detecting spin transport was found by Julliere [6], whenhe realized spin-polarized tunnelling between two FMs. In case of total current po-larization, as sketched in figure 1.1b, tunnelling is blocked when the two FMs aremagnetized anti-parallel, while tunnelling is possible in the parallel configuration. Itis straightforward to generalize the model to any polarizations (P1, P2) in the two FMs.The conductance is proportional to the density of states at the Fermi energy on bothsides of the tunnel junction. When the spins are not allowed to be scattered, the con-ductance in the parallel configuration GP is proportional to N1,min(EF)N2,min(EF) +N1,ma j(EF)N2,ma j(EF), whereas the conductance in the antiparallel configuration GAPis proportional to N1,min(EF)N2,ma j(EF)+ N1,ma j(EF)N2,min(EF). With the definitionof P equation (1.1) one finds:

∆GGP

=GP −GAP

GP=

2P1P2

1+P1P2(1.2)

The model is usually referred to as Jullieres model, and devices based on this prin-ciple as spin-valve devices. Spin valves have applications as magnetic memory andmagnetic read heads.

Spin transport may be achieved in nonmagnetic metals [7]. A magnetic current maybe injected from a FM lead into a normal metal and detected by another FM lead assketched in figure 1.1c. The spin-polarized transport is limited by the spin-relaxationlength in the normal metal. The relaxation length of spin may extend the length of theelectron mean-free path. In aluminum the spin-relaxation length was experimentallyobserved to be L = 0.1mm at the temperature T = 40K [7].

The effort for achieving spin injection in semiconductors was triggered by Datta and

Ferromagnetically Contacted Single-Wall Carbon Nanotubes

Spin-tronics 3

Figure 1.1: The spin-polarized transport represented by density of states diagrams.Top: no electron transport. Bottom: transport of spin-down electrons. a) Tunnellingexperiment on FM-superconductor systems. The Zeeman splitting in a magnetic fieldcreates effective probes for spin-polarized states in the FM. Electron transport oc-curs solely when the device is biased correctly and the spin states are aligned. b)Tunnelling current between two FMs is blocked in the antiparallel configuration andoccurs in the parallel configuration. c) Spin-polarized transport in a normal metal.The two FMs act as injector and detector of the spin-polarized transport.

Das’s proposal of the spin field-effect transistor (spin-FET) in 1990 [8]. The spin-FET utilizes a small-gap semiconductor, where the electron spin is manipulated via agate controlled spin-orbit effect [9]. The electron spin is injected and detected via FMleads contacted to the semiconductor, based on the principle sketched in figure 1.1c.Unfortunately, the simple injection and detection of spin-polarized current in a semi-conductor between two FM leads has proven to be complicated [10]. Primary researchresults display very small spin-transport effects in semiconductors [11, 12]. Obstacles,hindering spin injection into semiconductors, have now been defeated by introducingtunnel barriers between the FM and the semiconductor [13] or by making use of thefairly new class of semiconductors: the diluted magnetic semiconductors [14, 15].

Diluted magnetic semiconductors are important players in the spin-tronics field, forreviews see references [16, 17]. One widely used ferromagnetic iii-v semiconductor isGa1−xMnxAs (GaMnAs) first grown by Ohno and co-workers [18]. A concentration x


4 1. Introduction

of magnetic elements, Mn, is introduced in GaAs, thereby producing a ferromagneticsemiconductor. Ferromagnetism occurs for x & 2%. Mn has a very low solubility inthe semiconductor. This problem has been solved by low temperature (200−300C),non-equilibrium, molecular beam-epitaxial growth of the ferromagnetic semiconduc-tor. The Curie temperature of GaMnAs seems to be highly dependent on parametersrelated to the quality of the semiconductor crystal, and for thin films, the film thick-ness has a strong impact as well. Typically, it is found to be about 100 K, with thepresent record being TC = 150 K [19]. Mn introduced in GaAs acts as an accep-tor, hence, GaMnAs is a highly p-doped semiconductor, with Mn ions (2+) of spin5/2 on localized sites in the lattice. The localized spins are too far apart to interactdirectly, therefore the ferromagnetic coupling between Mn ions is believed to be me-diated by the hole carriers. The hole mediated ferromagnetism is described in a simpleand complete manner by the Zener model [17]. If the localized spins are ordered fer-romagnetically their interaction with the hole carriers will, in order to minimize theexchange energy, create a spin splitting of the bands. Of course this spin splitting de-creases the entropy and increases the free energy. But at low temperatures the energycost, from the increased free energy, is lower than the energy gain, from the mini-mization of the exchange energy. Therefore, a ferromagnetic ordering of Mn spins iscreated. The same result is obtained if the system is described in the Ruderman-Kitel-Kasuya-Yosida (RKKY) picture. In this picture, the sign of the RKKY interaction isalways ferromagnetic, as the cut-off length of the interaction between the holes is muchsmaller than the length at which the RKKY interaction changes sign. Theoretically, thecurrent polarization of the holes in GaMnAs is highly dependent of the carrier density,and it is supposed to reach 80% under the right conditions [17]. It has been shown,theoretically [17] and experimentally [20, 21] that there is a strong correlation betweenthe carrier density, or as well the current polarization, and the Curie temperature.

1.2 Carbon Nanotubes

Carbon nanotubes are nano-structured tubular molecules of carbon. The field of nano-tubes has attracted great interest because of their exotic electric as well as mechanicalproperties. It is a playground for investigations of fundamental physics, and nanotubesmay have potential for technological applications. A detailed review of the field isgiven by Dresselhaus et al. in reference [22]. Multi-wall carbon nanotubes (MWNTs)were discovered by Iijima in 1991 by transmission-electron microscopy in carbon-sootprepared by arc discharge. Arc discharge is a process where a high current betweentwo carbon electrodes creates a plasma in a He atmosphere [23]. Two years later thesingle-wall carbon nanotubes (SWNTs) were observed after arc discharge under co-evaporation of iron [24]. Soon after a new method, the laser-ablation method, fornanotube production was developed by Smalley and co-workers [25]. This method


Carbon Nanotubes 5

is a well controlled process, where carbon is evaporated by pulses of lasers. By thistechnique it is possible to produce large quantities of SWNTs, and it gave a burst tothe research in SWNTs. Another nanotube growth technique, chemical-vapor deposi-tion (CVD), developed by the group of H. Dai [26], is based on vapor phase growth,and utilizes decomposition of hydrocarbons at temperatures of about 1000C. Thistechnique may produce significant quantities of tubes at a very low cost.

Figure 1.2: a) A sketch of a two-dimensional sheet of graphite, with the chiral vectordefining a carbon nanotube. b) The reciprocal space for a sheet of graphite. The Fermisurface is in the K-points. c) Band diagram for a graphite sheet (from reference [22]).d) A SWNT (5,5). e) The reciprocal space for a (6,6) carbon nanotube. f) Banddiagram for a (6,6) nanotube. Two energy bands intersect the Fermi energy at theK-points indicated by the arrow (from reference [27]).

Carbon nanotubes are essentially cylinders of rolled-up two-dimensional graphite she-ets. SWNTs have the simplest structure, and consist of single sheets. The diameter ofa SWNT is of the order of 1 nm, limited by the energy-cost of bending the graphitesheet and the instability of a two-dimensional graphite sheet. In contrast, MWNTs areformed by several coaxial shells of rolled-up sheets, held together with weak van derWaals forces. MWNTs may obtain diameters in the order of 10s of nm.

The building block for carbon nanotubes is a sheet of graphite, see figure 1.2a, con-sisting of carbon atoms in an sp2 configuration and forming a planar hexagonal lattice.The fourth valance electron pz hybridizes with the rest of the pz-electrons, forming adelocalized π-band drawn in figure 1.2c. The Fermi surface occurs only in discretepoints of the hexagonal reciprocal lattice, the K-points, shown in figure 1.2b and c. Arolling up of the carbon sheet creates a new periodicity around the edge of the tube, andcauses boundary conditions for the wave vector. As a result, energy gaps will appearunless the K-points in the original hexagonal reciprocal lattice match the boundary


6 1. Introduction

conditions for the wave vector, as fulfilled in figure 1.2e and f. The rolling up of thegraphite sheet to form nanotubes, is conveniently described by the chiral vector, whichcircumferences the tube. The chiral vector connects two crystallographically equiva-lent points and is expressed by the integers (n,m) with respect to the lattice vectorsa1 and a2 of the graphite sheet. As a consequence of the boundary conditions for thewave vector, carbon nanotubes can be either metals or semiconductors, depending onthe chiral vector. For n = m the tubes are metallic, since the K-points match the bound-ary conditions for the wave vector. For n−m = 2p (p is an integer) almost metallictubes are formed, as the K-points are shifted a bit, due to the curvature of the graphitesheet, and the matching with the wave-vector is not exact. The rest of the tubes aresemiconducting. For metallic SWNTs two energy bands cross the Fermi energy, im-plying one-dimensional (1D) transport of electrons in the tube direction. The spacingbetween the energy subbands is fairly large, of the order of 1 eV as indicated in theband diagram figure 1.2f, and ensures 1D nature of SWNTs well above room tempera-ture. Typically, the scattering is small and ballistic transport is expected, thus the idealconductance of SWNTs is 2G0 = 4e2/h.

The electronic mixing between each shell in MWNTs is small, and the electronicproperties of MWNTs are very similar to those of SWNTs. The differences beingthat observations suggest quasi-ballistic or even diffusive transport properties, and thesize of MWNTs enable measurements of magnetoresistance originating from weak-localization effects [28].

The tube growth techniques are selective in the way, that the outcome is either SWNTsor MWNTs, depending on parameters such as catalytic materials. But a selectivegrowth of nanotubes with a specified chiral vector, and thereby specific electronicproperties, is not attainable with the present synthesis techniques.

1.2.1 Mesoscopic Transport in Carbon Nanotubes

Transport measurements on nanotubes are typically done on three terminal devices.The tube is directly contacted by two metallic leads; source and drain. The third ter-minal operates as a capacitatively coupled gate, which can modulate the charge on thetube. At room temperature two distinctive behaviors of conductance G, measured as afunction of gate voltage, are displayed. One originates from the semiconducting tubes,here G varies exponentially with the gate voltage as fist reported by Tans et al. [29],and one from metallic tubes, where G is independent of the gate voltage.

At low temperatures the size of the tube implies the formation of a Coulomb blockade(CB) regime. The CB regime has been investigated in devices of semiconductors [30]and in nanotubes [31, 32] forming quantum dots (QDs). In nanotube devices tunnelcontacts are usually formed between the nanotube and the leads. Hence, the nanotube


Carbon Nanotubes 7

Figure 1.3: A schematic presentation of a carbon nanotube QD in the CB regime.The tube is represented with discrete electron states, tunable via the gate voltage, andforming tunnel contacts to the leads: source and drain. a) The lowest empty stateof the tube is aligned with the Fermi energy in source and drain electrodes, allowingtunnelling through the QD. b) No empty states in the tube are present at the Fermienergy, therefore the tunnelling is blocked. c) A finite bias voltage is applied over thetube, whereby tunnelling to higher lying states is possible, when the Fermi energy ofthe source is aligned with the lowest empty state in the tube.

behaves as a QD, when the energy cost for adding a unit charge to the tube: Eadd islarger than the thermal energy (kBT ). Eadd is limiting the motion of charges on andoff the dot, leading to the CB sketched in figure 1.3. In the CB regime, the numberof electrons on the dot is quantized. Thereby, the CB devices may be referred to asartificial atoms. There are two characteristic contributions to Eadd . The first contri-bution is the electrostatic energy U = e2/CΣ, where CΣ is the total capacitance of thenanotube QD. If the capacitance to the leads may be neglected CΣ is determined asthe capacitance of the isolated tube. CΣ ≈ Ctube = 2πεrε0L/ ln(2z/r), where εr, L, z,and r are the average dielectric constant, tube length, distance between tube and ca-pacitatively coupled electrodes, and tube radius, respectively. A typical value wouldbe U ≈ 5 meV for L ≈ 1µm, z ≈ 350 nm, and the dielectric constant of SiO2: εr ≈ 4.SiO2 is the most widespread substrate for nanotube devices. In reality, the capacitancesbetween the leads and the tube may influence the electrostatic energy measured in nan-otube devices. The second contribution to Eadd is the single particle level spacing δE,approximated simply by the energy level spacing in a 1D box. Two sub-bands at theFermi energy reveal the energy level spacing: δE ≈ hv f /(4L)≈ 0.8 meV, h is Planck’sconstant, v f ≈ 8 · 105 m/s is the Fermi velocity taken from graphite, and L ≈ 1µm isthe length. The approximated values for the energies imply, that nanotube devices arein the CB regime at temperatures much lower than 70 K.

Experimental results for a metallic nanotube device of G versus gate voltage at varioustemperatures, are shown in figure 1.4. Oscillations in G appear at low temperatures.These oscillations evolve into sharp peaks as the temperature decreases further, due to


8 1. Introduction

the CB. Figure 1.3a displays a situation where the gate voltage corresponds to a CBpeak, where the energy of the lowest empty state aligns with the Fermi energy in theleads. Hence, single electrons can tunnel through the dot, and G has a maximum. Infigure 1.3b the gate voltage has been changed and the electron states in the QD are notaligned with the Fermi energies of the leads, therefore tunnelling and G is suppressed.Electron tunnelling through the dot is possible as well, when applying a finite biasvoltage V over the source and drain leads. In figure 1.3c the Fermi energy of the leftlead is pulled up to the energy of the first empty state enabling the electrons to tunnel,this give rise to a peak in the differential conductance dI/dV . Further increase willallow tunnelling through additional states. This process is symmetric in V , meaningthat tunnelling through occupied states for negative voltages occur as well. MeasuringdI/dV as a function of V and gate voltage is a powerful tool to visualize the energyspectrum of the nanotube-QD. Figure 1.5b presents a bias spectrum at T = 100 mK.The dark lines correspond to transitions through excited states, forming a characteristicdiamond structure. Inside the diamond no current flows. The uppermost point in biasvoltage, Vmax in the diamond, is a measure of the electrostatic energy, as U ≈ eVmax.

Figure 1.4: Coulomb blockade in a metallic nanotube device. G as a function of gatevoltage measured at various temperatures. The insert shows a LL-like behavior of Gversus T .

The 1D nature of metallic nanotubes may have pronounced effects. 1D systems aresupposed to obey the Luttinger liquid (LL) behavior [33]. Spin injection into a LLis analyzed by Balents and Egger [34]. The LL is a correlated ground state of theelectrons, implying a separation of the electron charge and spin variables. The LL isquantified by the parameter g. g 1 is a highly correlated 1D electron state, whereasa noninteracting electron gas has g = 1. The parameter g for a nanotube device is


Carbon Nanotubes 9

determined from the electrostatic energy and the energy level spacing as:

g =

(

1+2Utube

δE

)−1/2

(1.3)

where Utube = e2/Ctube and δE is defined for a nanotube-QD on page 7. The LL resultsin power-law dependencies. In the linear regime, G is related to the temperature T asG ∝ T α ; and for large applied bias voltage the differential conductance depends of thebias voltage as: dI/dV ∝ V α . Where α is dependent of the geometry of the systemand given by:

αend =14

(

1g−1)

, αbulk =18

(

1g

+g−2)

(1.4)

where end is to be used if the leads are at the effective end of the tube, whereas bulkapplies in the case where the leads couple to the bulk of the 1D nanotube system. In-sertion of the expressions for the electrostatic energy and energy level spacing, deter-mined for a nanotube-QD on a SiO2 substrate, gives g≈ 0.28, αend ≈ 0.65, and αbulk ≈0.24. Experimental evidences of the LL have been observed in SWNTs [35, 36] as wellas in MWNTs [28, 37]. The observation in figure 1.4 of a decreasing conductance asa function of decreasing temperature may indicate the LL behavior, which predicts apower law dependence of G ∝ T 0.5 when the device is above the CB regime (T & 40 K).

QDs of metallic SWNTs have revealed appealing characteristics associated with theelectron spin, such as Zeeman splitting as well as shell-filling and the Kondo effect.

An applied magnetic field causes a Zeeman splitting of the energy level spectrum,indicated by the arrow in figure 1.5c. The splitting is given by gµBB; g is the g-factor found to be 2.0 [38] and µB is the Bohr magneton. From the measurements itis deduced that the total spin on the dot alternates between 0 and 1/2, correspondingto an alternation between even and odd numbers of electrons on the tube. This effectis due to the pairing of the spins at the energy levels of the QD, also known as spinshells [39]. The same effect is indicated in the separation between energy levels. Two-electron spin shells have been reported in high-resistive devices [40], while a four-electron periodicity, originating from the two-electron bands at the Fermi energy, isreported in low resistivity devices [41].

The exchange interaction between the localized spin of a magnetic impurity ion andthe spins of the itinerant conduction electrons leads to the Kondo effect. The exchangeenergy is minimized, and the impurity spin is screened, when the impurity spin and amany-body coherent spin state of the conduction electrons condense into a singlet con-figuration [42]. Historically, the Kondo effect has been studied in metals with magneticimpurities, but the field has attracted new interest with the discovery of the Kondo ef-fect in QDs, where the dot acts as an artificial impurity with a tunable spin [43]. TheKondo effect has been observed in semiconductor single-electron transistors [44], andin devices of SWNTs [45] and MWNTs [46].


10 1. Introduction

Figure 1.5: CB in metallic nanotube devices. a) Discrete CB peaks in G at T =

100 mK. b) Gray scale bias spectrum for a small section of a, as indicated by lettersP, Q, and R. The differential conductance is plotted versus gate and bias voltage.The dark areas show high differential conductance. c) Gray scale bias spectrum forapplied magnetic field. From reference [38].

The unique electronic properties of carbon nanotubes may be utilized in an investiga-tion of the role of the spins in the transport of electrons. The transport in carbon nan-otubes is close to being ballistic. This implies a long spin-relaxation length, wherebynanotubes form an almost perfect spin-transport medium.

Spin transport has been investigated in carbon nanotubes by contacting them with twoFM leads. The diameter of the tubes, and thereby the size of the contact area betweentube and leads, is much smaller than the typical magnetic domain size. Hence, asweeping of the magnetic field will, most likely, cause abrupt alternation between thesaturated parallel and antiparallel configurations of the magnetization in the contactareas. Accordingly, a spin-valve effect may occur, as described by Jullieres model,equation (1.2). The spin-valve effect in MWNTs contacted by a FM was first reportedby Alphenaar and co-workers [47]. Afterwards, their results have been reproduced byseveral groups [48, 49], and some unexpected results have been observed as well. For


Carbon Nanotubes 11

instance, an increase of the spin-valve effect when applying high bias voltage [50], ora change in sign of the spin-valve effect [51].

For the investigations of spin transport SWNTs seem to have several advantages incomparison with MWNTs. First of all, the 1D and ballistic transport character, andthereby effects due to the LL and, at low temperatures, the CB regime, are muchmore pronounced in SWNTs. Furthermore, SWNTs, in contrast to MWNTs, have nointrinsic magnetoresistance, which may influence the observations. It may be difficultto distinguish between effects due to magnetoresistance and to spin transport. Thedrawback, for observing spin transport in SWNTs, is the difficulty of achieving goodtunnel contacts between FMs and SWNTs. The results on SWNTs contacted with FMreported so far, exhibit small effects from spin transport [52], in comparison with thosereported for ferromagnetically contacted MWNTs. This may be explained by a poorquality of the tunnel contacts.


12 1. Introduction


Chapter 2

Experimental Techniques

The experimental techniques for investigation of ferromagnetically contacted single-wall carbon nanotubes (SWNTs) are given here. Firstly, the sample production, in-cluding tube growth and fabrication of tube devices, are presented. Secondly, themeasurement setup is described.

2.1 Device Production

The sample production consists of two parts: The preparation techniques of the SWNTs,followed by the fabrication of devices with the tubes.

2.1.1 Preparation of Single Wall Carbon Nanotubes

The SWNTs for device fabrication have been produced by two different techniques:Laser ablation and chemical-vapor deposition (CVD).

Laser ablation The method is sketched in figure 2.1a and is in use by the group ofSmalley [25]. Intense laser pulses ablate a graphite target containinga small fraction of Ni and Co. The target is placed in a tube-furnace ata temperature of 1200C. Nanotubes grow during the ablation of thetarget and a gas flowing through the furnace carries the nanotubes forcollection downstream at a cold finger. The outcome, that is collectedat the cold finger, is shown in figure 2.1b and consists of entangledropes of SWNTs.

13

14 2. Experimental Techniques

Figure 2.1: a) A sketch of a nanotube furnace for the laser ablation. b) The SWNTsgrown by laser ablation by the group of Smalley [25]. c) An AFM picture of Smalleyslaser ablated SWNTs deposited on a substrate.

For fabrication of electrical nanotube devices a small grain of entan-gled SWNTs, produced by laser ablation, is suspended in a solutionof dichloroethane by use of ultrasound. The suspended nanotubes aredeposited on the substrate either by letting a drop of the suspensiondry on the substrate or, even better, by adding the suspension whilethe substrate is spinning. The result is randomly scattered SWNTson the sample surface. An atomic-force microscopy (AFM) image ofSWNTs on the surface of a sample is given in figure 2.2c.

CVD The tube furnace for CVD for nanotube production at the Ørsted Lab-oratory is shown in figure 2.2a. The tube furnace can be heated up to1200C, and it is connected to various gas sources. The incoming gas,gas pressure, and flow rate through the tube may be controlled.

In a hydrocarbon atmosphere at elevated temperatures carbon decom-poses at some catalyst material, whereby long nanotubes are spun


Device Production 15

Figure 2.2: a) The nanotube furnace at the Ørsted Laboratory. b) and c) Transmis-sion electron microscopy images of CVD-grown SWNTs (from [53]).

from the catalyst material. Several types of catalyst material and hy-drocarbon gasses have been utilized:

1. Islands of the catalyst material: Fe2O3/Mo supported by Al2O3-nano-sized particles, are defined in patterns on the substrate, bye-beam lithography and lift-off technique. The patterns are typi-cally islands of 4 by 6 µm2. The substrate is placed in the CVDfurnace and heated to 900C in an argon atmosphere. At 900Cthe argon is replaced by methane for ten minutes, whereby nan-otubes are grown. Finally the furnace is cooled to room temper-ature with an argon atmosphere. This method was developed byH. Dai and details may be found in references [26, 53].

2. Catalyst material in the form of ferric nitrate particles are dis-tributed randomly all over the substrate in the following way.The substrate is dipped in a solution of ferric nitrate nonahy-drate in 2-propanol for a few seconds and subsequently rinsed in



hexane and dried. The sample with catalyst material is loadedinto a CVD furnace. The first step, is to heat the substrate andanneal it at 850C in an atmosphere of argon and hydrogen forten minutes. During this procedure, the ferric nitrate is reducedand nano-sized particles of pure iron are formed. Thereafter, thesample is kept in an atmosphere of ethylene at the same temper-ature for ten minutes, whereby SWNTs grow catalytically fromthe iron particles. Finally, the furnace is cooled to room tem-perature with an atmosphere of argon. The technique is reportedby Hafner et al. [54] and is performed at Warwick University byNeil Wilson and David H. Cobden.

The critical parameters of SWNT growth are the growth temperaturetogether with the pressure and flow rate of the hydrocarbon gas. Theseparameters have to be calibrated carefully in order to achieve a uni-form production of SWNTs. After the calibration the results of theCVD processes are preferentially individual SWNTs spreading outfrom the catalyst material on the surface. The diameters of the tubesare inspected by AFM and are usually found to be from 1 to 3 nm. Ex-amples of transmission electron microscopy of the CVD grown tubesfrom the Ørsted Laboratory are presented in figure 2.2b and c. The im-ages show that the tubes are indeed single-walled, and that they mayattend lengths up to several µm.

2.1.2 Fabrication of Devices with SWNTs

The devices for transport measurements on SWNTs are three terminal devices: twoelectrically contacted leads, source and drain plus a capacitatively coupled gate. Dif-ferent fabrication techniques are applied to produce two sorts of devices. SWNTs con-tacted by the ferromagnetic metal: Fe, and SWNTs contacted by the dilute magneticsemiconductor: Ga1−xMnxAs (GaMnAs).



Figure 2.3: The fabrication of nanotube devices with Fe leads from CVD tubes,grown from islands of catalyst material. a) An optical micrograph of the islands ofcatalyst material (Catalyst: Fe2O3/Mo supported by Al2O3-nano particles), definedby e-beam lithography. b) A zoom-in on the catalyst material, showing where thenanotubes grow, imaged by SEM. c) Fe leads defined by e-beam lithography on topof the islands of catalyst material. d) A nanotube contacted by Fe leads. e) Thebonding pads and connectors to the Fe leads, defined by uv-lithography, together withthe outline of the substrate. f) A nanotube device bonded on a 14 leg chip carrier. Thedevice is ready for mounting in a cryostat.



Figure 2.4: SEMs of nanotube devices with Fe leads. The CVD tubes are grownfrom randomly scattered ferric nitrate catalyst material. a) The Fe leads defined bye-beam lithography. b) A zoom-in on a nanotube contacted by the Fe leads.

Fe This fabrication technique is, in principle, applicable for contactingSWNTs with any metal. Here is discussed the case where the metal isferromagnetic Fe.

• The substrate is heavily p-doped Si, serving as a back gate, cappedwith 350 nm insulating SiO2, as indicated in figure 2.3e.

• SWNTs are placed on the substrate: either from a suspension oflaser ablated tubes from Smalleys group (figure 2.1c) or CVDtubes grown directly on the substrate, as described in the pre-vious section. Figure 2.3b is a scanning electron micrograph(SEM) of CVD tubes grown from islands of catalyst. The nan-otubes appear either dark or bright on the insulating substrate.

• A metal film is evaporated on the sample. Leads are formed byuse of e-beam lithography and lift-off technique. The metal filmis about 50 nm of Fe capped in situ by 15 nm Au to prevent oxi-dation. Evaporation of the film is performed in a vacuum cham-ber at a pressure lower than 10−8 mbar, to ensure high quality ofthe Fe film.The design of the Fe leads is varied. In the first generation, theleads are rectangular of 6 by 8 µm2, figure 2.3d. In the secondgeneration of lead design, the goal is to contact the tubes by sin-gle ferromagnetic domain. These leads are elongated, with twodifferent aspect ratios of width to length, in order to attain differ-ent coercive fields, figure 2.4a. The distance between two leads,forming the nanotube device, is of the order of 500 nm, limitedby the e-beam lithography.In case of patterns of catalyst material, the leads are placed ontop of these, figure 2.3c, otherwise they are placed randomly on



the substrate 2.4a. In both situations SWNTs are contacted bychance. Taking into account how easily many metallic leads maybe produced, this method, of contacting the tubes by chance, be-comes very efficient. Especially, if the size of the leads are cor-related to the density of the tubes, so that the number of tubesbetween the leads ranges between none and a few.

• Large bonding pads of Au contacting the ferromagnetic leads,prepared from a 8 nm Cr (for adhesion) and 150 nm Au film, arethermally evaporated and defined by uv-lithography and lift-off.Figure 2.3e is an optical micrograph image of the bonding pads.

• About 10 nm Cr and 150 nm Au are deposited by thermal evap-oration on the back, as an electrode to the back-gate, figure 2.3e.

• In order to find the suitable devices with resistances below 1 MΩ,the resistances of the fabricated devices are checked in a probestation.

• The devices, which are found to be suitable, are bonded on a chipcarrier, figure 2.3f.

The outcome of this fabrication method is usually devices with a highcontact resistance (resistance from the metal to the tube) compared tosimilar samples e.g. with pure Au leads.

GaMnAs The technique for contacting SWNTs by a semiconductor has beendeveloped in cooperation with Jonas R. Hauptmann and Janusz Sad-owski.

• The substrate is heavily n-doped GaAs with a 100 layer super-lattice barrier of 2 nm GaAs plus 2 nm AlAs ended by 20 nmGaAs. On top, the wafer is caped by a layer of amorphous As,which ensures a clean and molecular smooth surface and is sig-nificant for a successful overgrowth. The wafer was grown byJanusz Sadowski in the molecular beam epitaxial (MBE) systemat Ørsted Laboratory. The various layers of the wafer are drawnschematically in figure 2.5.

• Substrates of about 1.5 by 1.5 cm2 are cleaved from the wafer.Laser ablated SWNTs from Smalleys group are deposited on thesurface of amorphous As, as described on page 13, the situationis sketched in figure 2.5b.



Figure 2.5: Nanotubes contacted by GaMnAs. a) The substrate of n-doped GaAswith the superlattice barrier and amorphous As, grown in the Ørsted Laboratory MBEsystem. b) Nanotubes are sprinkled on the surface of the substrate. c) In the LundMBE system, the amorphous As is dispersed, leaving the nanotubes on the substrate.After overgrowth the tubes are encapsulated under the GaMnAs. d) A trench etchedin the GaMnAs leaves a nanotube to connect two islands of GaMnAs. The trench andthe tube are imaged by AFM.

• The substrates with deposited tubes are entered in the MBE sys-tem in Lund by Janusz Sadowski, for ferromagnetic semiconduc-tor overgrowth. First, the amorphous As is removed by evapo-ration at a temperature of about T = 400C and the GaAs sur-face is As enriched in an atmosphere of As at T = 450−500C.This leaves the nanotubes on the clean and molecular smoothGaAs surface. Subsequently, the sample is overgrown with low-temperature Ga1−xMnxAs (T = 250C, x = 5%).

Thin films of GaMnAs are preferred for two reasons. The min-imum size of structures that can be attained by etching of theGaMnAs film, scales with the thickness. Furthermore, the mag-netic properties seem to be enhanced in thin films of GaMn-



Figure 2.6: Devices of GaMnAs contacted nanotubes. a) A Hall-bar mesa withtrenches and Au leads for tube devices. b) Uv-lithography defined bonding pads. c)Devices bonded on a 14-leg chip carrier.

As [55]. GaMnAs film thicknesses from 20 to 50 nm have beenprepared. The GaMnAs layer is capped by 5 nm GaAs to pre-vent oxidation. In order to optimize the magnetic properties ofthe semiconductor annealing of the GaMnAs film is performed,by keeping the substrate in the MBE system at the growth tem-perature for a couple of hours after growth.The result is SWNTs encapsulated under the GaMnAs film, seefigure 2.5c.

• Uv-lithographically defined Hall-bar mesas are formed by etch-ing. The semiconductor is etched by a wet etch: H3PO4:H2O2:H2O (1:1:38), with the etching rate of 100 nm/min. The depthof the etching is controlled by the etching time, and the aim is toreach a mesa hight of about 20 nm plus the GaMnAs thickness.One Hall bar on each sample is used for a characterization ofthe GaMnAs film. The rest of the Hall bars are formed into tubedevices.

• By use of e-beam lithography stripes on the GaMnAs are de-signed and etched away, leaving nanotubes as connectors be-tween the separated GaMnAs islands, figure 2.5d and leads 1-2,



2-3 etc. in figure 2.6a. The wet etch is the same as above and thedepth of the trenches are about 20 nm deeper than the GaMnAsfilm. Two leads are left without a trench, in order to create ref-erence devices of the leads: 7-8 in figure 2.6a. Also larger areasare etched away in order to make space for Au leads.As the tubes are scattered randomly under the GaMnAs, the for-mation of devices is by chance.

• Au leads contacting nanotubes are defined by e-beam lithogra-phy and lift-off, by metallization of 5 nm Cr and 20 nm Au. Inthis manner reference devices are fabricated. The structures ofthe reference devices are: GaMnAs-SWNT-Au 8-9 and 10-11,plus Au-SWNT-Au 9-10 in figure 2.6a.

• Uv-lithography and lift-off technique are used to design a metalfilm of 5 nm Au / 50 nm Zn / 150 nm Au compound. This filmis to contact the semiconductor and Au leads and to serve asbonding pads, figure 2.6b.

• The gate is contacted by thermally evaporation of 10 nm Cr and150 nm Au on the back of the substrate.

• The resistances of the devices are checked in the probe station.Devices with resistance below about 1 MΩ are bonded on a chipcarrier, figure 2.6c.

2.2 Setup for Transport Measurements

The tube device, bonded on a chip carrier, is mounted in a cryostat equipped withthe possibility of applying a magnetic field. For the lowest temperatures a 3He cryo-stat with base temperature of 300 mK has been utilized. Measurements at 4.2 K areperformed in liquid He. In the temperature range of 10 K to room temperature a cryo-cooler system is applied.

The transport measurements are kept as simple as possible, therefore two-point d.c.measurements are preferred. The setup is shown schematically in figure 2.7. A voltageV is applied to the source, and the current I is measured from drain to ground. Theconductance of the device is G = I/V in the linear regime. On the third terminal, thegate, a voltage Vg is applied. The external magnetic field is applied in the plane of theferromagnetic film, as indicated in figure 2.7. This is the easy magnetization axis ofthe Fe leads. The easy axis in GaMnAs is more questionable. It is in the plane, but theangle between an easy axis and the direction of the field is unknown, and may be from0 and up to 45. The random orientation of the tube, implies that the orientation of themagnetic field compared to the tube axis is somewhat uncontrollable.


Setup for Transport Measurements 23

Figure 2.7: Setup for transport measurements. Typical instrument values are givenin parenthesis. The applied magnetic field is indicated in the plane of the device.

The measurements are run by a computer via Labview programs, controlling a dataacquisition (DAC) card with two digital-to-analog outputs ±10 V with an accuracy of0.3 mV, and reading from an analog-to-digital (AD) converter. The current source forthe applied magnetic field is controlled by a Labview program as well.

To reach the desired values of V , a voltage divider is installed between the DAC cardoutput and the source. Abrupt changes in Vg and protection of the delicate devicein case of leakage between gate and tube are ensured by a low-pass filter in serieswith a resistance. I is measured by a low-noise current amplifier, which produces avoltage proportional to the current. The out-coming voltage from the current amplifieris decoupled from the device by an opto-coupler and read by the AD converter.


Chapter 3

Characterization of the Ga1−xMnxAsFilms

The chapter presents initial investigations of the films of the dilute magnetic semicon-ductor Ga1−xMnxAs, x = 5% (GaMnAs), which have been used as contacting leads forthe devices of ferromagnetically contacted single-wall carbon nanotubes (SWNTs).

Three substrates with SWNTs have been overgrown by GaMnAs, as described in chap-ter 2 on page 19. The fabricated GaMnAs films have different thicknesses of 20, 40,and 50 nm.

The characteristics of the three GaMnAs films may differ markedly, for several rea-sons. Firstly, the thicknesses vary. Secondly, the films were grown several weeks apart,which may imply alternating growth conditions for the three films. Lastly, the densityand the distribution of the SWNTs fluctuate in the three samples. This will, as well,result in alternating growth conditions. Consequently, general studies of each film arenecessary. Hall-bar measurements on the GaMnAs films have been performed. Andthe transport properties of the leads of GaMnAs, that are to form nanotube devices, areinvestigated. The results from the measurements will be presented and analyzed.

3.1 Hall-Bar Measurements

Hall-bar geometry devices of GaMnAs films with thicknesses d, width W = 20µm, andlengths L = 17 and 51µm, are examined by standard d.c. measurements, as sketchedin the insert of figure 3.1a. The measurements are performed in the temperature rangeT = 300 → 10 K. The sheet resistivity is defined as ρSheet = VxWd/(IL) and the Hallresistivity as ρHall = Vyd/I. The outcome of the measurements are summarized in

25

26 3. Characterization of the Ga1−xMnxAs Films

Figure 3.1: a) The sheet resistivity versus temperature for the three GaMnAs films ofthicknesses 20, 40, and 50 nm. A sketch of the Hall-bar geometry is inserted. b) andc) show results obtained for the 40 nm thick film. b) is the sheet resistivity and c) theHall resistivity, at the temperatures 80 and 10 K, as functions of a perpendicular field.The solid lines are obtained under sweep-up and the dashed lines under sweep-downconditions, as indicated by the arrows.

figure 3.1. The magnetic field dependence of ρSheet and ρHall for the two remainingfilms (20 nm and 50 nm) are not shown in the figure, but are qualitatively comparablewith the experimental results presented for the 40 nm film.

3.1.1 Discussion of the Results

A knowledge of easy magnetization axes, helps to understand the magnetization inthe GaMnAs film. The single-crystal nature of the GaMnAs films imply a cubic ori-entation of the easy magnetization directions. Because of a compressive strain in thecrystal, which arises because the lattice of GaMnAs is larger than the substrate latticeof GaAs, a hard axis is formed perpendicular to the plane [56]. The bi-axial directionsof the easy axes in the film plane seem not to be universally determined. Easy axeshave been observed along either [100] [57] or [110] [58].


Hall-Bar Measurements 27

Magnetization curves are plotted schematically in figure 3.2 for the magnetic fieldapplied along the hard or perpendicular direction and the easy or in-plane direction,corresponding to the measurements of Ohno et al. [18]. In the in-plane configuration,the magnetization behaves hysteretically, it changes sign abruptly at the coercive fields±BC. It is believed that the behavior in the perpendicular configuration of the magneticfield, is strongly affected by the large anisotropy [18, 56]. A fairly high magnetic fieldis required to saturate the magnetization out of the film plane, Bs ≈ 0.3 T. Furthermore,the magnetization direction of the GaMnAs film is supposed to turn gradually, and toalign in the film plane at zero magnetic field, as illustrated in figure 3.2a, a processwhich should show no hysteresis.

Figure 3.2: The magnetization curves for a GaMnAs film. a) The magnetic fieldis applied perpendicular to the film plane. The diagrams display the directions ofmagnetization in the GaMnAs film, seen as a side view of a film. b) The magneticfield is applied parallel to the film plane, resulting in a hysteresis in the magnetization.

The Hall effect is described by ρHall = R0B⊥ + RSM⊥ [56]. Where R0 = 1/(pe) isthe ordinary Hall coefficient, and p is the carrier density. RS is the anomalous Hallcoefficient. The anomalous Hall effect is the dominant one when the magnetization isnot saturated, i.e., at low applied magnetic fields.

The anisotropic magnetoresistance (AMR) is an effect, which imply that the resistancedepends on the angle between the magnetization and the direction of the electric cur-rent [59]. It originates from the coupling between the carrier spin and orbital motion.When the magnetization is in the plane of a film, the resistivity depends on, whetherthe current is oriented parallel ρ||, or perpendicular ρ⊥(Min−plane) to the in-plane mag-netization. When the magnetization is oriented perpendicular to the plane of a film,and the current, a third resistivity ρ⊥(Mperp) appears. In GaMnAs it is found experi-mentally that ρ|| < ρ⊥(Min−plane) < ρ⊥(Mperp) [58, 60], in contrast to the usual resultof ferromagnetic metals that ρ⊥(Min−plane) = ρ⊥(Mperp) < ρ|| [59].



The alignment of the spins of the Mn ions, the lattice spins, influences the resistance.The carrier spins are coupled to the lattice spins via the exchange interaction, and thecarrier scattering, and thereby the resistance, will be enhanced through disorder in thelattice spins [61].

Measurements of ρSheet versus temperature is presented in figure 3.1a. The temperaturedependence of ρSheet may be used for an estimate of the Curie temperature (TC) inthe GaMnAs film. A critical behavior of ρSheet is produced, due to enhanced spinfluctuations in the semiconductor lattice, around the phase transition [61]. Hence, amaximum in ρSheet is formed in the vicinity of TC. The maxima in the sheet resistivitiesare marked in figure 3.1a, and are the estimates of TC for the three GaMnAs films.The Curie temperatures are in the range of 40 to 70 K. This is somewhat lower thanwhat is normally found in films grown under the same conditions [55]. It is likelythat the presence of the tubes distorts the semiconductor crystal, whereby the Curietemperature is reduced.

GaMnAs is a semiconductor, consequently ρSheet increases with decreasing temper-ature. The measurements of ρSheet for the films of 40 and 50 nm are very similar.Whereas the 20 nm film displays a much higher resistance, the most pronounced semi-conductor behavior, and the far lowest Curie temperature.

The sheet resistivity versus a perpendicular magnetic field is presented in figure 3.1b.At T = 80 K, well above TC, negative magnetoresistance (MR), of decreasing resis-tivity with increasing magnetic field, is recognized in the GaMnAs films. GaMnAsbehaves paramagnetic above the Curie temperature, and the magnetization increaseswith the magnetic field, causing a decrease in ρSheet due to the increasing ordering ofthe lattice spins.

At temperatures lower than TC two opposite trends are detected in the MR (figure 3.1b,T = 10 K). At fields below the saturation field Bs ≈ 0.3 T positive MR, of increasingresistance with increasing magnetic field, is observed. Presumably, this may be ex-plained by the strong anisotropy in the GaMnAs films [56]. At zero magnetic field,the direction of magnetization is confined spontaneously to the plane of the film. Asthe field is increased the direction of magnetization rotates steadily from the in-planetowards the perpendicular direction. During this process the spin disorder should stayapproximately constant, however, the AMR effect may account for the resistance min-imum at zero field, because ρ|| and ρ⊥(Min plane) < ρ⊥(Mperp). At fields above Bs,the direction of magnetization stays constantly perpendicular to the film, but at 10 Kthe magnetization is still slightly below saturation leaving a small lattice spin-disorderscattering. The reduction of this scattering component with increasing field may ex-plain the small negative MR observed above Bs.

The Hall measurements 3.1c reflect that the anomalous Hall effect is the dominantone in the presented field range, as ρHall is not a linear function of the magnetic field.


GaMnAs Leads 29

This is the case as long as the perpendicular component of the magnetization is notsaturated. A reliable determination of R0, and thereby the of carrier density, requiresmeasurements at higher magnetic fields or lower temperatures than those presented infigure 3.1c.

Peculiar hysteretic behaviors are recorded in ρSheet and ρHall at the lowest tempera-tures, figure 3.1b and c at T = 10 K. The behaviors are unexpected, as hysteresis isusually not reported in Hall or sheet resistivities of GaMnAs films with a perpendic-ular magnetic field. I have found one single reference, where something similar hasbeen reported for a thin (5 nm) GaMnAs film [55], though no explanation of the hys-teresis is given. This may lead to the conclusion that the hysteretic behavior is a thinfilm property. A property, which might be enhanced in these GaMnAs films because,the presence of the tubes perturbs the GaMnAs film.

The origin of the hysteretic behaviors is as yet unknown, still a few aspects of thebehaviors may tentatively be determined. The fact that the hysteresis in ρSheet andρHall appears at the same magnetic field, imply that their hysteretic behaviors are twosides of the same effect. The hysteresis appears solely at temperatures lower than theCurie temperature, this imply that it must be related to the magnetization in the films.According to the magnetization process displayed in figure 3.2a, the perpendicularcomponent of the magnetization should change in a reversible way. The parallel com-ponent may accidentally lock-in to different in-plane easy directions, and this domainstructure must be the cause of the hysteresis, however, it is difficult to understand whysuch a domain structure affects the resistance differently, whether the field is increasingor decreasing.

3.2 GaMnAs Leads

Two-point measurements on GaMnAs leads, similar to those used in the nanotubedevices, are performed. The fabrication of the devices is described on page 19. TheGaMnAs leads are shown as leads 7− 8 in figure 2.6a. The measurement setup isdescribed in section 2.2.

The GaMnAs films behave metallic in the sense that a change of gate or bias voltagedoes not influence the conductance noticeably, at least for temperatures higher than1 K. Figure 3.3 displays the conductance of the GaMnAs leads versus in-plane mag-netic field, at various temperatures.

Negative MR, of increasing conductance with increasing magnetic field, is revealed inall three GaMnAs films. As described in the previous section, this occurs because theconductance increases when the ordering of the magnetic moment in the GaMnAs filmis enhanced by the increasing magnetic field.



Figure 3.3: The conductance of the GaMnAs leads versus in-plane magnetic fieldat various temperatures. Solid lines and dashed lines correspond to sweep-up and-down, respectively. All plots are averages of about 5 individual sweeps. a) 20 nm,b) 40 nm, and c) 50 nm GaMnAs films.


Main Results 31

A hysteretic behavior of the conductance in the leads is observed as well. This hys-teresis is a measure of the in-plane coercive field. Magnetic domains in a GaMnAsfilm have been observed to exceed several 100 of µm in size [62], with an in-planeconfiguration of the field. Accordingly, the GaMnAs leads are believed to consist ofa single magnetic domain in an applied magnetic field. A schematic magnetizationcurve of the GaMnAs films is presented in figure 3.2b. In the vicinity of the switching,at the coercive field, a multi-domain state may appear in the lead. This multi-domainstate reduce the conductance, due to enhancement of carrier scattering at the increasednumber of domain walls. The effect shows up as hysteretic dips in the conductance.The coercive fields are found to be of the order of 0.1 T, though they vary somewhatwith temperature and GaMnAs thickness. AMR effects may influence the feature ofthe hysteresis as well. Magnetic domains, that are formed when the magnetization isreversed, might imply variation in conductance, due to variation of the angle betweencurrent and magnetization.

For T ≥ 4 K the MR is relatively small, and is well understood as described above. Butat temperatures below 1 K more irregular features are displayed in the conductance.These features are present in the measurements of the 40 and 50 nm films in the linearregime at T = 300 mK. The 20 nm film displays the same irregularities at T = 300 mKin the linear regime, as well as when a finite bias voltage is applied. It is not clearhow these features may be explained, and it is not known whether they derive from thesemiconductor itself or from the tubes that are encapsulated in the semiconductor film.

From the measurements, the magnitude of the MR in the GaMnAs leads may be ob-tained. Within the hysteretic structure the absolute difference in resistance is of theorder of ∆R ≈ 30−40Ω in the films of thicknesses 40 and 50 nm. The value is slightlyhigher for the 20 nm film, where the difference in resistance is about ∆R ≈ 600Ω. Theirregularities, described above, have not been taken into account.

3.3 Main Results

From the experiments presented in this chapter, the numbers that characterize theGaMnAs films can be determined. The results are summarized in table 3.1.

GaMnAs film TC (K) BC (T) ∆R (Ω) Irregularities20 nm 40 0.1 600 T < 1 K40 nm 70 0.1 40 T < 1 K linear regime50 nm 60 0.1 30 T < 1 K linear regime

Table 3.1: Main results obtained from measurements on the GaMnAs films.


Chapter 4

Experimental Results

The experimental results from devices of single-wall carbon nanotubes (SWNTs) con-tacted by ferromagnetic leads are presented in this chapter. Two sorts of ferromagneticmaterial have been utilized as leads. i) Ferromagnetic metal: Fe. ii) Diluted magneticsemiconductor: Ga1−xMnxAs x = 5% (GaMnAs).

4.1 Experiments on Fe Contacted Nanotubes

Devices of SWNTs contacted by Fe leads have been fabricated as described on page 18and showed in figure 4.1.

The results presented here are mainly from two devices out of the same sample batch,meaning that the two devices are similar with respect of the CVD growth conditions ofthe tubes and the metallization of the Fe leads. The two devices are named Fe-T-Fe#1and Fe-T-Fe#2. The tubes are CVD grown tubes, method 1 (see page 15), grown at theØrsted Laboratory. The Fe leads are composed of about 60 nm Fe plus 20 nm Au caplayer. The leads have rectangular shape and the distance between the leads is of theorder of 300 nm, figure 4.1a and b.

A few results from devices named Fe-T-Fe#3 and Fe-T-Fe#4 will be presented as well.Fe-T-Fe#3 and Fe-T-Fe#4 are from the same sample batch of CVD grown tubes pro-duced at Warwick, method 2 (page 15). The leads consist of a metal film of 52 nm Feand 12 nm Au. They are elongated, presumably one-domain, structures (figure 2.4),which are placed with a distance between them of about 250 nm.

In addition, some comments on results from many other similar devices are given.

33

34 4. Experimental Results

4.1.1 Fe Leads

The magnetic characteristics of the Fe leads are studied by magnetic force microscopy(MFM). By this technique qualitative indications of the structure of magnetic domainsmay be revealed. In figure 4.1b an MFM image of a Fe lead is presented. The image isrecorded at room temperature and at zero magnetic field. A typical size of the magneticdomains of around 1 µm is observed, though domains at the edges tend to be smaller.

Figure 4.1: a) A device with an indication of the measurement setup. A SWNTcontacted by two Fe leads (source and drain) plus a back-gate. The tube and the Feleads are imaged by atomic force microscopy. b) An optical micrograph image of adevice. c) An MFM image of a Fe lead. Dashed lines are applied to indicate the Felead.

4.1.2 Devices of Fe Contacted Tubes

Fe-T-Fe#1

The room temperature resistance of this device is about 80kΩ, a typical resistance fornanotube devices that form quantum dots (QDs). At room temperature, the resistanceis found to be independent of the gate voltage, which implies that the tube is metal-lic. The conductance measured as a function of temperature indicates a power law


Experiments on Fe Contacted Nanotubes 35

dependence of the order of G ∝ T 0.7, as presented in the insert of figure 4.2a.

Figure 4.2: Fe-T-Fe#1 measured at T = 4.2 K. a) The conductance versus back-gatevoltage measured at the magnetic fields B = 1 T (thick), 0.5 T, and -0.05 T. The insertis the conductance as a function of the temperature. The line is a power-law fit. b) Theconductance measured as a function of magnetic field. The solid lines are sweep-up,and the dashed lines are sweep-down results, respectively, as specified by the arrows.Letters A, B, C, and D refer to the gate voltages indicated in a.

The conductance as a function of back-gate voltage measured at T = 4.2 K is presentedin figure 4.2a. The oscillating curves indicate that the device is behaving as a QD,entering the Coulomb blockade (CB) regime. The CB oscillations are separated bygate voltages of about ∆Vg ≈ 100 mV. This size of CB spacing is typical for nanotubedevices with substrates of 350 nm SiO2 that separates the tube from the back-gate.

A dramatic change in conductance, when changing the magnetic field is identified infigure 4.2a. The conductance is strongly suppressed when the magnetic field is almostzero. This is seen more directly in figure 4.2b, where the conductance is measuredwhile sweeping the magnetic field, for fixed gate voltages (A-D). Independent of gatevoltage one recognizes a hysteretic behavior with a minimum in conductance afterpassing zero field.



Figure 4.3: Fe-T-Fe#1. a) The bias spectrum measured at T = 350 mK and B =

−2 T. Gray scale plot of dI/dV versus gate and bias voltage (dark=high). A CBdiamond is indicated. b) Current versus magnetic field measured at temperaturesT = 350 mK, 1.6 K, and 4 K. The crosses in a and c indicate the parameters ofthese measurements. The curves are the average of six individual traces. c) T =

350 mK. The bias spectrum recorded at the hysteretic minimum at B = 0.08 T. dI/dVis presented in the same gray scale as a.



Fe-T-Fe#1 is studied at temperatures down to T = 350 mK. A bias spectrum, the differ-ential conductance, dI/dV , as a function of back-gate and bias voltage, for the device ispresented in figure 4.3a. The bias spectrum is recorded at T = 350 mK and B = −2 T.An indication of the diamond structure from the CB is visible. The dashed lines area guidance to the eyes. From the diamond structure, the electrostatic energy is deter-mined to be about U ≈ 5 meV. This is a typical value of the electrostatic energy, foundin the majority of similar devices. From the bias spectrum it is found that the device isnon-conducting in the linear-response regime at T = 350 mK.

Figure 4.3b shows measurements done in the temperature range T = 350 mK to 4 K,with a finite bias voltage of 3 mV applied. The graphs show current versus mag-netic field. The hysteretic behavior, present at T = 4.2 K (figure 4.2b), develops withdecreasing temperature. At T = 350 mK the device is almost totally blocked at theconductance minimum.

As already observed at T = 4.2 K, no qualitative gate or bias dependence was foundof the hysteretic behavior. At T = 350 mK the transport through the device is near tobe totally blocked at the conductance minimum for any values of gate or bias voltage.This is visualized by figure 4.3c, which is a bias spectrum of the devices measured inthe conductance minimum. Except for some noise at high bias voltage, almost zeroconductance is recorded in the entire bias and gate voltage region.

Measurements are performed on Fe-T-Fe#1 at higher temperatures as well. The hys-teretic behavior, of conductance versus magnetic field, is identified up to temperaturesof T = 20 K.

Fe-T-Fe#2

This metallic tube device exposes a room temperature resistance of about 1MΩ. Com-pared to similar nanotube devices, this device has a fairly high resistance. Also thedevice proved to be very fragile, as it hardly survived the first cool down. Accordingly,very few measurements are achieved for this device, preferentially at liquid heliumtemperature. Results for Fe-T-Fe#2 are summarized in figure 4.4.

Figure 4.4b displays the current as a function of applied bias voltage at T = 4.2 K. It isfound that the device does not conduct in the linear-response regime. The conductanceis strongly suppressed due to CB. The electrostatic energy of the CB is about U ≈6 meV. This is comparable to what was determined for the Fe-T-Fe#1 device.

At T = 4.2 K, a finite bias of 10 mV is applied, and a characteristic hysteretic behav-ior is found in the current, measured while sweeping the magnetic field, as shown infigure 4.4a. The device displays qualitatively the same hysteretic behavior indepen-dent of the applied bias voltage. The hysteretic behavior is similar to the one found in



Figure 4.4: Fe-T-Fe#2. a) T = 4.2 K. I as a function of magnetic field with appliedbias voltage V = 10 mV. The solid line is sweep-up and the dashed line is sweep-downresults. The curves are averaged over 8 individual measurements. b) T = 4.2 K. TheI-V characteristic measured at a magnetic field of B = 0.2 T. c) A measurement atthe second cool down at T = 9 K. The current versus magnetic field at V = 20 mV,averaged over 20 traces.

Fe-T-Fe#1 (figure 4.2b).

At the second cool down to T = 9 K of the device, the conductance is reduced dramat-ically, and a bias voltage of at least 20 mV has to be applied in order to achieve currentthrough the device. A hysteretic behavior of the current as a function of magneticfield is observed in these measurements as well. However, the sign of the hystereticstructure have changed, figure 4.4c.

Analysis of the Results

The results presented above from devices Fe-T-Fe#1 and #2 show clear characteristicsof a nanotube-device behavior, as discussed in section 1.2. Furthermore, distinctivebehaviors in the magnetic field dependencies are observed, which appear as a hys-



Figure 4.5: The temperature dependence of the magnitude of the hysteretic behaviorfor Fe-T-Fe#1,2,3,4. The values are plotted as the mean values of all measurementsof the HMR, together with error-bars, which indicate the variation in the measure-ments. Open symbols show the results measured in the linear regime, and the closedsymbols are the results of the non-linear regime. a) Magnitude of the HMR effect. b)Magnitude of the inverse HMR effect.

teretic magnetoresistance (HMR). In order to examine the HMR, Gex is defined as theconductance at the hysteretic extremum (dip or peak), and GB as the conductance atthe same magnetic field, but measured during the reverse sweep direction. Gex andGB are indicated in figure 4.2b. The magnitude of the HMR is thereby defined as∆G/GB = (GB −Gex)/GB. The magnitude of the HMRs for the two devices are plot-ted in figure 4.5 together with HMR results from two similar devices: Fe-T-Fe#3 and#4. Additional measurements of Fe-T-Fe#1, #3, and #4 are to be found in appendix A.

The positive HMR is plotted in figure 4.5a. Fe-T-Fe#1 displays almost 100% HMR atthe lowest temperatures. The HMR of Fe-T-Fe#1 decreases with increasing tempera-ture. The results of the Fe-T-Fe#1 and Fe-T-Fe#2 devices are comparable at T = 4.2 K.In Fe-T-Fe#3 and #4, the magnitude of the HMR is smaller than the magnitudes foundin the first two devices.

The negative or inverse HMR observed and shown in Fe-T-Fe#2 in figure 4.4c is re-vealed in the devices Fe-T-Fe#3 and #4 as well. The results of the inverse HMR are



summarized in figure 4.5b. The very few points in the plot, show no clear trend in thetemperature dependence of the inverse HMR.

Many, more than 35, similar devices of the form Fe-T-Fe are fabricated and studied. Afew devices demonstrate a tendency towards hysteretic behavior in conductance versusmagnetic field. However, the large magnitude of the positive HMR behavior is neverreproduced, as exemplified by the results from devices Fe-T-Fe#3 and #4. It is moststriking that, the majority of devices never show any HMR at all, though the devicesclearly display nanotube-device behavior. Devices with one ferromagnetic and onenormal metal lead, of the form Fe-T-Au, are fabricated as well. None of them evershow any change in conductance versus magnetic field.

4.2 Experiments on Ga1−xMnxAs Contacted Nanotubes

Figure 4.6: a) A Hall-bar mesa with trenches and Au leads forming nanotube de-vices. b) Device: GaMnAs-T-GaMnAs, with an outline of the measurement setup.

Experiments are performed on nanotube devices with GaMnAs leads, leads 1 − 2,2−3, etc. in figure 4.6a together with GaMnAs and Au leads, 8−9 and 10−11 in thefigure. The distances between the leads are of the order of 1µm. The technique forcontacting SWNTs by a semiconductor and fabricating devices thereof is describedon page 19. The outline of the sample and the measurement setup for the GaMnAsdevices are the same as used for the Fe devices, as indicated in figure 4.6b.

Properties of the GaMnAs films of thicknesses of 20, 40, and 50 nm and the GaMnAsleads are investigated and discussed in chapter 3. Here it is found that the Curie tem-peratures of the GaMnAs films are TC ≈ 40−70 K and the coercive fields BC ≈ 0.1 T.The total resistance differences are of the order of ∆R≈ 30−40Ω for the 40 and 50 nmfilms, and about 600Ω for the 20 nm film. Very little is known about the size of mag-netic domains in the GaMnAs films, and I had no possibility for performing the MFM


Experiments on Ga1−xMnxAs Contacted Nanotubes 41

at temperatures below TC. MFM results for a fairly thick (200 nm) GaMnAs film arereported by Fukumura et al. [62]. Here the size of the magnetic domains is found tobe of the order of a few µm.

The presentation of the results is divided into three subsections. The first subsectionis concentrating on the characteristic nanotube-device behaviors, such as CB and LLbehaviors. In the next subsection, results from devices with one GaMnAs lead and oneAu lead are presented and analyzed. The focus is on one device named GaMnAs-T-Au#1, made from the sample of the 40 nm thick GaMnAs film. In total, three devicesof this form is investigated. A few results from the two remaining devices GaMnAs-T-Au#2 from the 50 nm GaMnAs film, and GaMnAs-T-Au#3 from the 20 nm GaMnAsfilm are also presented. Finally, results from devices with two GaMnAs leads are given.The presented results are obtained from a device named GaMnAs-T-GaMnAs#1, madefrom the 50 nm GaMnAs film. Altogether 13 devices of this kind have been examined.The conclusions from the measurements of all devices will be reviewed briefly.

4.2.1 Devices of GaMnAs Contacted Tubes

QD and 1D Behavior

A majority of the examined devices display the behavior expected of devices of SWNTsforming QDs, as described in the introduction, section 1.2.

All the nanotubes reported here are metallic, and the devices reach the CB regime atlow temperatures, T . 4 K. Examples of this, are given for two devices, GaMnAs-T-Au#1 and GaMnAs-T-GaMnAs#1, in figures 4.7a and 4.9b. Bias spectra are pre-sented together with indications of CB diamond structures. The electrostatic energiesare determined to be U ≈ 1.5 meV for the GaMnAs-T-Au#1 and U ≈ 4 meV for theGaMnAs-T-GaMnAs#1 devices. Generally, the devices with GaMnAs leads show alarge variation of the electrostatic energy. In a single device the electrical contacts be-tween source and tube and between tube and drain may differ significantly from eachother. This difference is detectable in the diamond structures of the bias spectra, asthe two slopes on each side of the diamond are a measure of the source to tube con-tact and the tube to drain contact. The very asymmetric and tilted diamond structuresdemonstrated in figures 4.7a and 4.9b, reflect that the source and drain form markedlydifferent electric contacts to the tube in both of the two devices.

The spacings between the CB oscillations in the gate voltage of these devices are foundto be about ∆Vg ≈ 20±10 mV.

Figures 4.7b and 4.9a present the temperature dependence of the conductance in thelinear regime. The measurements indicate formation of a LL behavior in the devices,



and the power-law dependencies are determined to be G ∝ T 0.9 for GaMnAs-T-Au#1and G ∝ T 0.6 for GaMnAs-T-GaMnAs#1. In these devices the exponent of the powerlaw α are determined from 14 different measurements. The α-parameter is identifiedto lie within the interval of 0.53 ≤ α ≤ 1.1 with a mean of α ≈ 0.79 ± 0.2. Thedifferential conductance is also supposed to obey a power law according to dI/dV ∝V α . The insert of figure 4.9a reveal such a power law. Only two of the inspecteddevices expose a clear power-law in dI/dV , and the exponent is found to be: α ≈0.64±0.1.

Figure 4.7: GaMnAs-T-Au#1 a) The bias spectrum measured at T = 300 mK. dI/dVis plotted in gray scale (dark=high). The indications of diamond structures are madevisible by adding the dashed lines. b) The linear conductance as a function of temper-ature. The dashed line is a fitted power law dependence of G ∝ T 0.9. c) T = 300 mK.Current versus magnetic field with finite bias voltages of V = 1.0 and 1.5 mV. Theapplied bias voltages and gate voltage are indicated by x’es in a. d) T = 4.2 K. Theconductance versus magnetic field with gate voltages of Vg = 0 and 0.0025 V.



GaMnAs-T-Au Devices

The room temperature resistance of the metallic tube device GaMnAs-T-Au#1 is 20 kΩ.Low temperature measurements for this device at T = 300 mK to T = 4 K are pre-sented in figure 4.7.

Figure 4.7a and b are the bias spectrum measured at T = 300 mK and the conductanceas a function of temperature for GaMnAs-T-Au#1. These results show the formationof CB and LL in correspondence with the above discussion.

Figure 4.7c is a plot of the current as a function of magnetic field, measured at T =300 mK. Finite bias voltages of 1.0 and 1.5 mV are applied in order to exclude theirregularities in magnetoresistance found in the GaMnAs film at this temperature, fig-ure 3.3b. A HMR of inverse sign is observed with a bias voltage of V = 1.0 mV. By aslight change in bias voltage to V = 1.5 mV, the current as a function of magnetic fieldis changed, and the HMR is nearly cancelled.

The conductance of GaMnAs-T-Au#1 versus magnetic field at T = 4.2 K is presentedin figure 4.7d for two different gate voltages. CB oscillations in the conductance asa function of gate voltage is identified at this temperature, and the conductance ischanged drastically by the small difference in gate voltage. A HMR is recorded in thedevice at this temperature as well. However, the sign of the HMR is the opposite in thetwo cases of different gate voltages.

Figure 4.7c and d show that the observed HMR may change drastically, when changingthe bias or gate voltage. Still, these changes are not found to be related to the gate orbias voltage in a simple manner. Figure 4.8a summarizes the HMR for the GaMnAs-T-Au#1, together with measurement of HMR for GaMnAs-T-Au#2 and #3 as a functionof temperature. Examples of some of the measurements for GaMnAs-T-Au#2 and #3are presented in appendix B. The magnitude of the HMR: ∆G/GB = (GB −Gex)/GB,is defined in the previous section. Both positive and inverse HMRs are observed inGaMnAs-T-Au#1, whereas GaMnAs-T-Au#2 and #3 only show a positive HMR. Themagnitude of the HMR for GaMnAs-T-Au#1 seems to decrease with temperature. Themeasurements of the HMR in GaMnAs#3 are plotted in figure 4.8b as a function of1/GB. The plot shows, that the magnitude of the HMR depends linearly with 1/GB,but with several large departures.

In conclusion, HMR is detected in devices of GaMnAs-T-Au. The HMR in thesedevices is observed to be positive as well as negative. The magnitude of the HMRdecreases with increasing temperature. The HMR is observed to attain magnitude upto about 70%. No simple correlation was found between the HMR and gate and biasvoltage, but there is a correlation between the HMR and GB of some significance.



Figure 4.8: a) The HMR for GaMnAs-T-Au#1, #2, and #3 as a function of tem-perature. The mean values of the observed HMR are plotted with indications of thevariation in the measurements with the error-bars. Open symbols are measurementsin the linear regime, closed symbols are measurements in the non-linear regime. b)The HMR is plotted against 1/GB for a single device GaMnAs-T-Au#3 at T = 4.2 K.

GaMnAs-T-GaMnAs Devices

The device GaMnAs-T-GaMnAs#1 has a metallic tube and room-temperature resis-tance of about 200 kΩ. The temperature dependence of the conductance of GaMnAs-T-GaMnAs#1 is shown together with the differential conductance versus applied volt-age in figure 4.9a. Figure 4.9b shows a bias spectrum at T = 300 mK. The devicereveals very poor conductance in the linear regime at T = 300 mK. Formations of theLL and the CB regime have already been discussed for this device.

Conductance and current as functions of magnetic field are presented in figure 4.10 forGaMnAs-T-GaMnAs#1. The measurements are recorded at various temperatures andapplied bias voltages.

Figure 4.10a illustrates measurements at temperatures T = 14 K, T = 2 K, and T =310 mK. At the lowest temperature, a finite bias is applied in order to overcome zeroconductance in the linear regime (figure 4.9b) and the irregular magnetoresistance in



Figure 4.9: GaMnAs-T-GaMnAs#1 a) Conductance versus temperature. Insert: T =

10 K, the differential conductance as a function of applied bias voltage. Dashed linesare fit to power-law dependencies. b) A gray scale plot of the differential conductanceas a function of applied bias and gate voltage. A diamond structure is indicated bythe dashed lined.

the GaMnAs leads (see figure 3.3c). Clear HMR is exposed in the measurements. Themagnitude of the HMR is gradually increasing with decreasing temperature.

Measurements at T = 310 mK are presented in figure 4.10b for finite bias voltagesof 4, 3, and 2 mV. A HMR is recorded at bias voltages of 4 and 2 mV, though ofopposite sign. For bias voltage of 3 mV a sort of intermediate state with no clear HMRis recorded. This particular behavior is proven reproducible in a small gate-voltageregion in one cooling circle. During different cooling circles, and under various gateand bias voltage conditions, a non-regular behavior of the HMR has been found.

Recordings of current versus magnetic field at three different bias voltages at T = 4.2 Kare shown in figure 4.10c. The measurements are obtained during the same cool downand at the same gate voltage. A HMR of positive sign is found at all three bias voltages.The relative magnitude of the HMR increases with decreasing applied bias voltage.

The temperature dependence of the HMR for GaMnAs-T-GaMnAs#1 is summarizedin figure 4.11. Positive and inverse HMRs are plotted in figures 4.11a and b, respec-tively. Large variations in the magnitude and sign of the HMRs are revealed. Up toalmost 100% positive and inverse HMRs are recorded, at the lowest temperatures. Themagnitude of the HMR decreases with increasing temperature.

The HMR is observed to alternate as a function of applied bias voltage, when gatevoltage and temperature are kept relatively constant. Examples of this are presentedin figure 4.12. In figure 4.12a, the HMR derived at T = 300 mK are plotted. Circles



Figure 4.10: GaMnAs-T-GaMnAs#1, the conductance and current as a function ofmagnetic field sweep. a) Measurements at different temperatures: T = 14 K, 2 K,and 310 mK. b) T = 310 mK with applied bias voltages of: V = 4, 3, and 2 mV.c) T = 4.2 K, with applied bias voltages of: V = 50, 30, and 10 mV. All curves areaverage of about eight individual measurements.

and triangles represent measurements at two different cool downs. Two completelydifferent behaviors of the HMR are detected in the two cool downs. In one serious ofmeasurements (circles) the HMR is almost constant, around 60%. In the other seriousof measurements (triangles) a sign change in the HMR is observed. Figure 4.12b isthe magnitude of the HMR measured in one specific cool down and one gate voltageat T = 4.2 K. A maximum in the HMR is observed at V ≈ 20 mV. A fairly similar be-havior is observed at T = 10 K, as shown in figure 4.12c, which displays an equivalentmeasurement. Again a maximum in the HMR is found, and at this temperature it islocated at V ≈±7 mV.

About 12 devices similar to GaMnAs-T-GaMnAs#1 have been investigated as well.In all of them HMR is observed at least at low temperatures T . 4 K. The magni-tude of the HMR is found to vary from device to device. The behavior of the HMRin all the devices is comparable to the presented behavior of the HMR in GaMnAs-T-GaMnAs#1. In short, it is found that the magnitude of the HMR increases withdecreasing temperature, and that the magnitude and sign of the HMR is changeableby a variation of bias voltage, gate voltage, or temperature, but not in any regularmanner.



Figure 4.11: GaMnAs-T-GaMnAs#1. The magnitude of the average values of HMR,with error-bars to present the deviation in the measurements, as a function of thetemperature. Open circles are in the linear regime, closed circles are with a finite biasvoltage. a) HMR of positive sign. b) The inverse HMR.



Figure 4.12: GaMnAs-T-GaMnAs#1. The magnitude of the HMR as a functionof the bias voltage with error-bars to indicate the spread in the measurements. a)T = 300 mK. Circles and triangles are measurements at different cool downs anddifferent gate voltages. b) T = 4.2 K. Measurement of HMR at a fixed gate voltage.c) T = 10 K. The HMR measured at fixed gate voltage.


Chapter 5

Interpretation and Discussion

Single-wall carbon nanotubes (SWNTs) are contacted by ferromagnetic leads, eitherFe or Ga1−xMnxAs (GaMnAs), with the aim of investigating effects of spin-polarizedtransport in the tubes. Characteristic behaviors measured in the nanotube devices areevaluated. Successively, distinctive recordings, that must be related to the ferromag-netic leads are analyzed. In order to try to explain the observations simple models ofthe system are discussed.

5.1 Nanotube Devices

It is important to verify experimentally, the characteristic nanotube-device features,which are significant regardless of the lead material. Hereby, distinctive numbers forthe devices may be determined; and it is, for instance, of decisive importance to con-firm that the investigated devices are indeed devices of SWNTs.

The transport properties of devices of SWNTs are reviewed in the introduction, sec-tion 1.2. Usually, the leads and tubes form tunnel contacts in the devices, causing thetubes to behave as quantum dots (QDs). The size of the QDs determines the Coulombblockade (CB) behavior to occur at low temperatures (T . 4 K). In the metallic tubes,the formation of a Luttinger liquid (LL) may be a consequence of the one dimensional(1D) nature of the transport in the tube.

A fingerprint of CB in the tube devices is the oscillations in the conductance versusgate voltage at low temperatures, figure 1.4 and 1.5a. The single-electron tunnellingthat is a consequence of the CB, should be reflected in the bias spectrum as illustratedin figure 1.5b. Examples of this are presented for a device with Fe leads in figure 4.2aand 4.3a, and for devices with GaMnAs leads in figure 4.7a and 4.9b. The bias spec-

49

50 5. Interpretation and Discussion

tra, I have obtained, show the presence of diamond structures due to single-electrontunnelling, but not as clearly as in the example in the introduction. Since high-qualitytunnel contacts are essential for observing the tunnelling through single-electron states,this suggests that the tunnel contacts between Au leads and SWNTs are better definedor cleaner than those created between Fe or GaMnAs leads and SWNTs.

The electrostatic energies of the nanotube QDs are determined from the bias spectra.In devices with Fe contacts, the electrostatic energies are typically found to be U ≈5 meV. By neglecting the capacitances between leads and tube, the electrostatic energyis estimated to be Utube ≈ 2 meV, from the expressions on page 7, and a tube of lengthL ≈ 300 nm on a SiO2 substrate.

The devices with GaMnAs leads show a somewhat larger variation of the electrostaticenergy determined from the bias spectra. Typical values of the electrostatic energiesare observed within the interval from 1 to 5 meV. By introducing the relevant num-bers into the expression for a nanotube-QD, the estimated electrostatic energy is de-termined to be Utube ≈ 1.5 meV. The distance between the tubes and the back-gate inthese devices is about z ≈ 400 nm and the dielectric constant is about εr ≈ 12. Thedielectric constant of the substrate is considered to be an average of εr(GaAs) = 13.18and εr(AlAs) = 10.06 [63].

A rather large deviation between the experimentally determined electrostatic energiesand the estimations is found in both sorts of devices. This deviation may be related tothe uncertainty of the actual lengths of the nanotube-QDs. But primarily, the deviationoriginates from the omission of the capacitative couplings between the leads and thetube in the estimation. These capacitances may vary significantly, reflecting a corre-spondingly large variation in the quality of the electrical contacts between the tubesand the ferromagnetic leads. This trend is displayed, as well, by the asymmetry of thediamond structures, which indicates that the source and drain form markedly differentelectric contacts to the tube in most cases.

The efficiency of the gate depends on the dielectric constant of the insulating materialthat separates the tube from the back-gate. In the devices placed on top of a SiO2 sub-strate, the spacing in gate voltage between CB peaks is about ∆Vg ≈ 100 mV, and in thedevices placed on the superlattice of GaAs/AlAs ∆Vg ≈ 10−30 mV. Hence, the spac-ings between the CB peaks differ by almost a factor of 10 for the two sorts of nanotubedevices. A large difference in the efficiency of the gate is expected in these devices as aconsequence of the difference in the dielectric constants εr(GaAs/AlAs) εr(SiO2).

Evidences of 1D transport in the metallic tubes are detected from the LL-like behaviorof the conductance. The formation of a LL in a SWNT implies power-law dependen-cies: G ∝ T α in the linear regime, and dI/dV ∝ V α in the non-linear regime. The LLexponent α is not supposed to be affected by spin-polarized transport that may appearas a consequence of the ferromagnetic leads [34].


Nanotube Devices 51

The experiments presented for the device with Fe leads indicate a power-law in thelinear regime G ∝ T 0.7, see figure 4.2a. This behavior is typical in devices of thiskind. The experimentally determined values of α are in agreement with the theoreticalvalue of αend(theory) ≈ 0.65 [33], and correspond to what is found in other similardevices [35, 36]. All in all, signs of the formation of a LL in the Fe-lead devices arewell established.

Indications of power-law dependencies are observed, as well, in the devices producedon a substrate of a GaAs/AlAs superlattice (figure 4.7b and figure 4.9a). The LL ex-ponent of the linear regime is determined in 14 devices, and is found to lie in theinterval of 0.53 ≤ α ≤ 1.1 with an average of α ≈ 0.79±0.2. In the non-linear regimeα ≈ 0.64± 0.1 have been determined in two devices. Hence, α ≈ 0.7 is the typicalvalue of the LL exponent for the devices formed on a substrate of a GaAs/AlAs super-lattice. The theoretical value of α depends on the dielectric constant of the substrate.The insertion of εr(GaAs/AlAs) ≈ 12 in the expressions of equations (1.3) and (1.4)implies αend(theory) ≈ 0.3 and αbulk(theory) ≈ 0.08. The theoretical values of α arefar lower than the values determined experimentally in any one of the entire collec-tion of devices. It is unlikely, that this is a result of the tubes being suspended in air.The nanotubes may be air-suspended, as a consequence of the etching of the substratebeneath the tubes, which is unavoidable during the fabrication of the devices. Air-suspended tubes would be less affected by the high dielectric constant of the substrate.On the other hand, the small spacing between the CB oscillations is successfully ex-plained by the high dielectric constant. This indicates that the tubes are not suspendedin air, or, at least, that they are very close to the substrate. Furthermore, measurementsreported by Nygard and Cobden [64] on QD from air-suspended SWNTs did not revealany significant change of the α exponent. It is more likely that the unexpected highα value is explained by the following considerations. The tubes are being bend andstretched, due to the etching of the substrate beneath them. This may cause a numberof irregularities or kinks in the tubes. In addition, the distances between the leads, ofabout 1 µm, is fairly long in the present devices, increasing the probability of struc-tural defects along the tubes. These kinks and structural defects will create multipleQDs in each device, and it is known that the LL exponent is enhanced when QDs areplaced in series [33]. It is not possible to prove the formation of multiple QDs fromthe present measurements, and additional investigations are required in order to decideon the finale explanation for the large LL exponent of α ≈ 0.7. The substrate usedin the nanotube devices studied by other groups is usually SiO2, and no other similarmeasurements of transport in nanotube devices on a GaAs/AlAs superlattice substratehave been reported in the literature. Hoffer et al. [49] discuss experimental values ofthe LL parameter for multi-wall carbon nanotubes (MWNTs) located inside an alu-mina membrane. Their experiments determined 0 ≤ α ≤ 0.8, where high α values areexplained by tubes consisting of several QDs.

The main points of this section are: The characteristic features expected in the trans-



port properties of SWNT devices have been detected in all the devices included inthis report. The tunnel contacts formed between the ferromagnetic lead materials andthe SWNTs are in general of a lower quality than those which may be achieved be-tween SWNTs and Au leads. Devices prepared on a GaAs/AlAs substrate display anunexpected high LL exponent.

5.2 The Effects of the Ferromagnetic Leads

The basic reason for applying ferromagnetic leads to SWNTs is to investigate spin-polarized transport in the 1D tubes. The effects of the ferromagnetic leads, and therebyof spin-polarized transport, are extracted by measuring the transport properties at var-ious values of an applied magnetic field.

The transport in the SWNTs is supposed to be ballistic with practically no scatteringof the carrier spins, and SWNTs are believed to show no intrinsic magnetoresistance(MR). Accordingly, the nanotubes may be assumed to be almost perfect spin-ballisticwave guides.

The ferromagnetic leads of the devices may cause the appearance of MR. When themagnetic field is swept through their coercive fields, multi-domain states may beformed implying an enhancement of carrier scattering. This effect is utilized in thedetermination of the coercive fields of the GaMnAs leads, figure 3.3. The absolutechange in resistance was found to be about ∆R ≈ 30−600Ω. MR in nanoconstrictionsin GaMnAs have been investigated by Brian Skov Sørensen at the Ørsted Laboratory.Comparable effects of the MR of ∆R . 100Ω were determined in these experiments.The MR of the present Fe leads have not been investigated in details, but is expectedto correspond to that reported for similar leads of Ni/Fe alloys, where the changes inthe resistance was observed to be less than 1 Ω [65, 66].

5.2.1 Observations of Hysteretic Magnetoresistance

It is observed that the conductance, or current, of the ferromagnetically contactedSWNTs, as a function of an in-plane magnetic field, displays a characteristic behavior,i.e., a hysteretic magnetoresistance (HMR). The hysteresis disappears at a sufficientlyhigh value of the applied magnetic field (|B| & 0.2 T), and here the conductance issymmetric, independent of the sign of the field. One general trend, shown by the exper-imental results, is that the hysteretic features appear, not before, but after the sweepingfield has passed through zero. The feature is either a dip (figures 4.2b, 4.3b, 4.4a, 4.7d,and 4.10) or a peak (figures 4.4c, 4.7c and d, and 4.10b) in the conductance. The con-ductance in this hysteretic extremum is labeled Gex, and GB is the conductance without


The Effects of the Ferromagnetic Leads 53

the hysteretic feature, i.e., the conductance at the same magnetic field, but measuredin the case of opposite sweep direction. The magnitude of the HMR is defined as∆G/GB = (GB −Gex)/GB, and the dip structure corresponds to a positive HMR andthe peak to a negative or inverse HMR.

Except for the sign, the positive and the inverse HMR are structurally similar. Somedevices show positive HMR, some negative, and some show either a positive or aninverse HMR depending on temperature, gate or bias voltage.

The HMR is observed in a few of the investigated Fe-T-Fe devices. The results showfrom 50% to 100% positive HMR in two devices at T ≤ 4 K, and negative HMR, ofup to almost −80%, in three devices. However, in the majority of devices, more than35 in total, no hysteretic features are observed at all.

HMR is observed in all the investigated nanotube devices contacted by two GaMnAsleads: GaMnAs-T-GaMnAs. The positive, as well as, the inverse HMR attain magni-tudes of up to almost 100% at T ≤ 4 K.

In all three devices of one ferromagnetic semiconductor and one Au lead (GaMnAs-T-Au), the HMR is observed as well. Positive HMR of up to about 50% and inverseHMR of magnitudes of up to about −70% are the results of these investigations.

In order to analyze, or to approach an understanding of the observed HMR in theferromagnetically contacted SWNTs, the following characteristics of the HMR are theessential ones.

The SWNTs have no intrinsic MR, and MR in the leads alone cannot account forthe large magnitude and the change of sign observed in the HMR. This leaves spin-polarized transport to be the only effect, which may be responsible for the HMR. TheHMR is observed in devices with either one or two ferromagnetic leads, and never indevices with solely normal leads. The HMR must be related to the occurrence andirreversible switching of magnetic domains. The hysteretic dip or peak always occursafter the field has been swept through zero, and before the field reaches the coercivefield. Most often, the changes in the conductance are abrupt, indicating that only oneor a few domains in each lead are actively involved in the coupling to the tubes.

A large diversity in the values of HMR is observed, both between different devices,but also the HMR may vary strongly depending on the specific condition of the sin-gle device. In the current measurements the variation of the HMR in a single deviceappeared to be irregular, with no simple dependence on the gate or bias voltage.

In spite of the diversity in the observed hysteretic behaviors the observations are quali-tatively comparable to that reported for similar devices of MWNT [47, 48, 49, 50] andSWNT [52]. However, the magnitude of the HMR observed in some of the presentdevices is much larger than reported earlier.



It is generally found, that the absolute magnitude of the positive or inverse HMR in-crease with decreasing temperature, see figures 4.5, 4.8a, and 4.11. The HMR appearsat temperatures, where the nanotube-QDs are in the CB regime. A dramatic increase ofthe HMR of up to 100%, occurs in the low-temperature limit where the devices enterthe regime of strong CB. However, neither the magnitude nor the sign of the hystereticbehaviors show a relationship to the characteristic features of CB, i.e., the two effectsseem to co-exist without influencing each other directly. A trend of a decreasing ratioof the HMR at large applied bias voltages is determined, see figure 4.12. This trendmay be explained simply by the heating of the contact area of the leads caused byhigh bias voltages. The increase of the temperature implies a decrease of the magneticordering, whereby the effects due to spin-polarized transport are reduced.

5.2.2 Models of Spin-Polarized Transport

Two simple models of spin-polarized transport in the system are discussed in a searchfor an explanation of the HMR.



Figure 5.1: a) A sketch of the nanotube spin-valve device. A possible domain struc-ture, as a function of the magnetic field, is shown. b) Diagrams of spin-resolveddensity of states of the magnetic domains, contacting the SWNT. The diagramscorrespond to the sequence in a. c) A measurement of a Fe contacted SWNT atT = 350 mK (figure 4.3b). The arrows indicate the possible magnetization directionsof the different domains contacting the tube in each lead.



Jullieres Spin-Valve Model

The first attempt to describe the system is to apply Jullieres spin-valve model of spin-polarized transport through a tunnel barrier. It was introduced on page 2, and theresult is a relative change in the conductance from the parallel GP to the antiparal-lel GAP configurations of the magnetization of the ferromagnetic leads: ∆G/GP =(GP −GAP)/GP = 2P2/(1+P2), where P is the polarization of the leads. This modelis applicable to a SWNT device with ferromagnetic leads, since the tube may be viewedas a ballistic transport medium of the spin. The tube is coupled to one magnetic do-main in each ferromagnetic lead, which are capable of being in different magneticconfigurations, of either parallel, when a high magnetic field is applied, or antiparal-lel, when the magnetic field has passed zero and one of the contacting domains haschanged its direction of magnetization. The nanotube spin-valve device is sketched infigure 5.1a and b, and the observed HMR is tentatively interpreted as spin-polarizedtransport occurring in the nanotube, as indicated by the sequence of figure 5.1b andthe measurements in figure 5.1c. The measurement displays high conductance in theparallel configuration and low conductance in the antiparallel configuration. In reality,the magnetization of the domains may turn gradually or develop into sub-domains, re-sulting in intermediate configurations during the transition. This may produce a morecomplicated evolution of the conductance, as is usually seen in the measurements.

Qualitatively, the spin-valve model indicate, that the detected HMR is caused by spin-polarized tunnelling in the ferromagnetically contacted SWNTs. Still, the almost100% ratio of the HMR, which has been observed in Fe and GaMnAs contacted tubedevices, cannot be explained by Jullieres model, unless the polarization of the carriersin the ferromagnetic leads are 100%. The polarization of Fe is, to a large accuracy, de-termined to be about 44% [3, 4], and the polarization in GaMnAs has been predictedtheoretically to reach at most 80% [17]. The model is not capable of explaining howthe HMR ratio may exceed these limiting values. Furthermore, the model does not ex-plain why the inverse HMR does appear. In particular, the spin-valve model does notapply for the spin-polarized transport in SWNTs contacted by only one ferromagneticlead.

The Model of two Spin Channels

A model of spin-polarized transport in a tube device is proposed by Pavel Streda, andis described in appendix D. The idea of the model is to divide the spin-polarizedcurrent into two parallel channels, one for each direction of spin. Spin scattering isneglected, whereby the two channels are independent of each other and may be treatedindividually.



Figure 5.2: a) A sketch of the GaMnAs-T-Au device. The tube is coupled to oneor two magnetic domains as a function of magnetic field. b) Diagrams of the densityof states, following the sequence of a. c) A measurement of a GaMnAs-T-Au device(figure 4.7d).



The HMR recorded in the GaMnAs-T-Au devices came as a surprise, as the spin-valve model does not predict any HMR in devices with one ferromagnetic lead. Inorder to find an explanation, it is necessary to identify spin effects produced by asingle ferromagnetic lead. The starting point is that the conductance may change ifthe coupling to the tube alternates between one and two domains in the ferromagneticlead. This situation is analyzed in terms of the model of two spin channels.

The domains in a Fe lead have been examined by a magnetic force microscope at roomtemperature and at zero magnetic field, and the result is presented in figure 4.1c. Thesizes of the domains are generally smallest at the edges of the leads, where the contactto the tube will be formed. The size of the edge domains seems to be less than 1 µm.The size of the magnetic domains in the GaMnAs leads is unknown. A crude estimatewould be that they are comparable to the domains in the Fe leads.

In the present device design, the leads are placed on top of the tubes. Studies ofthe QD tube devices show that the contacts are formed in the vicinity of the edgeof the leads [38]. But a complete investigation of the contact and the length of thecontact area has yet to be done. A few theoretical papers have put focus on the subject.However, their results are not applicable to realistic and non-idealized contacts [67,68]. Therefore, a very simple model is applied in order to find a characteristic lengthof the contact area. A detailed description and an evaluation of the model is presentedin appendix C. The model assumes a uniformly distributed contact along the part ofthe tube which is under the lead, determined by a 1D contact resistivity ρC. This maynot be an accurate description of the contact area, as the contact may, just as well,consist of one or a few located spots. Still, for the purpose of finding an approximatelength of the contact area, the simple model may be adequate. A characteristic lengthof the contact area between the tube and the lead is derived to depend on a contactresistance RC, that may be estimated from the resistance of the device, and a mean-free path in the tube beneath the lead LC

m. In a typical device of resistance Rdevice ≈100 kΩ, the contact resistance is estimated to be RC ≈ (Rdevice −h/(2e2))/2 ≈ 44 kΩ.LC

m ≈ 0.1µm is supposed to be fairly short, this imply that the length of the contactarea is lC = RC4e2LC

m/h ≈ 0.7µm.

This estimate show that the size of the domains at the edges of the leads and the char-acteristic length of the contact area between the tube and the lead are of comparablesize . 1µm. This imply, that it is a possibility that the contact between the tube and alead may extent over more than one domain.

The two-channel model for a device with one ferromagnetic lead, where the contactarea may split into two domains, and one Au lead is analyzed in appendix D. Thesituation is shown in figure 5.2a. It is found that the conductance is enhanced whenboth of the spin channels are used, i.e., when two magnetic domains of opposite spinare coupled to the tube. The spin-polarized transport is indicated in figure 5.2b, andexemplified in the upper plot of figure 5.2c.



The model is able to describe the HMR in devices with one ferromagnetic lead, al-though solely the inverse HMR.

5.2.3 Discussion of the Spin-Polarized Transport

The models presented above do not account for the complexity of the observations,but at least, they give a qualitative understanding of the influence of the spin-polarizedtransport in devices with one or two ferromagnetic leads.

Spin scattering is neglected in both models. The spin scattering will probably implysome reduction of the effect, but it is unlikely that it is going to change the qualitativeoutcome of the models.

The picture of a spin-resolved density of states, applied in the models, is a simplifi-cation. Actually, the spin-resolved density of states has a very complicated structure.Tsymbal and Pettifor [69] analyze spin-polarized tunnelling from 3d ferromagnets.The spin-polarized tunnelling is found to be strongly dependent on the bonding sta-tus, or the microscopic nature, of the contact to the ferromagnetic lead. Alternationsin the bonding between the lead and the tube may even imply a sign change of thepolarization of the tunnelling electrons.

It is possible that a change of the bias voltage, or a circling of the temperature mayinfluence the bonding status of the electric contact between a tube and its lead in anuncontrollable manner. In some devices significant changes in sign and magnitude ofthe HMR have been observed to appear in an irregular way, by a variation of the biasvoltage or the heat circulations. This is in accordance with a strong dependence of thespin-polarized tunnelling on the bonding status between lead and tube. The importantissue is to understand the states of the electrical contact, which are formed between aferromagnetic lead and a tube.

The reason for the steep increase of the HMR with the temperature reduced to the mil-likelvin regime, is a puzzle. The temperature dependence suggests that some kind of aresonance is influencing the spin-polarized tunnelling. It is an open question though,how and where such a resonance may appear. Also, the presence of the CB regime mayinfluence the spin-polarized transport. Ono et al. [70] have investigated ferromagneticsingle-electron transistors (SETs). They report on an enhancement of the HMR ratiowhen the SET is in the CB regime. Wang and Brataas [71] analyze theoretically spin-polarized transport in highly transparent tunnelling contacts, which obviously does notapply for the present investigations of high-resistive contacts. A theoretical under-standing of the tunnel contacts occurring in the present study, are urgently needed inorder to clarify the importance of the CB regime on the spin polarized tunnelling.


Chapter 6

Conclusion

Experimental results on the transport properties of devices of single-wall carbon nan-otubes (SWNTs) have been presented. The purpose has been to investigate spin-polarized transport in one-dimensional tubes. Two sorts of ferromagnets have beenutilized as lead material: metallic Fe and semiconducting Ga1−xMnxAs (GaMnAs).

The one-dimensional nature and the quantum-dot behavior of the nanotube devices arefound. Indications of the formation of a Luttinger liquid is observed, and the devicesentered the Coulomb blockade (CB) regime at low temperatures. These findings are inaccordance with the results of other similar studies and with the theoretical predictionsfor mesoscopic transport in SWNT devices [22, chap. 7].

The employment of ferromagnetic leads to the nanotubes has been proven to be ableto produce significant effects of hysteretic magnetoresistance (HMR). All devices con-tacted by two GaMnAs leads, and all devices with one GaMnAs lead and one Au lead,show the HMR. In contrast, only a very few of the devices with two Fe leads displayedany hysteretic behavior. Important characteristics of the HMR are observed. It appearsat low temperatures (T . 4 K), and increases rapidly as the temperature is reducedfurther (down to T ≈ 300 mK), where the devices are in the strong CB regime. A largediversity of sign and magnitude of the HMR is observed.

The magnitude of the magnetoresistance in the ferromagnetic leads themselves issmall, compared to the observed HMR, and SWNTs show no magnetoresistance atall. This means that the large values of the HMR determined by the experiments mayonly result from spin-polarized transport through the tube devices. This transport isdescribed qualitatively in terms of simple models. In the case of two ferromagneticleads, Jullieres spin-valve model is applicable. In order to describe HMR in deviceswith one ferromagnetic lead, it is necessary to assume that the tube is coupled alter-nately to one and two ferromagnetic domains, which is described by Stredas model of

61

62 6. Conclusion

dividing the conductance into two spin-channels. The two models explain some of theobservations, but they are not able to account for the cases of sign changes or the hugemagnitude of the HMR, which in some cases exceeds the limit of the polarization ofthe leads.

A large diversity of sign and magnitude of the hysteretic magnetoresistance is ob-served for the complete collection of devices, and, as well, for some individual de-vices, when varying the temperature, gate or bias voltage. The single-device variationof the HMR indicates that the spin-polarized tunnelling is much dependent on theprecise conditions for the interface between the ferromagnetic lead and the nanotube.The theoretical knowledge about this interface is limited. Detailed investigations ofthe spin-resolved density of states in the ferromagnetic leads, and its influence on thespin-polarized tunnelling through the interface to the nanotube, are needed in order toreach a better understanding of the diversity of the presented HMR results.

Any explanation for the huge HMR which is observed at the lowest temperatures islacking. It is speculated that it might be a kind of a resonance phenomenon, possiblyappearing because the system is entering the strong CB regime.


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Appendix A

Measurements on Fe contactednanotubes

A.1 Fe-T-Fe#1

Figure A.1: Fe-T-Fe#1. The conductance as a function of magnetic field at temper-atures T = 20 K, 15 K, and 10 K. The curves are average of 15 individual measure-ments.

67

68 Appendix A

A.2 Fe-T-Fe#3

Figure A.2: Fe-T-Fe#3. The current versus magnetic field with a finite bias voltage.a) T = 4.2 K, V = 6 mV. Average of 10 individual sweeps. b) T = 350 mK, V =

20 mV. Average of 8 individual sweeps.


Fe-T-Fe#4 69

A.3 Fe-T-Fe#4

Figure A.3: Fe-T-Fe#4 T = 300 mK. The current versus magnetic field with a finitebias voltages of V = 1 and 0.1 mV. The curves are average of 10 individual measure-ments


70 Appendix A


Appendix B

Measurements on GaMnAs/Aucontacted nanotubes

B.1 GaMnAs-T-Au#2

Figure B.1: GaMnAs-T-Au#2 T = 4.2 K. The current versus magnetic field at biasvoltages V = 5 and 0.5 mV (average of 10 measurements). Insert: the conductanceas a function of the gate voltage. The X presents the gate voltage.

71

72 Appendix B

B.2 GaMnAs-T-Au#3

Figure B.2: GaMnAs-T-Au#3 T = 4.2 K. The current versus magnetic field at biasvoltages V = 10, 5, and 0.5 mV.


Appendix C

A Simple Model of the Contactbetween Lead and SWNT

A characteristic length of the contact region between a SWNT and a lead may bederived from a simple model of the electric contact. A sketch of the system togetherwith a diagram is presented in figure C.1. The system is a tube device of a SWNTcontacted by two leads, source and drain. The SWNT exceeds under the leads overa total distance l. The diagram focus on the source to tube contact and presents howthe contact is modelled. The contact between the lead and the tube is assumed to beuniformly distributed, whereby it may be expressed by a one dimensional (1D) contactresistivity ρC. The contact is modelled by a number of parallel contact points alongthe tube. There is a voltage drop V0 over the contact.

It is assumed that the resistance in the leads is small compared to all other resistancesin the device. This implies that the voltage on the source is a constant V0, and theresistance of the whole device may be written as: Rdevice ≈ 2RC + Rtube + h/(4e2).h/(4e2) is the 1D channel resistance. RC is the contact resistance, assumed to be thesame from source to tube and from tube to drain. Rtube is a Drude-like resistance ofthe tube supposed to be on the form Rtube ≈ (h/4e2)(L/Lm), L is the length of the tubeand Lm is the mean free path of carriers in the tube.

The total current, I, through the contact is divided into a number of sub currents (Ii =Ii(V0 −Vi)), as presented in the diagram.

I =N

∑i=1

Ii →∫ l

0J(V0 −V (x))dx (C.1)

where J is the 1D current density.

73

74 Appendix C

Figure C.1: a) The outline of a device. b) A diagram of the source to tube contact.

The voltage drop Vi −Vi−1 over Ri must be

Vi −Vi−1 = Ri

N

∑j=i

I j(V0 −V j) = Ri

(

I −i

∑j=1

I j(V0 −V j)

)

(C.2)

Ri is determined from the Drude-like resistance of the tube: Ri =(h/4e2)((xi−xi−1)/LCm),

where LCm here is the mean free path in the contact region. This imply:

dV =h

4e2dxLC

m

(

I −∫ x

0J(V0 −V (x′))dx′

)

(C.3)

The contact is assumed to be described by a 1D contact resistivity ρC, whereby J(V0−V (x)) = (V0 −V (x))/ρC.

dVdx

=h

4e21

LCm

(

I −1

ρC

∫ x

0(V0 −V (x′))dx′

)

d2Vdx2 = −

h4e2LC

m

1ρC

(V0 −V (x))(C.4)

The boundary conditions of V (0) = 0 and V (l) = V0 for l → ∞ imply:

V (x) = V0

(

1− exp(

−xlC

))

lC =

√

4e2LCm

hρC

(C.5)


A Simple Model of the Contact between Lead and SWNT 75

The result is valid as long as l lC. lC is the effective length of the contact. Theresistance of the contact is given by RC = ρC/lC. As a result, the contact length maybe expressed by the contact resistance and the mean-free path in the contact region ofthe tube:

lC = RC4e2LC

mh

(C.6)

A typical resistance for a device of a SWNT is about 100 kΩ at room temperature. Itmay be assumed, that the mean-free path of carriers in the tube is comparable to thetube length and fairly smaller in the contact area of LC

m ≈ 0.1µm. Thereby, an estimatefor the contact resistance and length of the contact is

RC ≈ (Rdevice −h

2e2 )/2 ≈ 44kΩ ⇒ lC ≈ 0.7µm (C.7)


76 Appendix C


Appendix D

Two Spin-Channel Conductance

The contents of this appendix is based on Pavel Stredas idea of a model for spin-polarized transport in a tube device, and his calculations.

The Model

A nanotube device consists of a tube, contacted by two leads source and drain. Thefollowing model describes spin-polarized transport in a nanotube device. The con-ductance through the device is divided into two parallel conducting channels, one foreach direction of spin, as sketched in figure D.1. It is assumed that the spins are notscattered. Thereby, the two channels are independent of each other and may be treatedindividually.

The device is separated into three regions. The central part is the tube itself. Theconductance of the spin-up (-down) channel in the tube is defined by T ↑(↓)

tube ≡ 1/R↑(↓)tube.

The conductances in the channels are the same T ↑tube = T ↓

tube ≡ Ttube. Furthermore, thereare two contact regions. One from source to tube, with the spin-channel conductancesT ↑(↓)

s ≡ 1/R↑(↓)s , and one from the tube to the drain with conductances T ↑(↓)

d ≡ 1/R↑(↓)d

of the spin channels.

Equivalent expressions of the conductances are given for the two spin channels

G↑(↓) =T ↑(↓)

s TtubeT ↑(↓)d

Ttube

(

T ↑(↓)s +T ↑(↓)

d

)

+2T ↑(↓)s T ↑(↓)

d

(D.1)

The total conductance is the sum of conductance in each channel

G = G↑ +G↓ (D.2)

77

78 Appendix D

Figure D.1: a) A sketch of the two spin channels. b) One domain couples to thetube. c) Two domains couple to the tube.

The System

The source is ferromagnetic with a 100% polarization of the carriers. The size of thedomains in the ferromagnet is smaller than the characteristic length of the electricalcontact between the source and tube. The drain is a normal metal.

Two situations, as sketched in figure D.1, are treated. i) One magnetic domain in thesource is coupled to the tube. ii) Two magnetic domains in the source, one spin-up andone spin-down, are coupled to the tube.

When the source is one domain, say spin-up, the conductances of the two channels inthe source contact are given by

T ↑s = Ts T ↓

s = 0 (D.3)

For the situation of two domains in the source, the two domains couple to the tubewith different probabilities p and 1− p for spin-up and spin-down, respectively. Thisis written as

T ↑s = pTs , T ↓

s = (1− p)Ts , 0 ≤ p ≤ 1 (D.4)


Two Spin-Channel Conductance 79

The drain is normal metal, whereby the conductances of the drain contact region are

T ↑d = T ↓

d ≡ Td (D.5)

Magnetoresistance

In an applied magnetic field, the magnetic domains in the source may be altered. Athigh magnetic fields one domain is present, and the one-domain conductance is namedGB. When the magnetic field is swept to become smaller than the coercive field ofthe source, the one domain breaks into several domains. A situation where two mag-netic domains in the source are coupled to the tube may occur. This will change theconductance to the value Gex.

The conductance, when the source contact is a single-domain is given by

GB = G↑B +G↓

B =TsTtubeTd

Ttube(Ts +Td)+2TsTd(D.6)

The conductance, when the source contact consists of two domains, is

Gex = G↑ex +G↓

ex

=pTsTtubeTd

Ttube(pTs +Td)+2pTsTd+

(1− p)TsTtubeTd

Ttube((1− p)Ts +Td)+2(1− p)TsTd

(D.7)

During a magnetic field sweep, the number of domains in the source vary between oneand two, and the relative change in conductance is

∆GGB

≡GB −Gex

GB= −

p(1− p)(2+ γ)γ(1+ pγ)[1+(1− p)γ]

(D.8)

whereγ ≡

TsTtube +2TsTd

TdTtube(D.9)

The expression for ∆G/GB is always negative. A transparent situation is Ttube andTd → ∞, then the quantity γ vanishes and no magnetoresistance effect appears. In theopposite limit of a high Coulomb blockade, there is a large resistance in the tube and inthe drain contact region, Ttube and Td → 0 ⇒ γ → ∞. In this limit, the relative changein conductance approaches unity.

The calculations were performed with the assumption of 100% spin-polarized carriersin the source lead. Qualitatively, the same result is achieved, if the polarization of thesource is less than 100%, only the relative change of the conductance will be smaller.


ferromagnetically contacted single-wall carbon nanotubesjjensen/publ/thesis-ii.pdf · 2009. 6....

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