Anomalous transport in ferromagnetic GaAs/InxGa1-xAs/GaAs quantum well delta-doped

with Mn and C

Kulbachinskii, Vladimir*, Shchurova, Ljudmila†, Kuznetsov, Nicolay* *M.V. Lomonosov Moscow State University, Low Temperature Physics Department, Moscow, RU

E-mail: kulb@mig.phys.msu.ru † P.N. Lebedev Physical Institute of RAS, Moscow, RU

E-mail: lju@sci.lebedev.ru

Abstract—Transport, magnetotransport and magnetic properties of structures with GaAs/In0.17Ga0.83As/GaAs quantum well (QW) in GaAs have been measured in the temperature interval 4.2<T<300 K. The structures were �-doped by Mn and carbon to provide magnetic properties and enhanced p-type conductivity. The ferromagnetic phase up to 400 K was detected by SQUID magnetometer. Anomalous Hall-effect and negative magnetoresistance was observed at low temperatures. The calculations of temperature dependence of resistance have been carried out. The contributions of various hole scattering mechanisms are analyzed. The quantitative consistency of the calculated and measured temperature dependence of sheet resistance is found. The reasons for occurrence of negative magnetoresistance are explained quantitatively as the reductionof the spin-flip scattering by aligning spins by magnetic field.

Keywords-component; spintronics; ferromagnetizm; GaAs; quantum well; negative magnetoresistance

I. INTRODUCTION It was shown by various researchers that the ferromagnetic

Curie temperature TC in Ga1–xMnxAs solid solutions increases with the hole concentration, as wellas upon an increase in the Mn content [1]. For this reason, additional doping is often used for increasing the hole concentration. The hole concentration can also be increased by reducing the number of defects in the structure. Such an effect is observed for the low-temperature growth of the structures with the help of molecular beam epitaxy (MBE). Although Mn is an acceptor in GaAs, the concentrations of the holes formed in it is insufficient since the efficiency of Mn is low due to the formation of compensating defects [2]. Such defects can be antistructural AsGa defects (which dominate in low-temperature MBE). The role of these defects can also be played by interstitial Mni and Asi atoms (donors). Compensating defects are the residual deep donors AsGa and deep acceptors GaAs. These two types of antistructural defects are usually present in identical amounts. In the case of p-type (Ga,Mn)As, both AsGa and interstitial atoms can play the role of compensation defects.

In the present study we investigated the influence of Mn delta-doping on magnetic and galvanomagnetic properties of

GaAs structures with GaAs/InxGa1-xAs/GaAs quantum well. The thermodynamic model have been formulated, and the exact analytical expressions for the thermodynamic characteristics of system with intermediate Fermi-Boltsman statistics have been received. For definition of hole density in the quantum well thermodynamic calculations of the composition of the system from free holes, atoms and ions Mn- have been carried out. Calculations of temperature dependence of resistance and magnetoresistance of free holes in quantum well have been obtained. The contributions of various hole scattering mechanisms in resistance are analyzed.

II. EXPERIMENTAL

A. Samples Samples were prepared with the combined method of

MOC-hydride epitaxy and laser deposition [3]. Although Mn acts as an acceptor in GaAs, the hole activation ratio is much less than unity and the hole concentration tends to saturate due to the compensation of Mn acceptors by the defects. Therefore, some additional doping of acceptor impurity is needed to achieve a high hole concentration. Samples were grown on GaAs (100) substrate and contain In0.17Ga0.83As QW, carbon �-layer (to provide enhanced p-type conductivity in the quantum dot layer) and laser-deposited Mn layer separated by GaAs spacers with width d=3 nm. A schematic diagram of the structure is given in fig. 1.

Figure 1. Sample with quantum well GaAs/InGaAs/GaAs structure doped by C and Mn.

978-1-4244-2717-8/08/$25.00 © 2008 IEEE COMMAD 200851

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Temperature dependence of resistance was measured in the temperature interval of 4.2–300K, magnetoresistance and Hall effect for 4.2�T�77 K in magnetic fields up to 6 T. Ferromagnetism was detected in the whole temperature interval 4.2�T�400 K with SQUID magnetometer. Negative magnetoresistance was detected in the temperature interval 4.2<T<35 K. Some parameters of samples are listed in table 1.

TABLE I. MOBILITY � AND CONCENTRATION OF HOLES "P" AT DIFFERENT TEMPERATURES

N Mn 1014 cm-3

p (300K)

1012cm-2

�(300K) cm2/Vs

µ cm2/Vs

p 1012�m-2

415 0 1.8 300 - - 419 3.4 3.4 450 4670(4.2�) 0.35 (4.2�) 420 6.6 5.7 190 1930 (77�) 1.2 (77�) 417 10 6.8 160 1920 (77�) 1.4 (77�) 421 13 7.9 150 95 (16�) 0.58 (16�)

B. Temperature dependence of resisitivity All samples had p-type conductivity. When temperature

decreased sheet resistivity RS of samples increased (fig. 2).

Figure 2. Temperature dependences of the sheet resistance Rs

For samples with Mn concentration less than 1015 cm-3 the dependence RS(T) has quasimetallic character for 77<T<300K. The behavior of RS(T) in a sample with a high Mn content changes radically. In this case, the dependence exhibits an activated behavior (sample 421) with two regions in which the conductivity activation energies differ substantially: �1=11 meV at T � 25 K, and �3=1.4 meV at T<25 K. A peculiarity is revealed in the RS(T) curve on a linear scale. In principle, this behavior of the temperature dependence of the resistivity is not surprising and has been repeatedly observed in Ga1–xMnxAs films in which the Mn content starts to exceed a certain critical value x=xc � 0.05–0.06 [4]. Under these conditions, the concentration in the samples decreases, the metallic behavior of the structures changes to a dielectric one, and the Curie temperature drops. At present, it is found [4] that this behavior is associated with the specific features of Mn atoms. When these atoms supersaturate GaAs, they start to occupy interstitial positions where they already act as double metastable donors, leading to compensation of Mn substitutional acceptor

impurities. It is also found that low-temperature annealing of such defects leads to a reverse transition from the dielectric to a metal [6]. Note, however, that a sufficiently strong AHE is observed in Ga1-xMnxAs films both at x lower than xc and higher than xc. The Curie temperature can be determined from an analysis of its temperature behavior [3].

C. Magnetism All samples showed ferromagnetism, as indicated by

hysteresis loop in the magnetization (all samples studied showed qualitatively similar magnetic behavior). The hysteresis loops show clear temperature dependence over the entire range of temperatures studied for QW samples, as can be seen in fig. 3 for sample 419. There are different magnetic phases in the samples, one (solid solution GaMnAs) with Tc about 50 K, others with Tc above room temperature. The first value of Tc is very typical for hole mediated ferromagnetism in Ga1-xMnxAs solid solutions. Next phase is due to formation of MnAs clusters. The Curie temperature for bulk MnAs is about 315 K. The peculiarity due to this transition is visible at this temperature in the temperature dependence of magnetic moment, plotted in fig. 4. Above this temperature ferromagnetism survived due to Ga1-xMnx clusters. Tc for such clusters depends on Mn content and may be as high as 600 K for x=0.6 [5].

Figure 3. Magnetization loops at different temperatures for sample 419 (diamagnetic background was subtracted).

Figure 4. Zero filed cooling (ZFC) and field cooling (FC, 5 T) magnetic moment M dependences on temperature for sample 419. Signal is negative

due to diamagnetic background of GaAs substrate

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D. Anomalous Hall effect In single-phase diluted magnetic semiconductors (DMS) of

the (III,Mn)V type, as well as in ferromagnetic metals, the Hall resistance Rxy obeys the relationship (1)

where d is the thickness of the DMS layer; R0 is the coefficient of the normal Hall effect, which is caused by the Lorentz force (proportional to the magnetic induction B); Ra is the constant of the anomalous Hall effect (AHE), determined by the effect of spin–orbit interaction proportional to the magnetization M) on carrier transport; and μ0 is the magnetic constant. It is important to note that the AHE is sensitive to the interaction of charge carriers with the magnetic subsystem, and its contribution turns out to be dominant in the (III,Mn)V systems (that is, Rxy�RaM) to temperatures exceeding Tc by a factor of 2 to 3. Therefore, Tc can be determined from the AHE data in two ways: i) in the ferromagnetic region of temperatures, from measurements of the temperature dependence of the Hall resistance Rxy(T) proportional to the magnetization M and ii) from measurements of the magnetic susceptibility �(dRxy/dB) for B=0 in the paramagnetic region and the use of the Curie–Weiss law (1/)�(T–Tc) [4]. Note that, in the case of 2D systems [6], the AHE served as a single method for studying magnetic ordering because of the strong effect of the substrate diamagnetism and difficulties of measuring the magnetization under these conditions. In this case, however, the values of Tc measured using the AHE may reflect the temperature of the transition of clusters from the ferromagnetic to superparamagnetic state. The magnetic-field dependences of the Hall resistance Rxy for sample 421 obtained at different temperatures are presented in Fig. 5.

Figure 5. Magnetic-field dependences of the Hall resistance for a sample 421. Temperatures T, K: (1) 16.7; (2) 25; (3) 31; (4) 39.4, and (5) 56.9. The temperature dependence of the relative value of the anomalous Hall effect is

shown in the inset.

An evident contribution of the AHE is observed for sample 421. To estimate the relative contribution of the AHE component, we extrapolated the Rxy(B) curves at B � 1 T by a linear dependence, thus having separated out the contribution of the conventional Hall effect, and then subtracted it from the Rxy(B) curve to obtain the AHE component under quasi-saturation conditions of RAS (at B � 1 T). The temperature dependence of the ratio of RAS to the resistance of the conventional Hall effect R0 at B = 1.2 T is shown in the inset in Fig. 5. For Ga1- xMnxAs films, the ratio RAS/R0 obtained in this way would increase to the Curie temperature with decreasing temperature, tending then to saturation. In our case, the AHE contribution in the ferromagnetic region sharply decreases at T � 30 K; at T � 17 K, the Hall effect is already linear with respect to the field, and the Hall resistance in the field B � 1.5 T is Rxy � 1.2x103 .

In spite of the importance of studying the AHE in (III,Mn)V materials, the question of its nature is still under discussion [7]. It is possible that the AHE in ferromagnetic materials includes contributions associated with skew scattering, side jump, and Berry phase. The latter contribution is due to the effect of the spin–orbit interaction on the matrix elements of the velocity operator; therefore, it is sometimes called the intrinsic or dissipationless AHE. It is a constituent of the side-jump contribution. In the case of skew scattering, the AHE constant Ra�A�xx+B�xx

2, where �xx is the resistivity and the second term is smaller than the first, while Ra��xx

2 in the case of the intrinsic AHE and side jump. The theoretical calculations and their comparison with experiment indicate that the intrinsic AHE dominates in (III,Mn)V semiconductors [7]. This is evidently associated with strong spin–orbit interaction in these systems and with the occurrence of degeneracy near the Fermi level. Note, however, that the ferromagnetic semiconductors and 2D systems based on them studied so far related to samples with a very low mobility of charge carriers (not exceeding 10 cm2/Vs. Under these conditions, in the case of scattering by ionized impurities or by a short-range potential, the calculations show that the Hall conductivity or the intrinsic AHE can actually exceed for skew scattering by more than an order of magnitude [7].

In this work, magnetic and magnetotransport properties of GaAs(delta-Mn)/In0.17Ga0.83As/GaAs quantum wells with a high hole mobility (��2000 cm2/Vs). The high mobility is due to the fact that delta-Mndoping is performed through a GaAs spacer rather than inside the two-dimensional channel. The primary emphasis is on studying and analyzing the AHE, which exhibits an unusual behavior: it is not observed in systems with quasi-metallic conductivity and exists in a restricted temperature range in the case of activated charge transfer.

E. Magnetoresistance Fig. 6 presents data on the magnetoresistance for structures

419 and 421 in the region T ~ 30 K. For structure 419 with a degenerate hole gas, a positive magnetoresistance dominates at T= 33.3 K caused by the high value of hole mobility (for the given structure in the fields �4 T, μB � 1).

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Figure 6. Relative magnetoresistance of a sample 419 and a sample 421 at different temperatures

However, the field dependence of R is not described by the classical law (�R/R) � B2, which points to the importance of the contribution of the spin-dependent negative magnetoresistance under these conditions. This contribution already becomes dominant below 30 K, while the region of transition to positive magnetoresistance shifts toward the region of high fields.

As the temperature is decreased, Shubnikov–de Haas oscillations appear against the background of negative magnetoresistance in sample 419 (see Fig. 6). One frequency from one filled dimensional quantization band in the quantum well is observed in the oscillations. The concentration of the two-dimensional electrons determined from this frequency equals 3.4 x 1011 cm–2, which agrees well with the Hall effect data. For samples with higher Mn content at low temperatures only negative magnetoresistance is visible without SdH oscillations.

III. DISCUSSION

A. Scattering of charged carriers We calculated contributions of various scattering

mechanisms to the resistance: contributions of spin-flip scattering, Coulomb scattering, LA-phonon scattering, alloy scattering, and interface roughness scattering. Coulomb scattering and also spin-flip scattering give comparable contributions to the sheet resistance at temperatures less than 50 K. At higher temperatures, the resistance increases with temperature and the influence of phonon scattering on the resistance becomes most significant. The theory and numerical calculations for experimental data is in Ref. [8].

B. Polarization Negative magnetoresistance (see fig.6), [(R(B)-R(0)]/R(0),

is caused by influence of spin polarization of holes in ferromagnetic material. The splitting of spin hole states is

HgE B�2� , where �B is the Bohr magneton, g is Lande

factor. We have calculated spin-polarozation nnn /)( �� �� , where )(� n is the spin up (down) hole

density and �� � nnn is the total hole density in an applied magnetic field B=0–4 Tesla for 2D hole system , n�nc=3.4·1011 cm-2 for T < 21 K (fig. 7).

Figure 7. Spin-polarozation � for 2D hole system at different T

We have carried out the exact analytical expression for )(� n . The part of holes do not participate in spin-flip

scattering because of spin polarization. The effective time of spin-flip scattering is increased proportionally to aligning spins by magnetic field. We assume that other scattering mechanisms remain without change. The influence of polarization leads to linear reduction of magnetoresistance on B. The contribution of the weak square-law of Lorentz force increases magnetoresistance and deflects the curves [R(B)-R(0)]/ R(0) on B. The results of our fits using g=0.45 quantitatively agree with the experimental data and are shown in Ref. [8].

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[5] M. Tanaka, J. P. Harbison, J. De Boeck, T. Sands, B. Philips, T. L. Cheeks, and V. G. Keramidas, " Epitaxial growth of ferromagnetic ultrathin MnGa films with perpendicular magnetization on GaAs", Appl. Phys. Lett. vol. 62, pp. 1565-7 (1993).

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[8] Ljudmila Shchurova, Vladimir Kulbachinskii, "Scattering of carries in �-doped by Mn InGaAs quantum well with hole-mediated ferromagnetism", this issue.

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