Direct Electronic Structure Measurements of the ColossalMagnetoresistive Oxides.

D.S. DESSAUDepartment of Physics, University of Colorado, Boulder CO, 80309, USA

and

Z.-X. SHENDepartment of Applied Physics, Stanford University, Stanford, CA 94305, USA

A chapter in “Colossal Magnetoresistive Oxides”Ed. by Y. Tokura

Monographs in Condensed Matter ScienceGordon And Breach

1998

Direct Electronic Structure Measurements of theColossal Magnetoresistive Oxides.

D.S. DESSAUDepartment of Physics, University of Colorado, Boulder CO, 80309, USA

and

Z.-X. SHENDepartment of Applied Physics, Stanford University, Stanford, CA 94305,

USA

1. Introduction

Colossal magnetoresistance (the CMR effect) has recently been observed [1]in doped manganese-oxide ceramics (manganites), sparking a great amount ofeffort aimed at understanding the electronic and magnetic properties of thesematerials. At low temperatures, properly doped manganites exhibitferromagnetic metallic or nearly metallic behavior, while at high temperaturesthey exhibit a paramagnetic insulating behavior. This generic behavior, as wellas the magnetoresistive effect which occurs near the transition, has beenunderstood to first order within the framework of double exchange theory, asdeveloped in the 1950's and 60's by Zener, DeGennes, and Anderson andHasegawa [2,3]. Recently however, there has been an increasing realizationthat although double-exchange is clearly important for understanding thebehavior of the manganites, it is not enough and other physics must beintroduced. While there has been a great amount of progress bothexperimentally and theoretically, it is not yet clear what the most importantmechanisms are for explaining the physics of the manganites.

In addition to the CMR effect, the manganites have been found to exhibit avery wide range of exotic and beautiful phenomena, including many types ofmagnetic ordering, metal-insulator transitions, charge and/or orbital ordering,and pressure induced phase transitions. It should also be remembered that themanganites belong to the class of materials where electron correlations aredeemed important - a problem that has challenged the condensed matter physicscommunity for over 50 years.

This chapter will focus on the electronic structure of the manganitesobtained by various spectroscopies, with an emphasis on angle-resolvedphotoemission spectroscopy (ARPES) and X-ray absorption spectroscopy(XAS) - two powerful and direct electronic structure probes. We will try toprovide a pedagogical introduction to the various subjects, as well as give ourinterpretation of some of the most important and challenging topics in the field.While we have tried to be relatively complete, it should not be considered acomplete review - rather it should be regarded a snapshot from a particular angleof a rapidly developing field.

Section 2 will discuss various starting points for understanding theelectronic structure of the manganites, including the atomic view, Double-

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Exchange theory, electron correlation effects, and polaronic effects. Section 3gives a quick introduction to the various experimental techniques andconsiderations. Section 4 gives an overview of the measured electronicstructure of the manganites, briefly touching on the doping dependences,temperature dependences, and sample type dependences. It also introduces thepseudogap, which appears to be one of the most central aspects of all the data.Section 5 discusses many more details of the unoccupied electronic structure, aswell as discussing a determination of some of the important energy scales suchas the bare bandwidth W, the Hund's rule energy J, and the Jahn-Teller energyEJ-T. Section 6 discusses the low-energy k -dependent electronic structure indetail, including temperature-dependent data taken across the phase transition.Section 7 summarizes and concludes.

2. Starting points for understanding the electronic structure ofthe manganites

2.1 Structure and dopingThe crystal structure of the manganites is schematically illustrated in figure

1. In all cases, the Mn ions are surrounded by 6 oxygen ions in anapproximately octahedral arrangement, as shown in panel 1a. The Mn and Oions are arranged in an MnO2 plane as shown in panel 1b. The structure ofthese planes is completely analogous to the CuO2 planes found in the cuprateHigh Temperature superconductors (HTSC's). The MnO2 planes are thenstacked in a variety of sequences with MnO2 planes interleaved with (La,Sr)Oplanes, as shown in panel 1c. The compounds are annotated depending uponhow many MnO2 planes are arranged between a bi-layer of (La,Sr)O planes (Laand Sr can be replaced by many other tri- and di-valent ions). This series iscalled the Ruddelson-Popper series, and has the general formula unit(La,Sr)n+1MnnO3n+1. The n=1 compounds have formula unit (La,Sr)2MnO4and are analogous to the HTSC compounds (La,Sr)2CuO4. The n=infinitycompounds have no (La,Sr)O bilayers, and have the formula unit (La,Sr)MnO3.They are cubic or distorted cubic compounds, and the most heavily studied ofthe manganites. The layered compounds (n ≠ infinity) cleave much morereadily than the cubic compounds, and so are more suitable for thespectroscopic measurements reported here.

The "parent" compounds of the manganites, e.g. LaMnO3 areantiferromagnetic "Mott" insulator with properties dominated by the strongCoulomb interactions between the electrons. Substitution of the trivalent (3+)La ions with a divalent ion such as Sr, Ca, or Ba dopes holes into themanganites, creating a material with poorly understood and very unusualproperties. At the appropriate doping level, these doped manganites display acombination of a metal-insulator (M-I) transition, a ferromagnetic-paramagnetic(FM-PM) transition, and the colossal magnetoresistance.

2.2 Ionic view of electronic structureFigure 2a shows the electronic configuration for the parent (undoped)

compound LaMnO3 in a simple ionic picture. Ionic LaMnO3 has a 3d4

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configuration, meaning the 3d valence orbitals are filled with 4 electrons. Thecubic crystal field splits the degeneracy of the d orbitals into the 3-folddegenerate t2g (dxy,dxz,dyz) and 2-fold degenerate eg (dx2-y2, d3z2-r2)orbitals.The eg orbitals point directly at the oxygen atoms, and should hybridizestrongly with the O 2p states, forming dispersive bands containing the electronsresponsible for the conduction. The t2g orbitals point 45 degrees from theoxygens, and so will hybridize less strongly to those states. Therefore, weexpect less dispersion from these states and to a good approximation can treatthem as localized core states, with a net spin S=3/2.

An intra-atomic exchange term JH promotes alignment of the eg electronspins with the core-like t2g spins. As we will see, JH is relatively large in thesematerials, implying that all electron spins should be aligned (Hund's rulecoupling).

2.3 Double exchange, electronic correlations, and othertheoretical considerations for the manganites.

The starting point for most discussions of the mechanism of themagnetoresistance, M-I , and FM-PM transitions in the manganites is thedouble exchange model [2,3]. The physics of double exchange is illustrated infigure 2. As worked out by Anderson and Hasegawa [3] and shown in figure2c, the hopping amplitude of the eg hole from one site to another is a function ofthe relative spin alignment at the two sites. Complete ferromagnetic alignmentof the neighboring spins gives the greatest hopping amplitude ˜ t and the greatestbandwidths, uncorrelated spins will have a reduction in hopping amplitude ofroughly 1/ 2 , and complete antiferromagnetic alignment gives a˜ t =0 implyinga non-dispersive band with zero bandwidth. Therefore, there is a kinetic energygain in the eg band for ferromagnetic alignment, which competes with thesuperexchange energy favoring antiferromagnetic alignment as well as with thethermal fluctuations which favor disorder.

This model intuitively explains why a properly doped material at lowtemperatures is a ferromagnetic metal which will become a paramagneticinsulator at high temperatures. Slightly above Tc, a large magnetic field willserve to align the core (t2g) spins, increasing the hopping amplitude between egelectrons and driving the material more metallic.

While double-exchange gives a nice intuitive explanation for the coupling ofthe spin and charge degrees of freedom and for the trends in conductivity ongoing across the transitions, the magnitude of the effect is not well predicted bydouble-exchange. As shown in figure 2d, for the paramagnetic case (T>Tc) tofirst order the neighboring spins will have a relative angle of 90°, and so thehopping probability t will be reduced to cos(90°/2) =.7 times that of theferromagnetic case. This would imply a first-order conductivity decrease to .7times that in the ferromagnetic case (more detailed explanations can be found inthe chapter by Millis [4]), while experimentally it is seen that the conductivitydecrease across the F-P transition may be many orders of magnitude. Thisindicates that some other physics beyond D-E is necessary to explain theconductivity change across the transition. Another closely related prediction of

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double-exchange theory is that the one-electron bandwidth W measured in theparamagnetic state should be reduced to .7 of its value in the ferromagnetic state(figure 2e) [5]. For intermediate doping levels, this would mean a slightincrease in the density of states at EF upon going to the paramagnetic state. Asdiscussed in section 6.4, the experimental findings are qualitatively verydifferent from this prediction. This also indicates that we need to go far beyonddouble-exchange to understand the behavior of the manganites.

To first order, we can understand a metal-insulator transition as originatingfrom one of two things - either a change in the number of carriers or a change intheir mobility. This is immediately apparent from the equation for theconductivity σ=neµ, where n is the number of carriers, e is their charge and µ isthe mobility. Within double-exchange theory the change in mobility (change inhopping probability) is the dominant effect on the conductivity. Significantmobility reductions can also be obtained from Anderson localization effects dueto disorder, for instance due to the disorder of the local t2g spins. Neither ofthese effects should significantly affect the density of states at the Fermi level.Therefore, if mobility changes were the dominant mechanism for the metal-insulator transition we should expect a significant density of states at the Fermienergy even in the insulating paramagnetic case. We will show that this is notobserved, indicating that a change in effective carrier number (a gapping of thenear-Fermi energy states) is more important than a change in mobility.

As in most other transition metal based systems, electronic correlations dueto the on-site Coulomb interaction U are believed to be important in themanganites. Indeed, the undoped parent compound LaMnO3 has a partiallyfilled d-band, and so to first order is expected to be a metal within a single-electron theory such as band theory. However, LaMnO3 is in fact anantiferromagnetic insulator with a relatively large gap of 2 eV. This breakdownof the 1-electron theory is often attributed to electron correlations, i.e. LaMnO3can be considered to be a Mott insulator, in which the on-site Coulomb energyU is responsible for the insulating behavior. More specifically, under theZaanen-Sawatzky-Allen classification scheme [6], they should probably beconsidered charge-transfer insulators because ∆, the p-d charge fluctuationenergy, has been estimated to be smaller than U, the d-d charge fluctuationenergy. For example, using fits to Mn 2p core level photoemission data,Bocquet et al. have estimated U to be approximately 8 eV for both LaMnO3 andSrMnO3, and ∆ to be 4.5 eV for LaMnO3 and 2 eV for SrMnO3 [7]. Slightlydifferent values have been estimated by Chainani et al.[8]. However, we alsonote that Jahn-Teller distortions can explain the insulating nature of LaMnO3within the band theory view [9].

2.5 Polaron problem and the Jahn-Teller effect

One of the major classes of proposals for supplementing double-exchange isa strong coupling to the lattice, with a resultant polaron formation. To firstorder, these scenarios state that the conductivity in the high temperatureinsulating state is due hopping of these lattice polarons, while below the Tc thepolarons break up and conductivity is due to the individual electrons. The

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presence or absence of the polarons is a very delicate balance which will becontrolled by the ratio of the electron-lattice coupling and the hopping energy t(related to the kinetic energy gain for the electrons to delocalize).

One of the reasons why the coupling to the lattice is expected to be sostrong in the manganites is because the d4 ion is unstable to a Jahn-Tellerdistortion, giving a strong electron-lattice coupling. A schematic of the Jahn-Teller distortion is shown in figure 3. By distorting the MnO6 octahedron asshown, the degeneracy of the eg levels is lifted and there is an electronic energygain linear with the distortion. There is a loss of lattice energy quadratic withthe distortion, with a resultant total energy gain equal to 1/4 of the splitting ofthe eg levels [10].

Extensive diffraction results indicate that the d4 parent compound LaMnO3is Jahn-Teller distorted, with bond length differences between the long andshort Mn-O bonds of approximately .2 Å.[11] The d3 parent compoundSrMnO3 has no eg electrons and so, as expected, has an un-distorted cubicstructure. In the intermediate doping regimes relevant to CMR, diffractionresults do not show distortions, although local structural measurements such asneutron PDF analysis [12,13] and EXAFS [14] do show distortions, albeit thatthere are still discrepancies and questions regarding these results. From theelectronic structure viewpoint, we have observed the eg level splittings due tothese distortions, thereby obtaining information about the energetics of theprocess. As will be discussed in section 5.3, the Jahn-Teller splitting is not aslarge as might be hoped to explain the observed properties, and so other modessuch as breathing modes may be necessary. It also should be noted that belowTc the electron-lattice coupling still appears to be strong, and so the propertiesmay still be largely affected by the coupling to the lattice. A more completediscussion of this is contained in section 6.

In this chapter we will show how a variety of advanced spectroscopictechniques can address these most fundamental questions about the electronic,magnetic, and structural aspects of the manganites.

3. Techniques3.1 Angle-resolved Photoemission - k-dependent occupied

statesPhotoemission spectroscopy is a very powerful and direct probe of the

occupied electronic structure, bonding, and chemical nature of a material. Theintroduction of high energy resolution (∆E<30 meV) to the technique in thepast few years has moved the technique into the forefront of physics andmaterials research, since the most crucial low-energy excitations near the Fermisurface may be directly probed. The k-space resolution of the angle-resolvedversion of the technique is a very powerful and unique aspect which givesinformation which typically can not be obtained by any other method.

A schematic of the photoemission process is shown in figure 4a. In aphotoemission experiment, monochromatic photons of known energy impingeupon a sample. An electron with initial energy Ei inside the sample is excitedand ejected out of the sample with a kinetic energy Ek. The ejectedphotoelectrons are collected and energy analyzed, the energy distribution of

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which gives us the energy distribution of the initial states Ei in the sample. Inthe simplest approximation, the photoelectron spectrum therefore tells us theoccupied density of states of the system.

In angle-resolved photoemission spectroscopy the emission angle of thephotoelectrons from the surface normal is also constrained, and so we obtainthe electron's momentum information in addition to its energy. Because thecomponent of the electron's momentum parallel to the surface will be conservedas it traverses the sample-vacuum interface and the perpendicular component isaffected by the known work function, we can relate the electron's momentumoutside the sample (final state) to it's initial momentum or k in the crystallattice.

Typically one will compare the Ei(k) determined from the angle-resolvedphotoemission experiments with the Ei(k) from a band theory calculation.However, it is important to realize that the density of states or the Ei(k)measured by photoemission spectroscopy is not a ground state measurement,but is a measurement of the energy required to remove an electron from thesystem, that is, it is a measurement of the excitation spectrum of the system. Inthe Green's function approach to many-body physics, this is just the spectral

weight function A(k,ω) = 1π Im{G(k,ω)} (assuming the sudden approximation

holds and we ignore matrix element effects). Even within the framework of the

quasiparticle picture, the peaks of A(k,ω) will not in general lie at the Ei(k) ofband theory calculations, but will be shifted slightly due to "self energy" effectsarising from interactions of the injected hole with the medium. In addition, thefinal state of the photoemission process will not in general be an eigenstate ofthe interacting system and so will have a finite lifetime. This will have the effectof smearing out the delta function in Ei(k). The precise manner in which thedelta function peaks are smeared out can tell us important physical informationabout the interactions of the system. There is also the possibility that thequasiparticle picture may break down completely, as is currently beingdiscussed for the high Tc materials [15,16,17].

An illustration of what a series of ideal angle-resolved photoemissionspectra taken from a two-dimensional system would look like is shown infigure 4b. The photoemission peak is observed at a different energy for eachemission angle, corresponding to the E vs. k dispersion of the band beingstudied. The peaks are narrower for the states closer to the Fermi level,corresponding to a reduced phase-space for scattering and hence longerlifetimes. Finally, the peak disappears after the band crosses through the Fermilevel into the region of unoccupied states.

Due to the short escape depths of the photoelectrons, photoemission is asurface sensitive spectroscopy, with probing depths typically on the order of 5-50Å. Depending upon the specific experiment, this surface sensitivity may beeither an asset (for the interface studies) or a hindrance. To overcome thislimitation for studies of the bulk electronic structure, a fresh sample surfaceshould be obtained by a cleave and measurement in ultra-high vacuumconditions (P < 10-10 torr). Samples are also typically kept at low temperatures

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in order to reduce effects such as the out diffusion of oxygen from the samplesurface. Also critically important is the selection of materials with goodcleavage properties, for no other precautions can overcome this most seriouslimitation.

3.2 X-ray absorption spectroscopy - unoccupied statesIf we measure the absorptivity of a material as a function of incident x-ray

energy, we will observe a series of step-wise increases, each stepcorresponding to the energy separation between a certain core level and theFermi energy (core binding energy). This increase in absorption is due to thefact that an additional channel for absorption, the promotion of a core electron toan empty state just above the Fermi level, is enabled. A knowledge of thenature of the core level as well as the matrix element for the transition will lendinformation of the unoccupied density of states of the material. The dipoleselection rule for photon-excited transitions states that the change in the angularmomentum quantum number (∆L) is ±1, while the spin is not changed. For theoxygen 1s edge (L=0) this means that only oxygen p character (L=1) can bereached. To first order, we can therefore view the resulting O 1s XASspectrum as an image of the oxygen p projected unoccupied density of states.

X-ray absorption measurements performed in the electron-yield modetypically have a surface sensitivity of approximately 100Å, so surface issues arenot nearly as important as they are in photoemission.

3.3 Classes of samples and experimental considerations.As shown in figure 1 there are two main classes of manganites - layered and

three dimensional. Each are composed principally of MnO2 planes which arestructurally similar to the CuO2 planes in the cuprates. Between the MnO2planes there is either a single or a double layer of (La,Sr)O planes. The numberof MnO2 planes between the (La,Sr)O biplanes is the main distinguishingcharacteristic between the families.

For photoemission measurements of the bulk electronic structure of a solid,great care must be taken to ensure that the measured results are representative ofthe bulk and are not contaminated by surface effects. The best precaution is touse high quality single crystals that have natural cleavage planes, and then toperform the cleaves in vacuum at low temperatures immediately beforemeasuring. The layered manganites have two (La,Sr)O planes adjacent to eachother which should be almost completely ionically bound. It is found that thecrystals cleave nicely between these planes, leaving mirror like surfaces whichproduce sharp LEED patterns without evidence of surface reconstruction. Theionic nature of the bonds in and between the (La,Sr)O planes means that thereshould be no dangling bonds or free charge left on the cleaved surface. Thethree dimensional compounds do not have such a natural cleavage plane, and sothe cleavage process does not yield flat surfaces. ARPES studies have thereforenot yet been possible on the three-dimensional samples, and while angle-integrated data does exist, it may be less reliable. However, it is found that thephotoemission data from the three dimensional samples displays a high degreeof consistency both with itself, with data from layered samples, and with opticalmeasurements. This consistency leads us to believe that the photoemission data

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on the cubic samples should also be considered reliable, although certainly morecaution should be applied when interpreting these data.

4. Overview of measured electronic structure

4.1 Valence band overview

Fig 6 shows an overview of the measured electronic structure ofpolycrystalline samples of the La1-xCaxMnO3 series, as measured by J.H. Parket al. [18]. A clean surface for the measurements was obtained by scraping thesurface with a diamond file in-situ immediately before the measurement. Panela shows the valence band and shallow core levels as a function of doping. Theratio of the intensities of the La and Ca core levels changes with the doping levelx, as expected. In addition, it is found that the core levels shift monotonicallyas a function of doping, implying a monotonic chemical potential shift withdoping as shown in the inset to panel a. This is partly important as acomparison to the unusual and hotly debated behavior of the chemical potentialshift in the high Tc superconductors [19]. Similar chemical potential shifts havealso been observed by Saitoh et al. [20]

Concentrating on the main valence band extending to a binding energy of 8eV (panel b), we see a large density of states region composed principally ofMn d and oxygen p states. As the doping is changed from x=1 (CaMnO3, witha d3 initial state) to x=0 (LaMnO3, with a d4 initial state), new states are built upnear the Fermi energy because the chemical potential is moving into themanifold of eg symmetry states. Similar angle-integrated results from cleavedsingle-crystals of the La1-xSrxMnO3 series were obtained by Dessau et. al.[21]. The near-EF region for these samples is shown in figure 7. Theintermediate doped samples show a real Fermi edge cutoff, indicating a finiteN(EF) for these samples. The d3.6 and d3.7 samples show the greatest spectralintensity at EF, and correspondingly show the highest Tc’s and highest lowtemperature conductivities [22]. The d3.5 and d3.82 samples are on the verge ofmetallicity according to the doping phase diagram [22] and show a drasticallyreduced N(EF). Finally, the d4 (x=0) end member is a known insulator with alarge gap, consistent with the data of Fig. 7.

A very important point is that even though there are clear Fermi edge cutoffsfor the more metallic samples, the observed spectral weight at EF is reducedfrom expectations (band theory or simple electron counting) by a factor of 10 ormore [see section 6]. Similar behavior is observed in optical conductivityexperiments in that the Drude weight is severely depressed from expectations bya similar amount. This is the first piece of evidence we will discuss for the“pseudogap” which reduces N(EF) for all the manganites.

4.2 Temperature dependence - overviewAssociated with the metal-insulator and ferromagnetic-paramagnetic phase

transition, there are expected to be clear changes in the electronic structure. Inthis chapter we will concentrate on the temperature-dependent changes thatoccur near the Fermi energy, as these are directly related to the transport

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properties. We do note that there has also been some discussion in the literatureabout temperature-dependent changes to the main valence band[23].

The first clear temperature dependent near-EF spectra of the manganites waspresented by J.H. Park et al.[18]. Figure 8 shows their angle-integrated datafor a Tc= 260K sample (left) and a Tc= 330K sample (right). At the lowesttemperatures in the ferromagnetic state a clear Fermi edge is observable.Increasing the temperature cuts this near-EF weight significantly, even fortemperatures still well below Tc. This behavior was made more quantitative bySaitoh et al. [24]. Saitoh et. al. cleaved single crystals of the x=.18 cubicsample La.82Sr.18MnO3. The sample was cleaved and measured first at thehighest temperature, and then progressively cooled, with the lowest temperaturemeasurement last. At higher temperatures the spectral weight near EF isseverely depleted and a Fermi edge cutoff is no longer observed. Figure 9 plotstheir measured spectral weight near EF as a function of temperature. Because ofthe very low spectral intensity, good statistics for this plot were only attainableby integrating the spectral weight over a finite energy interval. The results areshown for two different energy intervals around EF. It is seen that the weightnear EF only starts increasing for temperatures below Tc, and then continuesincreasing monotonically as the temperature is lowered further. The structurenear .7Tc in the smaller energy window is presumed to be due to noise. It isalso presumed that above Tc N(EF) is zero, and the offset away from zero in thefigure is due to the finite energy window used in the integration. The Drudeweight observed in optical conductivity experiments by Okimoto et al. (opencircles) [25] is also observed to have a similar temperature dependence.

The fact that the spectral weight increase is observed to begin at Tc is a goodindication that the photoemission spectra are observing bulk-like properties, andare not overly affected by potential problems with the surface termination.Many other internal consistencies, particularly for the layered samples, similarlyindicate that the photoemission spectra from the cleaved single crystal samplesyield reliable information about the bulk electronic structure of the material, andnot just about the surface region.

An important point about the data of figures 8 and 9 is that even at thelowest temperatures the spectral weight at EF always remains very low. Theleft axis of figure 9 tells the ratio of the weight compared to LSDA predictions,with cross section effects properly taken into account. Using the smaller energywindow of figure 9, we see that the spectral weight is reduced by a factor of 10or more relative to the expectations from band theory calculations [26]. Takingthe finite energy window into account, the real reduction is much greater,probably a factor of 20 or more. Samples with a doping near x=.3 or .4 haveapproximately twice as much spectral weight at EF (see figure 7) so are stillreduced by a factor of 10 relative to expectations. A similar reduction in theDrude weight is observed As will be discussed in section 6, the layeredsamples have an even greater reduction in near-EF spectral weight and Drudeweight.

This anomalous reduction in the spectral weight near EF has been termed a“pseudogap”, because while it removes the spectral weight it may not alwaysremove it completely. We believe that this pseudogap is very important for

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understanding the CMR problem. It will be discussed in more detail in section5.

4.3 Spin-polarization of the electronic bandsAs discussed in section 2.1, the large Hund’s-rule coupling makes us

expect only spin-up states near the Fermi energy. This has been nicelyconfirmed by a spin-polarized angle-integrated photoemission experiment byJ.H. Park et al.[27]. The experiment was performed on thin-film sampleswhich, unlike most of the bulk single crystal samples, display a remnantmagnetization. To clean the surfaces, a series of in-situ annealing processeswere used. While this method has clear limitations, the attainment of a clearFermi edge in the low temperature data gives some confidence in the quality ofthe attained surfaces. The photoemission data from both the up and down spinstates is shown in Fig. 10. In the low temperature ferromagnetic state the Fermiedge is attained only for the up-spin states, while in the high temperatureparamagnetic state there is no difference between the up and down spin statesand there is also no Fermi edge observed. This is the first spectroscopicconfirmation for the existence of a half-metallic ferromagnetic, a fact which isimportant for spin-polarized tunnel junctions (see the chapter by J. Sun [28]).These results are consistent with the development of a full saturation magneticmoment near 4 Bohr magnetons observed in (La,Sr)MnO3 [29]. Other systemssuch as the Heusler alloys and CrO2 have also been predicted to be half-metallic[30], but solid experimental evidence for this has not yet been observed [31].

5. Unoccupied electronic structure and some energy scaledetermination

Section 6 will show many more details of the low energy spectral propertiesof the manganites, with special attention paid to the layered manganites forwhich the crucial k-dependent information is also obtained. Before doing thathowever, we will discuss some of the X-ray absorption measurements whichhave enabled an accurate determination of some of the key energy scales of themanganites. We will show oxygen 1s absorption data, which within the dipoleapproximation can be interpreted as the oxygen 2p-projected unoccupied densityof states.

Oxygen 1s spectra of polycrystalline samples of the manganites have beenmeasured by several groups[18,20,32,33]. While the experimental dataobtained by these groups are mostly consistent with each other, there had notbeen a complete agreement on the interpretation of the data. Recently, C.H.Park et al. have made measurements on single crystalline samples of the layeredmanganites, as well as made new high resolution measurements on singlecrystalline samples of the pseudocubic manganites [34]. The higher resolutionand especially a polarization analysis made possible from the layered singlecrystalline samples has lead to a new interpretation of the XAS data. Alongwith this new interpretation comes a determination of many of the importantenergy scales of the problem.

5.1 Review of earlier XAS results of pseudocubicpolycrystalline manganites

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The first detailed O 1s XAS data of the manganites was published byAbbate et al. [32], with the data shown in figure 11. As annotated in the figure,the lowest energy feature near 531 eV was ascribed to the Mn 3d states near EF.They argued that the strong intensity of this peak implies strong Mn-Oadmixing. They also noted that the intensity of this peak increased with Srconcentration, indicating more unoccupied d electrons, as expected. Abbateassigned the first peak to be composed of eg majority states and t2g minoritystates. The second structure at 533 eV at the high Sr concentrations wasassigned to eg minority states, which were argued to not be observable at lowSr concentrations due to an overlap with the La 5d states.

Saitoh et al. published oxygen 1s XAS data of the pseudocubic manganitesand performed a cluster model calculation to model the data [20] (see figure 12).Their calculations placed the t2g minority states a few volts higher in energy,and also showed that they should have much weaker intensity. This is becausethe t2g states hybridize more weakly to the oxygen states (a π bond instead of aσ bond) and so have a weaker projection onto the oxygen partial density ofstates obtained by the measurement. From these model calculations, Saitoh alsoestimated the d-d exchange coupling to be .85 eV, the Coulomb energy Udd tobe near 7 eV, and the charge transfer energy ∆ to be 2 eV (SrMnO 3) and 4.5 eV(LaMnO3). ∆ < Udd implies that these compounds should be considered chargetransfer insulators instead of classic Mott-Hubbard insulators.

5.2 XAS results of d3 and d4 end member layered compoundsand a determination of the Hund’s rule energy J

Figure 13 shows the O 1s XAS pre-edge region for both end member ofdoping (d3 & d4) of the single layer (n=1) compound Sr2MnO4 & LaSrMnO4,from C.-H. Park et. al. [34]. The near-edge region consists of the Mn 3d-O 2phybridized unoccupied states, which are labeled by the d-symmetry labels.Considering the crystal field splitting and the typical assumption of strongHund's rule coupling, the relevant states in the near-edge region should be theeg (d3z2-r2 and dx2-y2) up spin states, the t2g (dxy, dxz, dyz) down spin states,and at higher energy, the eg down spin states. We also expect to distinguishbetween the d3z2-r2 (hereafter called dz2) and dx2-y2 states in the layeredmaterial by the polarization effect assuming the dz2 (dx2-y2) is the out-of-plane(in-plane) state. The polarization effects are highlighted by performing thesubtraction of the two spectra, as shown in the lowest curve of each figure (in-plane minus out-of-plane). This subtraction helps pinpoint the location of thepeaks and their splitting.

From the subtracted curve in figure 13 a, it is seen that the dz2 up state (528eV) has a lower energy than the dx2-y2 up state (529 eV). Furthermore,another set of out-of-plane states (530.7 eV) and in-plane states (531.7 eV) isobserved. This is expected since the eg down-spin states should exist above thespin up states due to the additional energy cost to add a down spin electroncompared to an up spin electron, which is the definition for the exchange energyJ. From this data we can determine that J is 2.7 eV, which is in very goodagreement with the theoretical [35] or ionic [20] values for the exchange

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integral (about 0.9 eV) since there are 3 t2g electrons to couple to. The similarexchange splitting (2.7 eV) observed for both symmetry states confirms theconsistency of the data and the subtraction procedure. The lower spectralweight of the down-spin states is probably due to a reduced Mn-Ohybridization since these states are farther in energy from the main portion ofthe O 2p band (the absorption process at the O 1s edge occurs through aprojection onto the O 2p states).

Going from d3 to d4, the extra electron will occupy the lowest availablestate (dz2 up) and therefore the dx2-y2 up (530.2 eV) should be the lowestunoccupied state, followed by the dz2 down state (531.3 eV). This is exactlywhat is observed in figure 13b. Although we also expect t2g down spin states inthis energy range, they show up only very weakly, as expected because of theweak hybridization between the O 2p and Mn t2g states. This is consistent withthe model calculations presented by Saitoh et al. [20] and presented in Figure12.

5.3 XAS of intermediately doped layered and cubic compoundsand the Jahn-Teller energy EJ-T

Figure 14 shows polarization-dependent XAS data for x=.4 (d3.6) samplesas a function of layer number, from C.-H. Park et. al. [34]. The cubic sample(n=infinity) shows no polarization effects. The large polarization effect of thepeak shown near 533 eV is due to states in the (La, Sr)-O plane because itvaries with layer number and does not exist in the 3-dim case. The general trendof the data and the polarization effects in the near-edge region are similar to thatfor the d3 sample - the lowest energy portion (528.5eV) has principally out-of-plane character (dz2) while the higher energy portion (529.5eV) has principallyin-plane character (dx2-y2). While the splitting between the centroids of thetwo states (as determined by the subtracted spectra) are very similar to thatdetermined from the d3 sample, the peaks are in general broader and morewashed out. We attribute this to an increase in the electron itinerancy energy forthe doped samples.

From the similarity of the pre-edge structures of the layered and cubicsamples in figure 14, it is natural to assume that the two bumps in the pre-edgeof all samples are of the same origin, i.e. they are from eg-symmetry stateswhich have had their degeneracy broken by a distortion of the MnO6 octahedra.For the layered samples this is a static elongation along the z-axis, while for thecubic sample it should be due to a Jahn-Teller distortion (note that the cubic d3

sample of figure 13 does not show the splitting, as expected since the d3 ion isnot Jahn-Teller active). It is important that this distortion must be short-rangeand dynamic, because diffraction studies sensitive to the long range order havenot indicated a distortion [11]. The XAS should not be limited by the dynamicnature of a lattice distortion since the electronic transitions are much faster thanthe time scale of a lattice distortion. Structural studies sensitive to the short-range distortions such as EXAFS [14] and neutron PDF [12,13] have alsoshown distortions of the octahedra in doped cubic manganites, although there isstill a degree of variation in the reported results.

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The Jahn-Teller interpretation of the splitting of the 529 eV XAS peak isdifferent from interpretations made by previous investigators. The splitting wasnot explicitly addressed by Abbate [32] or Saitoh [20]. J.H. Park et al. [18] andE. Pelligren et. al.[33] assigned the lower of the two peaks to both eg up statesand the higher of the two peaks (~ 530 eV) to the t2g down states. While the t2gdown spin states will likely contribute to the spectra, we expect them to showup more weakly than the eg states due to a reduced hybridization to the oxygen2p states (see Saitoh's calculation in figure 12). In addition, the dopingdependences as well as the polarization dependences appear to make C.H.Park’s interpretation of the data most reasonable.

The splitting of the levels is expected to be near 4EJ-T , where EJ-T is theenergy gain for the distortion. This can be seen from the following discussion:as the electron goes into the lower of the distorted levels, it gains an electronicenergy equal to 1/2 of the total splitting of the levels. At the same time there isan energy cost for structurally distorting the lattice. In the harmonicapproximation this cost is half the electronic energy gain, meaning the totalenergy gain is 1/4 of the splitting of the levels. Therefore, since theexperimentally observed splitting is near 1 eV, EJ-T is estimated to beapproximately 0.25 eV.

The magnitude of EJ-T is mostly important in comparison to other energyscales such as the one-electron bandwidth W. These comparisons and theirimplications will be discussed in section 6.6.

6. Low energy k-dependent electronic structureIn this section we focus on the momentum dependence of the near-EF states

as measured by high energy resolution ARPES. At the time of this writing, theonly reported data has been from the Colorado/Stanford/Tokyo collaboration.We will concentrate on measurements from the bilayer materialLa1.2Sr1.8Mn2O7. This material has a nominal doping level of .4 holes per Mnsite (d3.6) and more than two orders of magnitude decrease in resistivity at theferromagnetic Tc of 130K. The low temperature resistivity is unusually high -greater than 3 x10-3 ohm-cm and even has a slight upturn at the lowesttemperatures.

6.1 Low temperature k-dependent data and a large "ghost"Fermi surface

Figure 15 shows these near-EF states along various k-space directions,measured at 10K (ferromagnetic phase), after Dessau et. al. [36]. Directions ofthese cuts in the two-dimensional Brillouin zone are indicated in panel e.Concentrating first on the spectra along the (0,0)-->(π,0) line (panel a), weobserve a strong feature first visible at (.27π,0) which disperses towards theFermi energy as we progress towards (π,0). In addition, there is a weak andbroad feature at about -.6 eV which is strongest near the (0,0) point (at higherphoton energies this feature evolves into a clearly resolvable peak, so we areconfident that it is real). Panel c shows a continuation of the dispersion alongthe (π,0) --> (π,π) direction. In the first part of this cut the peak continues todisperse towards the Fermi energy, but surprisingly never reaches EF. Instead,

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it attains its minimum energy near the angle (π,.27π), at which point it rapidlyloses intensity as if weight was transferred above the Fermi energy. Beyondthis point, the spectra in addition exhibit some evidence of bending back awayfrom EF in a similar way from what would be expected for the opening of anexcitation gap centered at EF. A very similar result is seen for the cut shown inpanel b, with the minimum energy at the k-position (.63π,.27π).

Panel f shows a plot of the peak positions (indicated by the tick marks inpanels b and d) vs. crystal momentum along the (0,0) --> (π,0) --> (π,π)direction compared to the up-spin dispersion predicted by the local spin densityapproximation (LSDA+U) band structure calculations [37]. The calculationpredicts a set of dispersive bands of eg symmetry mostly separated from aregion of many relatively non-dispersive bands (t2g d and oxygen p states).The band crossing EF near the (0,0) point is predicted to have principally d3z2-r2out-of-plane character, while the two bands crossing between (π,0) and (π,π)are predicted to have primarily dx2-y2 in-plane character.

We find that there is a correspondence between many aspects of theexperimental and theoretical data. First, the agreement in both energy positionand dispersion rate between the experiment and theory along the (0,0)-(π,0) lineis reasonably good, especially considering that we have not rescaled or shiftedthe energy scales to account for the often observed renormalization effects.Second, by taking advantage of the polarization of the incident photons we haveperformed a symmetry analysis on the main dispersive features (the onespredicted to cross EF along (π,0) - (π,π)) and found them to have primarily dx2-y2 character [34], in agreement with the band theory prediction. Third thelocations of the experimental minima in binding energy as well as the locationswhere the spectral weight is rapidly being depleted agree well with the predictedFermi surface crossings. In other words, there is a locus of points in k-spacewhere critical spectral behavior occurs, and this locus is found to closelyresemble the band structure Fermi surface. This indicates that Luttinger'stheorem [38] is obeyed for these compounds.

Despite these agreements there are clear deviations between the experimentand theory, signaling additional physics not contained in the calculation. Thesedeviations can tell us many of the details of the interactions responsible for thevery unusual properties of the manganites. In particular, 1) The width of theARPES features are anomalously broad, and do not sharpen up as theyapproach the Fermi momentum kF. This indicates that the dispersive peaks cannot be described as single Fermi-Liquid-like quasiparticle (q.p.) excitations. 2)The spectral behavior at the locus of critical k-points discussed above isdifferent from that expected at a real Fermi surface. This is why we call thelocus a "ghost" Fermi surface. Specifically, we find a) the centroids of theexperimental peaks never approach closer than approximately 0.65 eV to EF,while theoretically they are expected to reach EF. b) There is never more than avanishingly small spectral weight at EF, even though the measurements weremade in the ferromagnetic "metallic" state of the compound. This lack ofspectral weight is termed the "pseudogap." To make sure that we simply didn'tmiss a Fermi crossing, we have made measurements along all the highsymmetry directions as well as along many off-symmetry points (not shown),

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have used a variety of photon polarizations and photon energies, and haverepeated the measurements on more than 10 samples.

6.2 Bandwidth of the in-plane dx2-y2 statesExperimentally, the occupied part of the dx2-y2 up-spin band starts

approximately 1.5 eV below EF (Fig.15) and the unoccupied part of the dx2-y2up-spin band can be seen at least 1.5 eV above EF (Fig. 14). The total barebandwidth of the dx2-y2 state is therefore at least 3 eV, which is similar to thepredictions of the LSDA calculation of Hamada [38]. This is not surprisingsince the dispersion rate of the experimental and theoretical bands was found tobe similar. For the 3-dimensional compounds with similar doping (e.g.La.6Sr.4MnO3) we expect the bare bandwidth to be up to 1.5 times larger due todimensionality effects, although this will be reduced somewhat due to adistorted O-Mn-O bond-angle. Therefore, to first order we can expectLa.6Sr.4MnO3 to have a bare bandwidth of 4 eV.

We schematically illustrate the ferromagnetic band structure for the mostrelevant dx2-y2 (including dz2-x2 and dz2-y2 for the 3-d samples) symmetrystates in Figure 16. Assuming JH to be the same for all compounds (it is anIntra-atomic term), the bandwidth W is larger or slightly larger than JH (4.5 eVand 3 eV vs. 2.7 eV), and so we expect that the up and down spin dx2-y2 bandswill not be completely separated but will overlap slightly. This implies that themanganites may not fit completely into the DE limit, in which JH→∞.However, because EF is still far from the bottom of the down-spin states, thenear-EF states should still be mostly spin polarized. This is consistent with thefull spin polarization of the near-EF states observed by J.H. Park et al. [27](see section 4.3) .

The large bandwidths are rather surprising, especially in the context of asystem which may be expected to have strong correlations or polaronic effects.However, the quoted bandwidth should only be considered the bare or one-electron bandwidth, which may be renormalized due to electron-phonon orother effects. Typically, these effects would be expected to change theobserved dispersion rate of the ARPES peaks. However, as discussed insection 6.6, if the coupling is very strong, then the weight of the truequasiparticle peak can go to near zero and the dispersive ARPES peaks(consisting only of the incoherent part of the spectrum) may disperse as thebare particle.

6.3 Temperature dependent dispersion of La1 .2Sr1 .8Mn2O7Figure 17 shows the temperature dependence of the near-EF bands of

La1.2Sr1.8Mn2O7 along the entire (0,0)-->(π,0)--> (π,π) line, after Saitoh et al.[24]. To ensure that the main changes were not due to aging effects (which aremore severe at high temperatures) the sample was cleaved and initially measuredat high temperature, after which it was cooled to low temperature andremeasured. Measurements on other samples were made in which the samplewas cleaved cold and then warmed, with qualitatively consistent results. It isobserved that along the (0,0)-->(π,0) direction where the states are farther fromEF, the temperature-dependent effects are rather weak, whereas they are the

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strongest at (π,.27π) which corresponds to the closest approach of the featureto EF, as well as to the kF predicted by the band theory calculation. It is seenthat the high temperature spectrum is pushed back to higher energies and theamount of spectral weight near EF is reduced further, i.e. the pseudogap isaffecting the high temperature spectra more dramatically than the lowtemperature spectra. This must be at least partially responsible for the largechanges in the conductivity that occur across the phase transition. However,even at (π,.27π) the ARPES peak always remains pulled far back from EF, andthe spectral weight reaching EF is vanishingly small.

More details of the temperature dependence of the spectra ofLa1.2Sr1.8Mn2O7 at (π,.27π) are shown in Fig.18. The triangles indicate thespectral weight found very near EF obtained over two different energyintegration windows, and the diamonds show the energy shift of the leadingedge (at two different positions on the edge) as a function of temperature. It isseen that both the near-EF weight and the position of the leading edge beginincreasing at Tc and then rise monotonically without saturation as thetemperature is lowered. The onset of the changes at the sample's Tc clearlyindicate that they are directly associated with or responsible for the very largechanges in conductivity at Tc. Similar effects have also been observed bySaitoh et al. for the cubic perovskite La.82Sr.18MnO3 (see figure 9).

The temperature dependence of the observed changes is qualitativelyincompatible with the prediction of double-exchange theory, which predicts avery small change in spectral weight in the opposite direction to that observedexperimentally (see figure 2e). The fact that the spectral change saturate muchmore slowly than the magnetization saturates as the temperature is lowered(figure 18) also indicates that double-exchange can not explain the data.

In addition to predictions about the spectral weight, double exchange theorymakes predictions about the temperature dependence of the one-electronbandwidth W. As discussed in section 2.2 and shown in figure 2, doubleexchange tells us that to first order the hopping probability and hence thebandwidth should decrease by about 30% when going from the ferromagneticto the paramagnetic phases. Considering the dx2-y2 up-spin states, the bandstarts at the (0,0) point more than 1.5 eV below EF and extends to at least 1.5eV above EF (see section 6.2). If the bandwidth was to change due to thedouble-exchange effect, we expect the change to be centered near the meanvalue of the band energy. In other words, the states at the extremum of theband near 1.5 eV binding energy should show a significant (30%) energy shifttowards EF. Instead, we observe a small energy shift of approximately .06 eV,or a change in the bandwidth of just a few percent (.06/3.0).

Our interpretation of this effect is that the paramagnetic state is composed ofrather large regions of in-plane ferromagnetic order, so that the local hoppingprobability is barely changed upon going through Tc. This idea is consistentwith recent transport and neutron scattering studies of the x=.3 bilayercompound, which have been interpreted as having 3D ferromagnetic orderbelow the Tc of 90K, and 2D ferromagnetic order between 90K and 300K [39].Much more work needs to be done to understand this behavior, especially itsconnection to the pseudogap

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6.4 Discussion of anomalous spectral properties - thephotoemission lineshape and pseudogap

The ARPES features of the manganites are anomalously broad and do notsharpen appreciably as kF is approached. Broad ARPES features are alsoobserved in the high Tc superconductors, and have been taken to indicate veryanomalous non Fermi-Liquid like behavior [15,17]. In those materials, thenormal-state features obtain a minimum width of a few tenths of a volt, which ismuch worse than the energy resolution. In the manganites, the features aremuch broader, with widths approaching 1 eV.

The manganites also have a strongly suppressed spectral weight near EFwhich is termed a pseudogap. ARPES (as well as many other) measurementson the high Tc superconductors have likewise observed a pseudogap in the highTc superconductors[40]. In the high Tc’s, the magnitude of this effect is on theorder of 20 meV and is observed to occur primarily near the (π,0) points of theBrillouin zone. In the manganites the pseudogap effect is observed throughoutthe entire Brillouin zone and has a much larger magnitude of many tenths of aneV (note that the pseudogap is a “soft” gap, and so does not simply determinethe activation energies). It is expected that much work will be needed to fullyunderstand their properties. Here, we will try to give some first orderexplanations of these anomalous properties.

We explore a couple of possible explanations for the anomalous spectral andphysical properties of the manganites. Mechanisms that should be consideredinclude gap formation due to static or fluctuating charge, spin, or orbital order; aMott-Hubbard type gap; a splitting of the levels due to the Jahn-Teller effect; aCoulomb gap; and strong electron-lattice coupling.

Although it is expected that correlation effects will play a role in thesematerials, the Mott-Hubbard type gap is expected to be centered at EF only forsamples of integral electron-filling and so can not be responsible for theobserved pseudogap. The splitting of the eg symmetry levels due to the Jahn-Teller effect should also only be centered at EF at special doping levels. ACoulomb gap is usually discussed in terms of localized (impurity) states [41].The large amount of dispersion observed in figure 15 is in opposition with suchlocalized states.

On the other hand, the coupling of the electrons to a Boson such as a latticedistortion can give a qualitative explanation for many of the anomalous spectralproperties. We begin by discussing the exact solution of the problem of a singleelectron coupled to a bath of Einstein phonons (or any other Boson) offrequency ω0 [42]. The electron spectral function for this problem is an

envelope of many individual peaks separated by ω0, as illustrated in figures 19aand b. The multiple peaks indicate that a single electron is not an eigenstate ofthe system -- therefore the removal of an electron from the system occurs with aprobability of shaking off a certain number of phonons. The quasiparticle peakor ``coherent'' part of the spectrum is the one with zero phonons shaken off andis the peak closest to the Fermi energy. In the strong coupling case the envelopefunction is broad and the quasiparticle peak will have very little spectral weight.An important point about this result is that irrespective of the strength of the

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coupling, the centroid or first moment of the distribution is equal to the energyof the electron in the absence of the coupling [42]. A known example of thistype of distribution is the measured photoemission spectrum of gaseousHydrogen, which shows a clear progression of many peaks, corresponding tothe many different vibrational levels [17].

Following this logic, we suggest that the dispersive peaks we havemeasured should not be considered to be a single quasiparticle peak but shouldbe considered to be an envelope of many individual peaks, in the spirit of thestrong coupling arguments above (the individual peaks are probably notresolved due to lifetime, solid-state, and resolution effects). Second, in analogyto the single-electron calculation above, we argue that the centroid of theARPES spectrum should have an energy equal or similar to the energy in theabsence of the coupling, which in this case is the LSDA band energy. Whilethis may not be a rigorous result in general, it does explain the surprisinglygood agreement of the experiment and theory through much of the zone (seeFig. 19d). The quasiparticle peak, if it existed, would correspond to the portionof the spectrum nearest EF, and is found to have an almost vanishingly smallweight for this material, indicating that the coupling is strong (this is also seenby the large width of the peaks). By Luttinger's theorem [38], we expect thequasiparticle peak to cross EF at the location predicted by the band theorycalculation (non-interacting limit). A key point here is that when thequasiparticle peak crosses EF the entire photoemission peak must rapidly loseweight because the excitation can no longer be created (Fig. 19d). The centroidof the envelope therefore always stays well below EF with a minimum bindingenergy equal to the distance between the centroid of the distribution and thequasiparticle peak.

The above scenario can give a first order explanation for both the broadARPES peaks and the large reduction in spectral weight at EF (pseudogap). Animportant question within this scenario is then what type of Boson are theelectrons coupling to? We gain insight into this question by examining the k-space dependence of the pseudogap. We have found that the pseudogap affectsthe entire Fermi surface to a similar degree with little or no anisotropy. Thisgeneral lack of k-space dependence makes it less likely that charge, spin, ororbital ordering should play a dominant role in the gap opening, as theseordering phenomena should occur with a wavevector which will affect certainparts of the Brillouin zone more strongly than others. An example of this is therecently observed pseudogap effect in the high-Tc superconductors which has apronounced k-space dependence [40]. In those materials, the maximal gappingeffect is near the (π,0) point of the Brillouin zone, signaling a possible originfrom the antiferromagnetic fluctuations with wave vector near (π,π). A localeffect, such as a lattice distortion, is more likely to give the isotropic effectsobserved in the manganites. This is consistent with the temperature-dependentstructural distortions observed in the manganites [12-14] as well as the verylarge isotope effects [43].

However, the collective modes can also derive from degrees of freedomother than phonons. As the correlation effects are quite strong in thesematerials, which is manifested in the propensity of the material to have charge

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and orbital order and/or inhomogeneity [44], other collective excitations mayprovide alternative explanation to the photoemission data.

6.5 Franck Condon analysis and lattice relaxation energiesThe Frank-Condon picture is an essentially equivalent way to discuss the

strong coupling to phonons in the photoemission spectra. As illustrated infigure 20, we consider a configurational coordinate diagram where there is aparabola describing the phonon potential energy curve both for the ground state(N electron system) and the final state (N-1 electron system) of thephotoemission absorption process. Due to the strong lattice effects, the twoparabolas are displaced by an amount Q1-Q0. We consider transitions betweenthe ground state and any of the (vibrational) levels of the excited state, with thephotoemission spectrum being a superposition of the possible transitions (dueto additional broadening effects in the solid the individual levels may not beseparately observable). The lowest energy transition occurs without excitingany phonons and will give rise to the portion of the spectrum closest to theFermi energy. The vertical transition is the most probable and will correspondto the most intense portion of the spectrum. The difference between these tworepresents the difference in energy between the relaxed and unrelaxed state, thatis, it represents the lattice relaxation energy EL. Looking at the most intenseportion of the spectra at (π, .27π) or (.63π, .27π) which roughly correspond tok=kF, we estimate the lattice relaxation energy to be .65 eV in the ferromagneticcase (50K) and .8 eV for the paramagnetic case (200K) (see Fig 17).

6.6 Dimensionless coupling parametersThe magnitude of the lattice relaxation energy EL discussed in section 6.5 or

the Jahn-Teller energy EJ-T discussed in section 5.3 are mostly important incomparison to the electron kinetic energy or hopping parameter t. To firstorder, we can obtain these quantities by a measurement of the dispersivebandwidth W, as discussed in section 6.2. For instance, in the lattice-electroncoupling model proposed by Millis, there is a coupling constant, λ =2EJ-T/t,which must be about unity for the metal-insulator transition to be allowed [45].Assuming a full bandwidth for the doped cubic compounds of 4 eV in either theferro or paramagnetic cases (see section 6.2 and 6.3) and following Millis'sconvention of a t which is 1/4 the bandwidth, we obtain a value for t of about 1eV. We therefore find a coupling constant λ ~ .5 eV/1 eV ~ .5 which is lessthan but on the order of unity. A strict interpretation of this number withinMillis’ model would tell us that the Jahn-Teller distortion is not strong enoughto localize the electrons into polarons.

Within the same model we can likewise determine the dimensionlesscoupling parameter λ associated with the lattice relaxation discussed in section6.5 for the bilayer compound La1.2Sr1.8Mn2O7. Using a full bandwidth W of3 eV for the in-plane dx2-y2 states and lattice relaxation energies EL of .65 eVand .8 eV, we obtain a coupling parameter slightly less than 2 for theferromagnetic case and near 2.5 for the paramagnetic case. This indicates thatthese materials are in the strong coupling regime in both the ferromagnetic and

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paramagnetic states. Within the picture outlined in section 6.5, this is consistentwith the broad ARPES peaks and the vanishingly small quasiparticle weight(and hence pseudogap). However, because the energy scale for the Jahn-Tellereffect is relatively weak, this indicates that some other distortions (such as forinstance a breathing mode) or completely different types of collective excitationsor local inhomogeneities should be considered.

Implicit in the above discussions is that there is primarily one mechanismthat competes with the kinetic energy to renormalize the physics. A distinctpossibility is that there are two or more mechanisms, neither of which is strongenough on its own to localize an electron, but which can cooperate to have astrong effect. An example of this is the discussion by Emin of the cooperationbetween large and small polaron physics in localizing an electron [46].

6.7 Summary of data from different samples and differenttemperatures

Figure 21a shows a compilation of photoemission data from the threedifferent families of the manganites, all with the same doping level of x=.4holes per Mn site, while Fig. 21b shows the behavior of ρ vs. T for the samesamples. The n=infinity sample has a finite N(EF) and is metallic, the n=1sample has a clear gap and is insulating, while the n=2 sample has a vanishinglysmall weight at EF and is barely metallic. As discussed in section 6.5, we canexplain the pseudogap to first order within the context of strong coupling of theelectrons to the lattice. As discussed in section 6.6, the coupling parameter λ isa dimensionless ratio of the lattice distortion energy over the one electronbandwidth W. Since W is largest (by dimensionality arguments) for then=infinity sample and smallest for the n=1 sample, we expect that λ and hencethe pseudogap effects should be smallest for the n=infinity samples and largestfor the n=1 sample, as observed. We also have discussed how λ is observed tochange across the ferromagnetic transition temperature. Therefore, the changesin the spectral weight at EF (pseudogap) with changing temperature also can beunderstood to first order within this simple model.

Fig 22 is an attempt to summarize the layer-number and temperaturedependent properties for a variety of the compounds into one plot, within thepretext that the coupling of the electrons to some boson (e.g. phonons)dominates the problem.

The vertical axis is the density of states at EF, and the horizontal axis is theelectron-boson coupling parameter λ. As the coupling is increased, thequasiparticle weight is reduced by the factor 1/Z for the reasons described in Fig19 a and b. In concert with this reduction in quasiparticle weight, thequasiparticle band should exhibit reduced dispersion, or an effective massincrease by the same factor Z. The net result of this is that in the weak couplinglimit N(EF) is unchanged as a function of λ. In the very strong coupling limit,the system is composed of completely localized small polarons which cantransport current only by tunneling from one lattice site to another, i.e. there are

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no free carriers and no spectral weight at EF. Connecting these two limits theremust be a region where the spectral weight is of an intermediate value, which istermed the intermediate coupling regime.

In figures 8,9 and 18 we have shown that the spectral weight at EF is astrong function of temperature, with the increase starting just as the temperatureis lowered through Tc. We have also discussed how the coupling parameter λchanges as we change temperature. We illustrate the changing λ withtemperature on this plot for the n=1, n=2, and n=infinity. At high temperaturesthey are all in the strong coupling regime where N(EF) is zero and they areinsulating. As the temperature is lowered double-exchange takes effect, theelectron itinerancy energy increases, and λ decreases so that the system entersthe intermediate coupling regime and the weight at EF is finite but stilldrastically reduced. Continued lowering of the temperature increases N(EF)continuously, as seen in figures 9 and 18. However, as discussed before,N(EF) is always well reduced from its expected (weak-coupling) value, so weargue that the coupling to the lattice is very significant even at the lowesttemperatures. This is in opposition with the usual arguments which state thatthe strong coupling (e.g. polaronic) effects should only be important in the hightemperature state, with the low temperature state consisting of essentially freeelectrons. The results shown here indicate that for the layered samples theelectron-boson coupling critically affects the electronic structure even below Tc,and probably is also important below Tc for the 3-dimensional manganites.

7.0 Summary, Conclusions and OutlookThe colossal magnetoresistive oxides display a large amount of unusual

electronic and physical properties. It is therefore not surprising that theelectronic structure of these materials is also found to be very unusual. In thischapter we have reviewed the current status of measurements of the electronicstructure of the CMR oxides.

Angle-integrated photoemission data from the (pseudo) cubic manganiteshave indicated:

1) A finite but very low spectral intensity at the Fermi energy EF in the lowtemperature ferromagnetic state, and zero weight at the Fermi energy in the hightemperature paramagnetic state. This indicates that the metal-insulator transitionis likely due to a change in the effective number of carriers, instead of a changein the carrier mobility.

2) A total spin polarization of the near-EF bands for measurements made inthe low temperature ferromagnetic state.

3) The low energy charge fluctuations in the undoped parent insulators areprimarily p-d type, i.e. they should be considered charge-transfer insulators.

Angle-resolved photoemission (ARPES) measurements have beensuccessfully obtained from cleaved single crystals of the layered manganites. Inparticular, measurements on the bi-layer sample La1.2Sr1.8Mn2O7 have shown:

1) A temperature-dependent pseudogap centered at EF, similar in manyrespects to that seen in the pseudo cubic compounds. This pseudogap kills all

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the weight at EF in the paramagnetic regime and leaves only a vanishingly smallweight below Tc.

2) Broad yet highly dispersive peaks which can not be interpreted as singlequasiparticle excitations.

3) A locus of k-space regions where critical behavior is observed, whichroughly matches the large Fermi surfaces predicted by band theory calculations.Since no clear Fermi surface crossing behavior is observed, the locus isdescribed as a "ghost" Fermi surface.

4) Temperature dependent behavior which is qualitatively in contrast to theDouble Exchange predictions. In particular, the spectral weight at EF increasescontinuously without an apparent saturation as the temperature is lowered belowTc.

Another important aspect of the work has been the determination of some ofthe key energy scales and coupling parameters for the CMR oxides. Inparticular, it is seen that:

1) The one-electron bandwidth W is approximately 3 eV for theferromagnetic state of the bilayer manganites. W is expected to be higher (~ 4eV) for the most metallic of the pseudocubic manganites.

2) The energy gain for Jahn-Teller distortions in the doped pseudocubicmanganites is of order .25 eV or less.

3) The Hund's rule coupling energy JH is of order 2.7 eV (energydifference to add a down spin eg electron vs. an up-spin eg electron).

4) The lattice relaxation energy (Jahn-Teller plus other contributions) forthe bilayer manganites of order .65 eV for the ferromagnetic state and .8 eV forthe paramagnetic state.

In general it is found that the low temperature ferromagnetic state of theCMR oxides can not be described as a normal metal. This is somewhatdifferent from many of the earlier expectations, which considered only the hightemperature paramagnetic state to be unusual (and probably controlled bypolaronic effects).

A discussion based upon strong (but varying) electron-lattice coupling inboth the ferro and paramagnetic states appears to be able to qualitatively explainmuch of the anomalous behavior. Much more work both experimentally andtheoretically needs to be done to fully understand and perhaps harness thebeautiful and exotic behavior that the CMR oxides display.

8.0 AcknowledgmentsThe authors are particularly grateful to Chul-Hong Park and Tom Saitoh

who were instrumental to most of the experiments and analysis discussed here.Additional thanks go to P. Villella, N. Hamada, T. Kimura, Y. Moritomo, andY. Tokura for fruitful collaborations and discussions.

The authors have also benefited greatly from helpful discussions with A.Bishop, S. Doniach, A. Fujimori, H.-Y. Kee, A. Millis, L. Radzihovsky, H.Röder, and G. Sawatzky. D.S.D. thanks the Office of Naval Research YoungInvestigator Program for generous support. Most of the experiments were

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performed at the Stanford Synchrotron Radiation Laboratory, which issupported by the Department of Energy. The Stanford work was supported bythe Office’s Division of Materials Science.

9.0 References

[1] R. M. Kusters et al., Physica B 155 , 362 (1989); Y. Tokura et al., J.Phys. Soc. Jpn. 63 , 3931 (1994); S. Jin et al., Science 264 , 413 (1994).

[2] C. Zener, Phys. Rev. B 82 , 403 (1951); P. -G. de Gennes, Phys. Rev.118 ,141 (1960)

[3] P. W. Anderson and H. Hasegawa, Phys. Rev. 100 , 675 (1955).[4] A.J. Millis in “Colossal Magnetoresistive Oxides”, Gordon and Breach

Science Publishers, Ed. by Y. Tokura[5] K. Kubo, J. Phys. Soc. Jpn. 33 , 929 (1972).[6] J. Zaanen, G. A. Sawatzky and J.W. Allen, Phys. Rev. Lett. 55, 418

(1985)[7] A. Bocquet et al., Phys. Rev. B 46 , 3771 (1992)[8] A. Chainani et al., Phys. Rev. B 47, 15397 (1993)[9] W.E. Pickett and D.J. Singh, Phys. Rev. B 53 , 1146 (1996)[10] K.I. Kugel and D.I. Khomskii, Sov. Phys. Usp. 25 , 231 (1982)[11] A. Urushibara et al. Phys. Rev. B 51 , 14103 (1995).[12] S.J.L. Billinge et al., Phys. Rev. Lett. 77 , 715 (1996)[13] D. Louca et al., Phys. Rev B. 56 , R8475 (1997)[14] C. H. Booth et al., Phys. Rev. B 54 , R15606 (1996); C.H. Booth et al.,

Phys. Rev. Lett. 54 , 853 (1998); T.A. Tyson et al., Phys. Rev. B53 ,13985 (1996)

[15] P.W. Anderson, Physical Review B 42, 2624 (1990)[16] C.M. Varma et al., Phys. Rev. Lett. 63 , 1996 (1989)[17] G. A. Sawatzky, Nature 342 , 480 (1989)[18] J.-H. Park et al., Phys. Rev. Lett. 76 , 4215 (1996)[19] Z.-X. Shen and D.S. Dessau, Physics Reports 253 , 1 (1995)[20] T. Saitoh et al., Phys. Rev. B 51, 13942 (1995)[21] D.S. Dessau et al. unpublished data[22] P. Schiffer, Physical Review Letters, 75 , 3336 (1995)[23] D.D. Sarma et al., Phys. Rev. B, 53 , 6873 (1996); T. Saitoh et al., Phys.

Rev. B. 568836 (1997)[24] T. Saitoh et al., Science preprint[25] Y. Okimoto et al., Phys. Rev. B 55 , 4206 (1997)[26] W.E. Pickett and D.J. Singh, Phys. Rev. B 53 , 1146 (1996)[27] J.H. Park et al., (unpublished)[28] J. Sun, in “Colossal Magnetoresistive Oxides”, Gordon and Breach

Science Publishers, Ed. by Y. Tokura[29] A. Urushibara et al. Phys. Rev. B 51, 14103 (1995)[30] F.M.F. deGroot et al., Phys. Rev. Lett. 50 , 2024 (1983); K.J. Schwarz,

Phys. F 16 , L211 (1986)[31] G.L. Bona et al., Solid State Comm. 56 , 391 (1985); K.P. Kamper et al.,

Phys. Rev. Lett. 59 , 2788 (1988)

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[32] M. Abbatte et al. Phys. Rev. B 46 , 4511 (1992)[33] E. Pelligren et al., J. Elect. Spectr. and Related Phenom. 86 , 115 (1997)[34] C.H. Park et al. (unpublished)[35] S. Satpathy et al., Phys. Rev. Lett. 76, 910 (1996)[36] D.S. Dessau et al., Phys. Rev. Lett. (submitted)[37] N. Hamada et al., (unpublished)[38] J.M. Luttinger, Phys. Rev. 119, 1153 (1960).[39] T. Kimura et al., Science 274 ,1698 (1996)[40] D.S. Marshall et. al., Phys. Rev. Lett. (1996); A.G. Loeser et al., Science

(1996); H. Ding et al., Nature (1996); Z.-X. Shen and J.R. Schrieffer,Phys. Rev. Lett., 78, 1771 (1997).

[41] A.L. Efros and B.I. Shklovskii, J. Phys. C. 8, L49 (1975).[42] See for example the discussion in chapter 4.3.C of Many Particle Physics,

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Nickel, R. Ramesh and Y. Tokura, eds., (Materials Research Society, 1998)[47] Y. Moritomo et al., Nature 380 , 141 (1996)

24

Figure 1 - a) An MnO6 octahedron. b) The MnO2 plane, which isidentical in structure to the CuO2 planes of the high temperaturesuperconductors. c) The crystal structure of the layered and cubic manganites.

Figure 2. (a) The d4 ion. (b) The d3 ion. (c,d) An illustration of theconcept of double exchange - the hopping matrix element as a function of spinalignment. (e) The double-exchange prediction for the bandwidths for theferromagnetic and paramagnetic cases.

Figure 3. An illustration of the Jahn Teller effect for the d4 ion.Figure 4 a) A schematic of the photoemission process. b) An illustration

of angle-resolved photoemission (ARPES) from a band crossing the Fermienergy.

Figure 5 An illustration of the X-ray absorption (XAS) process, whichgives unoccupied density of states information.

Figure 6 Doping dependence of angle-integrated photoemissionmeasurements of (La1-xCax)MnO3, from J.H. Park et al. [18] (a) Valence bandand shallow core levels. The inset shows the doping dependence of thechemical potential shift. (b) Valence band spectra from panel a, aftercompensating for the chemical potential shifts.

Figure 7 Doping dependence of angle-integrated photoemissionmeasurements of (La1-xSrx)MnO3, from Dessau et al [21]. The data is fromsingle crystals cleaved and measured at T=10K.

Figure 8 a) Temperature dependent angle-integrated photoemissionspectra from J.H. Park et al. [18] from Tc=260K La .67Ca.33MnO3 (left panel)and from Tc=330K La.7Pb.3MnO3 (right panel).

Figure 9 A plot of the near-EF spectral weight of pseudo-cubicLa.82Sr.18MnO3 (for two energy intervals) as a function of temperature, fromSaitoh et al. [24]. The vertical axis is the relative weight compared to what isexpected by band theory calculations, i.e. even at the lowest temperature, thereis approximately a factor of 10 less spectral weight at EF than expected. Thedata is compared to the temperature dependent Drude weight measured byOkimoto et al. [25].

Figure 10 - Spin-resolved photoemission spectra by J.H. Park et al. [27]from a Tc=350K thin film sample of La.7Sr.3MnO3 at (a) T=40K and (b)T=380K.

Figure 11 - Oxygen 1s XAS data of La(1-x)SrxMnO3 from M. Abbate etal.[32]

Figure 12 - UPS and O 1s XAS of LaMnO3 and SrMnO3 and clustermodel analysis from Saitoh et al. [20]

Figure 13. Oxygen 1s XAS data from a single-layer d3 (panel a) and d4

sample (panel b) from C.-H. Park et al. [34]. The solid curves were themeasurements at grazing incidence (E field out-of-plane) and the dotted curveswere measurements at normal incidence (E field in-plane). The bottom curvesof each panel show the subtraction of the dotted from the solid curves.

Figure 14. Oxygen 1s XAS data from a variety of samples with x=.4(d3.6) after C.-H. Park et al. [34]. The data includes 3-dimensional samples

25

(set C) and layered samples with one (set A) and two (set B) MnO2 layers perunit cell . Set D shows the subtraction of the dotted from the solid curves fromsets A and B.

Figure 15 . (a)-(d) Low temperature high resolution ARPES spectra fromDessau et al. [36] of La1.2Sr1.8Mn2O7 along various high symmetry directions,as indicated at the top of each panel and by the arrows along the two-dimensional Brillouin zone of panel (e). The 3 curved lines in panel f are theFermi surfaces for the up-spin bands in LDA+U band theory calculations. Thetwo x's are the experimental locations of closest approach to EF. (f) The up-spin bands in an LDA+U band theory calculation [37] vs. experimentallydetermined peak centroids from panels a and c (tick marks).

Figure 16. A schematic illustrating the up and down-spin density of statesfor both the layered and 3-dimensional manganites. The experimentallyobserved pseudogap at EF is also indicated.

Figure 17 Temperature dependence of the near-EF bandstructure ofLa1.2Sr1.8Mn2O7, after Saitoh et al. [24].

Figure 18. A compilation of temperature dependent data ofLa1.2Sr1.8Mn2O7 taken at the k-space point (π,.27π), after Saitoh et al. [24].The triangles indicate the spectral weight found very near EF obtained over twodifferent energy integration windows, and the diamonds show the energy shiftof the leading edge (at two different positions on the edge) as a function oftemperature.

Figure 19. a) Weak and strong coupling lineshapes for the problem of asingle electron coupled to a bath of Einstein phonons c) k-dependent dispersionof a weakly coupled electron phonon system. d) extension to dispersion ofstrongly coupled electron-phonon system.

Figure 20. A schematic of photoemission from a strongly coupledelectron-phonon system (right panel), where Q is a generalized distortion. Inthe spirit of the Franck-Condon approximation, the vertical transition is themost probable and will correspond to the most intense portion of the spectrum.The left panel shows how the photoemission peak is sharp in the absence of theelectron-lattice coupling.

Figure 21. a) Near-EF ARPES weight (pseudogap strength) vs. layernumber n for (La,Sr)n+1MnnO3n+1 (x=.4 holes per Mn site), from Dessau etal. [21] b) ρ vs. T for the same samples, from Moritomo et al.[47].

Figure 22. Schematic diagram showing the spectral weight at EF as afunction of electron-boson coupling parameter λ. Included are approximateplacements of three-dimensional, bi-layer and single-layer manganites as afunction of temperature.

26

Fig 1

Cleave ----->

----->----->

layered cubic

c)

a) MnO6 cluster b) MnO2 p laneMn

O

eg

t2g

Mn3+ 3d4θ

t = tocos(θ/2)~

t2g electronscore-likeS=3/2

eg electronitinerant

eg

t2g

Mn4+ 3d3

LaMnO3x=0

SrMnO3x=1

a) b) c)

d)

t = to~

Ferro Para

t ~.707 to~ Ferro

EFρ(E) Para

EJ

~0.7W oW o

e) Fig 2

Mn ion

Oxygen ion

eg

t2g

dx2-y2, d3z2-r2

dxy, dxz, dyz

d3 e.g. CaMnO3

eg

t2g

dx2-y2

d3z2-r2

dxydxz, dyz

d4 e.g. LaMnO3

stretch

MnO6

Fig 3

Band Structure (metal) ARPES Spectra

EF

••

••

•

E

k

k1 k2 k3 k4 k5

θ1θ2θ3

θ5

θ4

EF

VL

hν hν

Energy

EF

Density of States

a) b)

DO

S

Energy above EF

0

b)

Core level

Valence band

Unoccupied states

Continuum

EF

hν

a)

Fig 4

Fig 5

-1.2 -0.8 -0.4 0

Energy Relative to EF (eV)

d4

d3.5

d3.6

d3.7

d3.82

La1-xSrxMnO3

x=0

x=.5

Fig 7

Inte

nsity

(A

rb U

nits

)

Fig 6

Fig 8

La0.67Ca0.33MnO3Tc=260K

La0.7Pb0.3MnO3Tc=330K

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

Wei

ght R

atio

(E

xp/B

and)

1.41.21.00.80.60.40.20.0T/Tc

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Drude W

eight (x10 -2)

-0.06 − 0.06 eV -0.30 − 0.06 eV Drude weight

Fig 9

Fig 10

Fig 11

Fig 12

-15 -10 -5 0 5 10

ENERGY RELATIVE TO EF (eV)

(b) SrMnO3

Sr 4p

Sr 4d

d3L

d2

d4L

2

d4

d5L

d6L

2

t2g↑ eg↑ eg↓t2g↓

-15 -10 -5 0 5 10

ENERGY RELATIVE TO EF (eV)

(a) LaMnO3

La 5p

La 5d

d3

d4L

t2g↑

eg↑

eg↑

eg↓eg↓

t2g↓

d5L

2

d5

d6L

d7L

2

Figure 13

Photon energy (eV)527 530 533

subtracted

dx2-y2 updz2 downb) Mn d4

(La,Sr)O

In-plane states (dx2-y2)

Out of-plane states(d3z2-r2)

n=1LaSrMnO4

a) Mn d3

n=1Sr2MnO4

subtracted

dx2-y2

down

dz2

downdz2 up

dx2-y2 up

J SrO J

t2gdown

527 530 533Photon energy (eV)

3-dim

n=2

n=1

n=2 subtracted

n=1 subtracted

Set A

Set B

Set C

Set D

shortbondlong

bond

(La,Sr)O

(La,Sr)O

Mn d3.6

Figure 14

Figure 15

(0,0) (π,0) (π,π)

Rapid weight loss

-2 eV

EF

-1 eV

f)

LDA+U up-spinFerromagnetic bands

e) (π,0)

(π,π)

(0,0)

X

a

c

d

b

-1 0

(0,0) --> (π,0)

-1 0

(0,0) --> (π,π)

-1 0

0

.09

.18

.27

.36

.45

.54

.63

(π,0) --> (π,π)(.63π,0) --> (.63π,.63π)

-1 0Energy Relative to EF (eV)

Cou

nts

(arb

itrar

y un

its)

xx

a) b) c) d)

Au (.63π,yπ)

y = 0

.09

.18

.27

.36

.45

.54

.71

.89

.98

(π,yπ)

y =

(yπ,0)

0

.09

.18

.27

.45

.63

.80

.98y =

(yπ,yπ)

0

.18

.27

.45

.63

.80

.36

.54

.71

y = XX

T=10K (Ferromagnetic state) of La1.2Sr1.8Mn2O7

Figure 16

J ~ 2.7 eV

W~ 3 eV

EF

W ~ 4 eV

EF

Layered 3-dimensionalEnergy Scales of Manganites x~ .4

J ~ 2.7 eV

-2 -1.5 -1 -0.5 0

0/0

π/0

(0/0) (π/0)

(π,π)

-2 -1.5 -1 -0.5 0

π/0

π,π

(0/0) (π/0)

(π,π)

50K Ferro

200K Para

Energy Relative to EF (eV)

kF

kF

Fig 17

100

80

60

40

20

1.41.21.00.80.60.40.20.0T/Tc

0.20

0.15

0.10

0.05

0.00

-0.05

-0.10

-0.1 − 0.05 eV

-0.3 − 0.05 eV ( ×0.1)

La1.2Sr1.8Mn2O7 Tc=126K

Peak position

Edge@-0.3 eV

M/Ms

Shift

Weight

Fig 18

kEF

Ene

rgy

AR

PE

SIP

ES

incoherent portion of spectrum

band theory dispersion

q.p. peakdispersion

ωo

quasiparticle peak

a) weak coupling

b) strong coupling

εc

εc

kEF

Ene

rgy

AR

PE

SIP

ES

band theory dispersion

Centroid ofARPES peak

q.p. peakdispersion

c) weak coupling dispersion d) strong coupling dispersiona,b) single electron spectral function

Fig 19

E

Q

Ground state (N electrons)

ARPES final state (N-1 electrons)

Q0 Q1

zero

-pho

non

vert

ical

EE

Q

Ground state (N electrons)

ARPES final state (N-1 electrons)

Q0

k=kF

spectral function

E

without coupling strong coupling case

EF EF

Lattice relaxationenergy or polaron binding energy E

B

k=kF

spectral function

Fig 20

q.p. weight as 1/Zm* as Z

localizedtunneling of small polarons

weak intermediate strong

N(EF)

λλc 1-layer

-2 -1 0 1

Au hv=40

n=∞ hv=40

n=2 hv=48

n=1 hv=48

Energy relative to EF (eV)

0 100 200 300

105

100

10-5

Temperature (K)

Res

istiv

ity (

ohm

-cm

)

x=.4

n=1

n=2

n=∞(cubic)

All normal emission (0/0)T ~ 150K

Fig 21

Fig 22