Direct Electronic Structure Measurements of the Colossal Magnetoresistive Oxides.

Transcription

1 Direct Electronic Structure Measurements of the Colossal Magnetoresistive Oxides. D.S. DESSAU Department of Physics, University of Colorado, Boulder CO, 80309, USA and Z.-X. SHEN Department of Applied Physics, Stanford University, Stanford, CA 94305, USA A chapter in Colossal Magnetoresistive Oxides Ed. by Y. Tokura Monographs in Condensed Matter Science Gordon And Breach 1998

2 Direct Electronic Structure Measurements of the Colossal Magnetoresistive Oxides. D.S. DESSAU Department of Physics, University of Colorado, Boulder CO, 80309, USA and Z.-X. SHEN Department 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 of effort aimed at understanding the electronic and magnetic properties of these materials. At low temperatures, properly doped manganites exhibit ferromagnetic metallic or nearly metallic behavior, while at high temperatures they exhibit a paramagnetic insulating behavior. This generic behavior, as well as the magnetoresistive effect which occurs near the transition, has been understood to first order within the framework of double exchange theory, as developed in the 1950's and 60's by Zener, DeGennes, and Anderson and Hasegawa [2,3]. Recently however, there has been an increasing realization that although double-exchange is clearly important for understanding the behavior of the manganites, it is not enough and other physics must be introduced. While there has been a great amount of progress both experimentally and theoretically, it is not yet clear what the most important mechanisms are for explaining the physics of the manganites. In addition to the CMR effect, the manganites have been found to exhibit a very wide range of exotic and beautiful phenomena, including many types of magnetic ordering, metal-insulator transitions, charge and/or orbital ordering, and pressure induced phase transitions. It should also be remembered that the manganites belong to the class of materials where electron correlations are deemed important - a problem that has challenged the condensed matter physics community for over 50 years. This chapter will focus on the electronic structure of the manganites obtained by various spectroscopies, with an emphasis on angle-resolved photoemission spectroscopy (ARPES) and X-ray absorption spectroscopy (XAS) - two powerful and direct electronic structure probes. We will try to provide a pedagogical introduction to the various subjects, as well as give our interpretation 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 a complete review - rather it should be regarded a snapshot from a particular angle of a rapidly developing field. Section 2 will discuss various starting points for understanding the electronic structure of the manganites, including the atomic view, Double- 1

3 Exchange theory, electron correlation effects, and polaronic effects. Section 3 gives a quick introduction to the various experimental techniques and considerations. Section 4 gives an overview of the measured electronic structure of the manganites, briefly touching on the doping dependences, temperature dependences, and sample type dependences. It also introduces the pseudogap, 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, as well as discussing a determination of some of the important energy scales such as the bare bandwidth W, the Hund's rule energy J, and the Jahn-Teller energy E J-T. Section 6 discusses the low-energy k -dependent electronic structure in detail, including temperature-dependent data taken across the phase transition. Section 7 summarizes and concludes. 2. Starting points for understanding the electronic structure of the manganites 2.1 Structure and doping The crystal structure of the manganites is schematically illustrated in figure 1. In all cases, the Mn ions are surrounded by 6 oxygen ions in an approximately octahedral arrangement, as shown in panel 1a. The Mn and O ions are arranged in an MnO 2 plane as shown in panel 1b. The structure of these planes is completely analogous to the CuO 2 planes found in the cuprate High Temperature superconductors (HTSC's). The MnO 2 planes are then stacked in a variety of sequences with MnO 2 planes interleaved with (La,Sr)O planes, as shown in panel 1c. The compounds are annotated depending upon how many MnO 2 planes are arranged between a bi-layer of (La,Sr)O planes (La and Sr can be replaced by many other tri- and di-valent ions). This series is called the Ruddelson-Popper series, and has the general formula unit (La,Sr) n+1 Mn n O 3n+1. The n=1 compounds have formula unit (La,Sr) 2 MnO 4 and are analogous to the HTSC compounds (La,Sr) 2 CuO 4. The n=infinity compounds have no (La,Sr)O bilayers, and have the formula unit (La,Sr)MnO 3. They are cubic or distorted cubic compounds, and the most heavily studied of the manganites. The layered compounds (n infinity) cleave much more readily than the cubic compounds, and so are more suitable for the spectroscopic measurements reported here. The "parent" compounds of the manganites, e.g. LaMnO 3 are antiferromagnetic "Mott" insulator with properties dominated by the strong Coulomb interactions between the electrons. Substitution of the trivalent (3+) La ions with a divalent ion such as Sr, Ca, or Ba dopes holes into the manganites, creating a material with poorly understood and very unusual properties. At the appropriate doping level, these doped manganites display a combination of a metal-insulator (M-I) transition, a ferromagnetic-paramagnetic (FM-PM) transition, and the colossal magnetoresistance. 2.2 Ionic view of electronic structure Figure 2a shows the electronic configuration for the parent (undoped) compound LaMnO 3 in a simple ionic picture. Ionic LaMnO 3 has a 3d 4 2

4 configuration, meaning the 3d valence orbitals are filled with 4 electrons. The cubic crystal field splits the degeneracy of the d orbitals into the 3-fold degenerate t 2g (d xy,d xz,d yz ) and 2-fold degenerate e g (d x 2-y2, d 3z 2-r2)orbitals. The e g orbitals point directly at the oxygen atoms, and should hybridize strongly with the O 2p states, forming dispersive bands containing the electrons responsible for the conduction. The t 2g orbitals point 45 degrees from the oxygens, and so will hybridize less strongly to those states. Therefore, we expect less dispersion from these states and to a good approximation can treat them as localized core states, with a net spin S=3/2. An intra-atomic exchange term J H promotes alignment of the e g electron spins with the core-like t 2g spins. As we will see, J H is relatively large in these materials, implying that all electron spins should be aligned (Hund's rule coupling). 2.3 Double exchange, electronic correlations, and other theoretical considerations for the manganites. The starting point for most discussions of the mechanism of the magnetoresistance, M-I, and FM-PM transitions in the manganites is the double exchange model [2,3]. The physics of double exchange is illustrated in figure 2. As worked out by Anderson and Hasegawa [3] and shown in figure 2c, the hopping amplitude of the e g hole from one site to another is a function of the relative spin alignment at the two sites. Complete ferromagnetic alignment of the neighboring spins gives the greatest hopping amplitude t and the greatest bandwidths, uncorrelated spins will have a reduction in hopping amplitude of roughly 1/ 2, and complete antiferromagnetic alignment gives a t =0 implying a non-dispersive band with zero bandwidth. Therefore, there is a kinetic energy gain in the e g band for ferromagnetic alignment, which competes with the superexchange energy favoring antiferromagnetic alignment as well as with the thermal fluctuations which favor disorder. This model intuitively explains why a properly doped material at low temperatures is a ferromagnetic metal which will become a paramagnetic insulator at high temperatures. Slightly above T c, a large magnetic field will serve to align the core (t 2g ) spins, increasing the hopping amplitude between e g electrons and driving the material more metallic. While double-exchange gives a nice intuitive explanation for the coupling of the spin and charge degrees of freedom and for the trends in conductivity on going across the transitions, the magnitude of the effect is not well predicted by double-exchange. As shown in figure 2d, for the paramagnetic case (T>T c ) to first order the neighboring spins will have a relative angle of 90, and so the hopping probability t will be reduced to cos(90 /2) =.7 times that of the ferromagnetic case. This would imply a first-order conductivity decrease to.7 times that in the ferromagnetic case (more detailed explanations can be found in the chapter by Millis [4]), while experimentally it is seen that the conductivity decrease across the F-P transition may be many orders of magnitude. This indicates that some other physics beyond D-E is necessary to explain the conductivity change across the transition. Another closely related prediction of 3

5 double-exchange theory is that the one-electron bandwidth W measured in the paramagnetic state should be reduced to.7 of its value in the ferromagnetic state (figure 2e) [5]. For intermediate doping levels, this would mean a slight increase in the density of states at E F upon going to the paramagnetic state. As discussed in section 6.4, the experimental findings are qualitatively very different from this prediction. This also indicates that we need to go far beyond double-exchange to understand the behavior of the manganites. To first order, we can understand a metal-insulator transition as originating from one of two things - either a change in the number of carriers or a change in their mobility. This is immediately apparent from the equation for the conductivity σ=neµ, where n is the number of carriers, e is their charge and µ is the mobility. Within double-exchange theory the change in mobility (change in hopping probability) is the dominant effect on the conductivity. Significant mobility reductions can also be obtained from Anderson localization effects due to disorder, for instance due to the disorder of the local t 2g spins. Neither of these effects should significantly affect the density of states at the Fermi level. Therefore, if mobility changes were the dominant mechanism for the metalinsulator transition we should expect a significant density of states at the Fermi energy even in the insulating paramagnetic case. We will show that this is not observed, indicating that a change in effective carrier number (a gapping of the near-fermi energy states) is more important than a change in mobility. As in most other transition metal based systems, electronic correlations due to the on-site Coulomb interaction U are believed to be important in the manganites. Indeed, the undoped parent compound LaMnO 3 has a partially filled d-band, and so to first order is expected to be a metal within a singleelectron theory such as band theory. However, LaMnO 3 is in fact an antiferromagnetic insulator with a relatively large gap of 2 ev. This breakdown of the 1-electron theory is often attributed to electron correlations, i.e. LaMnO 3 can be considered to be a Mott insulator, in which the on-site Coulomb energy U is responsible for the insulating behavior. More specifically, under the Zaanen-Sawatzky-Allen classification scheme [6], they should probably be considered charge-transfer insulators because, the p-d charge fluctuation energy, has been estimated to be smaller than U, the d-d charge fluctuation energy. For example, using fits to Mn 2p core level photoemission data, Bocquet et al. have estimated U to be approximately 8 ev for both LaMnO 3 and SrMnO 3, and to be 4.5 ev for LaMnO 3 and 2 ev for SrMnO 3 [7]. Slightly different values have been estimated by Chainani et al.[8]. However, we also note that Jahn-Teller distortions can explain the insulating nature of LaMnO 3 within 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 is a strong coupling to the lattice, with a resultant polaron formation. To first order, these scenarios state that the conductivity in the high temperature insulating state is due hopping of these lattice polarons, while below the T c the polarons break up and conductivity is due to the individual electrons. The 4

6 presence or absence of the polarons is a very delicate balance which will be controlled 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 so strong in the manganites is because the d 4 ion is unstable to a Jahn-Teller distortion, giving a strong electron-lattice coupling. A schematic of the Jahn- Teller distortion is shown in figure 3. By distorting the MnO 6 octahedron as shown, the degeneracy of the e g levels is lifted and there is an electronic energy gain linear with the distortion. There is a loss of lattice energy quadratic with the distortion, with a resultant total energy gain equal to 1/4 of the splitting of the e g levels [10]. Extensive diffraction results indicate that the d 4 parent compound LaMnO 3 is Jahn-Teller distorted, with bond length differences between the long and short Mn-O bonds of approximately.2 Å.[11] The d 3 parent compound SrMnO 3 has no e g electrons and so, as expected, has an un-distorted cubic structure. In the intermediate doping regimes relevant to CMR, diffraction results do not show distortions, although local structural measurements such as neutron PDF analysis [12,13] and EXAFS [14] do show distortions, albeit that there are still discrepancies and questions regarding these results. From the electronic structure viewpoint, we have observed the e g level splittings due to these distortions, thereby obtaining information about the energetics of the process. As will be discussed in section 5.3, the Jahn-Teller splitting is not as large as might be hoped to explain the observed properties, and so other modes such as breathing modes may be necessary. It also should be noted that below T c the electron-lattice coupling still appears to be strong, and so the properties may still be largely affected by the coupling to the lattice. A more complete discussion of this is contained in section 6. In this chapter we will show how a variety of advanced spectroscopic techniques can address these most fundamental questions about the electronic, magnetic, and structural aspects of the manganites. 3. Techniques 3.1 Angle-resolved Photoemission - k-dependent occupied states Photoemission spectroscopy is a very powerful and direct probe of the occupied electronic structure, bonding, and chemical nature of a material. The introduction of high energy resolution ( E<30 mev) to the technique in the past few years has moved the technique into the forefront of physics and materials research, since the most crucial low-energy excitations near the Fermi surface may be directly probed. The k-space resolution of the angle-resolved version of the technique is a very powerful and unique aspect which gives information which typically can not be obtained by any other method. A schematic of the photoemission process is shown in figure 4a. In a photoemission experiment, monochromatic photons of known energy impinge upon a sample. An electron with initial energy E i inside the sample is excited and ejected out of the sample with a kinetic energy E k. The ejected photoelectrons are collected and energy analyzed, the energy distribution of 5

7 which gives us the energy distribution of the initial states E i in the sample. In the simplest approximation, the photoelectron spectrum therefore tells us the occupied density of states of the system. In angle-resolved photoemission spectroscopy the emission angle of the photoelectrons from the surface normal is also constrained, and so we obtain the electron's momentum information in addition to its energy. Because the component of the electron's momentum parallel to the surface will be conserved as it traverses the sample-vacuum interface and the perpendicular component is affected by the known work function, we can relate the electron's momentum outside the sample (final state) to it's initial momentum or k in the crystal lattice. Typically one will compare the E i (k) determined from the angle-resolved photoemission experiments with the E i (k) from a band theory calculation. However, it is important to realize that the density of states or the E i (k) measured by photoemission spectroscopy is not a ground state measurement, but is a measurement of the energy required to remove an electron from the system, that is, it is a measurement of the excitation spectrum of the system. In the Green's function approach to many-body physics, this is just the spectral weight function A(k,ω) = 1 π 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 E i (k) of band theory calculations, but will be shifted slightly due to "self energy" effects arising from interactions of the injected hole with the medium. In addition, the final state of the photoemission process will not in general be an eigenstate of the interacting system and so will have a finite lifetime. This will have the effect of smearing out the delta function in E i (k). The precise manner in which the delta function peaks are smeared out can tell us important physical information about the interactions of the system. There is also the possibility that the quasiparticle picture may break down completely, as is currently being discussed for the high T c materials [15,16,17]. An illustration of what a series of ideal angle-resolved photoemission spectra taken from a two-dimensional system would look like is shown in figure 4b. The photoemission peak is observed at a different energy for each emission angle, corresponding to the E vs. k dispersion of the band being studied. The peaks are narrower for the states closer to the Fermi level, corresponding to a reduced phase-space for scattering and hence longer lifetimes. Finally, the peak disappears after the band crosses through the Fermi level into the region of unoccupied states. Due to the short escape depths of the photoelectrons, photoemission is a surface sensitive spectroscopy, with probing depths typically on the order of 5-50Å. Depending upon the specific experiment, this surface sensitivity may be either an asset (for the interface studies) or a hindrance. To overcome this limitation for studies of the bulk electronic structure, a fresh sample surface should be obtained by a cleave and measurement in ultra-high vacuum conditions (P < torr). Samples are also typically kept at low temperatures 6

8 in order to reduce effects such as the out diffusion of oxygen from the sample surface. Also critically important is the selection of materials with good cleavage properties, for no other precautions can overcome this most serious limitation. 3.2 X-ray absorption spectroscopy - unoccupied states If 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 step corresponding to the energy separation between a certain core level and the Fermi energy (core binding energy). This increase in absorption is due to the fact that an additional channel for absorption, the promotion of a core electron to an empty state just above the Fermi level, is enabled. A knowledge of the nature of the core level as well as the matrix element for the transition will lend information of the unoccupied density of states of the material. The dipole selection rule for photon-excited transitions states that the change in the angular momentum quantum number ( L) is ±1, while the spin is not changed. For the oxygen 1s edge (L=0) this means that only oxygen p character (L=1) can be reached. To first order, we can therefore view the resulting O 1s XAS spectrum as an image of the oxygen p projected unoccupied density of states. X-ray absorption measurements performed in the electron-yield mode typically have a surface sensitivity of approximately 100Å, so surface issues are not 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 MnO 2 planes which are structurally similar to the CuO 2 planes in the cuprates. Between the MnO 2 planes there is either a single or a double layer of (La,Sr)O planes. The number of MnO 2 planes between the (La,Sr)O biplanes is the main distinguishing characteristic 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 of the bulk and are not contaminated by surface effects. The best precaution is to use high quality single crystals that have natural cleavage planes, and then to perform the cleaves in vacuum at low temperatures immediately before measuring. The layered manganites have two (La,Sr)O planes adjacent to each other which should be almost completely ionically bound. It is found that the crystals cleave nicely between these planes, leaving mirror like surfaces which produce sharp LEED patterns without evidence of surface reconstruction. The ionic nature of the bonds in and between the (La,Sr)O planes means that there should be no dangling bonds or free charge left on the cleaved surface. The three dimensional compounds do not have such a natural cleavage plane, and so the cleavage process does not yield flat surfaces. ARPES studies have therefore not yet been possible on the three-dimensional samples, and while angleintegrated data does exist, it may be less reliable. However, it is found that the photoemission data from the three dimensional samples displays a high degree of consistency both with itself, with data from layered samples, and with optical measurements. This consistency leads us to believe that the photoemission data 7

9 on the cubic samples should also be considered reliable, although certainly more caution 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 of polycrystalline samples of the La 1-x Ca x MnO 3 series, as measured by J.H. Park et al. [18]. A clean surface for the measurements was obtained by scraping the surface with a diamond file in-situ immediately before the measurement. Panel a shows the valence band and shallow core levels as a function of doping. The ratio of the intensities of the La and Ca core levels changes with the doping level x, as expected. In addition, it is found that the core levels shift monotonically as a function of doping, implying a monotonic chemical potential shift with doping as shown in the inset to panel a. This is partly important as a comparison to the unusual and hotly debated behavior of the chemical potential shift in the high T c superconductors [19]. Similar chemical potential shifts have also been observed by Saitoh et al. [20] Concentrating on the main valence band extending to a binding energy of 8 ev (panel b), we see a large density of states region composed principally of Mn d and oxygen p states. As the doping is changed from x=1 (CaMnO 3, with a d 3 initial state) to x=0 (LaMnO 3, with a d 4 initial state), new states are built up near the Fermi energy because the chemical potential is moving into the manifold of e g symmetry states. Similar angle-integrated results from cleaved single-crystals of the La 1-x Sr x MnO 3 series were obtained by Dessau et. al. [21]. The near-e F region for these samples is shown in figure 7. The intermediate doped samples show a real Fermi edge cutoff, indicating a finite N(E F ) for these samples. The d 3.6 and d 3.7 samples show the greatest spectral intensity at E F, and correspondingly show the highest T c s and highest low temperature conductivities [22]. The d 3.5 and d 3.82 samples are on the verge of metallicity according to the doping phase diagram [22] and show a drastically reduced N(E F ). Finally, the d 4 (x=0) end member is a known insulator with a large gap, consistent with the data of Fig. 7. A very important point is that even though there are clear Fermi edge cutoffs for the more metallic samples, the observed spectral weight at E F is reduced from expectations (band theory or simple electron counting) by a factor of 10 or more [see section 6]. Similar behavior is observed in optical conductivity experiments in that the Drude weight is severely depressed from expectations by a similar amount. This is the first piece of evidence we will discuss for the pseudogap which reduces N(E F ) for all the manganites. 4.2 Temperature dependence - overview Associated with the metal-insulator and ferromagnetic-paramagnetic phase transition, there are expected to be clear changes in the electronic structure. In this chapter we will concentrate on the temperature-dependent changes that occur near the Fermi energy, as these are directly related to the transport 8

10 properties. We do note that there has also been some discussion in the literature about temperature-dependent changes to the main valence band[23]. The first clear temperature dependent near-e F spectra of the manganites was presented by J.H. Park et al.[18]. Figure 8 shows their angle-integrated data for a T c = 260K sample (left) and a T c = 330K sample (right). At the lowest temperatures in the ferromagnetic state a clear Fermi edge is observable. Increasing the temperature cuts this near-e F weight significantly, even for temperatures still well below T c. This behavior was made more quantitative by Saitoh et al. [24]. Saitoh et. al. cleaved single crystals of the x=.18 cubic sample La.82 Sr.18 MnO 3. The sample was cleaved and measured first at the highest temperature, and then progressively cooled, with the lowest temperature measurement last. At higher temperatures the spectral weight near E F is severely depleted and a Fermi edge cutoff is no longer observed. Figure 9 plots their measured spectral weight near E F as a function of temperature. Because of the very low spectral intensity, good statistics for this plot were only attainable by integrating the spectral weight over a finite energy interval. The results are shown for two different energy intervals around E F. It is seen that the weight near E F only starts increasing for temperatures below T c, and then continues increasing monotonically as the temperature is lowered further. The structure near.7t c in the smaller energy window is presumed to be due to noise. It is also presumed that above T c N(E F ) is zero, and the offset away from zero in the figure is due to the finite energy window used in the integration. The Drude weight observed in optical conductivity experiments by Okimoto et al. (open circles) [25] is also observed to have a similar temperature dependence. The fact that the spectral weight increase is observed to begin at T c is a good indication that the photoemission spectra are observing bulk-like properties, and are not overly affected by potential problems with the surface termination. Many other internal consistencies, particularly for the layered samples, similarly indicate that the photoemission spectra from the cleaved single crystal samples yield reliable information about the bulk electronic structure of the material, and not just about the surface region. An important point about the data of figures 8 and 9 is that even at the lowest temperatures the spectral weight at E F always remains very low. The left 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 energy window of figure 9, we see that the spectral weight is reduced by a factor of 10 or more relative to the expectations from band theory calculations [26]. Taking the 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 have approximately twice as much spectral weight at E F (see figure 7) so are still reduced by a factor of 10 relative to expectations. A similar reduction in the Drude weight is observed As will be discussed in section 6, the layered samples have an even greater reduction in near-e F spectral weight and Drude weight. This anomalous reduction in the spectral weight near E F has been termed a pseudogap, because while it removes the spectral weight it may not always remove it completely. We believe that this pseudogap is very important for 9

11 understanding the CMR problem. It will be discussed in more detail in section Spin-polarization of the electronic bands As 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 nicely confirmed by a spin-polarized angle-integrated photoemission experiment by J.H. Park et al.[27]. The experiment was performed on thin-film samples which, unlike most of the bulk single crystal samples, display a remnant magnetization. To clean the surfaces, a series of in-situ annealing processes were used. While this method has clear limitations, the attainment of a clear Fermi edge in the low temperature data gives some confidence in the quality of the attained surfaces. The photoemission data from both the up and down spin states is shown in Fig. 10. In the low temperature ferromagnetic state the Fermi edge is attained only for the up-spin states, while in the high temperature paramagnetic state there is no difference between the up and down spin states and there is also no Fermi edge observed. This is the first spectroscopic confirmation for the existence of a half-metallic ferromagnetic, a fact which is important for spin-polarized tunnel junctions (see the chapter by J. Sun [28]). These results are consistent with the development of a full saturation magnetic moment near 4 Bohr magnetons observed in (La,Sr)MnO 3 [29]. Other systems such as the Heusler alloys and CrO 2 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 scale determination Section 6 will show many more details of the low energy spectral properties of the manganites, with special attention paid to the layered manganites for which the crucial k-dependent information is also obtained. Before doing that however, we will discuss some of the X-ray absorption measurements which have enabled an accurate determination of some of the key energy scales of the manganites. We will show oxygen 1s absorption data, which within the dipole approximation can be interpreted as the oxygen 2p-projected unoccupied density of states. Oxygen 1s spectra of polycrystalline samples of the manganites have been measured by several groups[18,20,32,33]. While the experimental data obtained by these groups are mostly consistent with each other, there had not been a complete agreement on the interpretation of the data. Recently, C.H. Park et al. have made measurements on single crystalline samples of the layered manganites, as well as made new high resolution measurements on single crystalline samples of the pseudocubic manganites [34]. The higher resolution and especially a polarization analysis made possible from the layered single crystalline samples has lead to a new interpretation of the XAS data. Along with this new interpretation comes a determination of many of the important energy scales of the problem. 5.1 Review of earlier XAS results of pseudocubic polycrystalline manganites 10

12 The first detailed O 1s XAS data of the manganites was published by Abbate 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 E F. They argued that the strong intensity of this peak implies strong Mn-O admixing. They also noted that the intensity of this peak increased with Sr concentration, indicating more unoccupied d electrons, as expected. Abbate assigned the first peak to be composed of e g majority states and t 2g minority states. The second structure at 533 ev at the high Sr concentrations was assigned to e g minority states, which were argued to not be observable at low Sr concentrations due to an overlap with the La 5d states. Saitoh et al. published oxygen 1s XAS data of the pseudocubic manganites and performed a cluster model calculation to model the data [20] (see figure 12). Their calculations placed the t 2g minority states a few volts higher in energy, and also showed that they should have much weaker intensity. This is because the t 2g states hybridize more weakly to the oxygen states (a π bond instead of a σ bond) and so have a weaker projection onto the oxygen partial density of states obtained by the measurement. From these model calculations, Saitoh also estimated the d-d exchange coupling to be.85 ev, the Coulomb energy U dd to be near 7 ev, and the charge transfer energy to be 2 ev (SrMnO 3 ) and 4.5 ev (LaMnO 3 ). < U dd implies that these compounds should be considered charge transfer insulators instead of classic Mott-Hubbard insulators. 5.2 XAS results of d 3 and d 4 end member layered compounds and a determination of the Hund s rule energy J Figure 13 shows the O 1s XAS pre-edge region for both end member of doping (d 3 & d 4 ) of the single layer (n=1) compound Sr 2 MnO 4 & LaSrMnO 4, from C.-H. Park et. al. [34]. The near-edge region consists of the Mn 3d-O 2p hybridized unoccupied states, which are labeled by the d-symmetry labels. Considering the crystal field splitting and the typical assumption of strong Hund's rule coupling, the relevant states in the near-edge region should be the eg (d 3z 2 - r 2 and dx2-y2) up spin states, the t2g (d xy, d xz, d yz ) down spin states, and at higher energy, the eg down spin states. We also expect to distinguish between the d 3z 2 - r 2 (hereafter called d z 2) and dx2-y2 states in the layered material by the polarization effect assuming the dz 2 (dx2-y2) is the out-of-plane (in-plane) state. The polarization effects are highlighted by performing the subtraction of the two spectra, as shown in the lowest curve of each figure (inplane minus out-of-plane). This subtraction helps pinpoint the location of the peaks and their splitting. From the subtracted curve in figure 13 a, it is seen that the d z 2 up state (528 ev) 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) is observed. This is expected since the e g down-spin states should exist above the spin up states due to the additional energy cost to add a down spin electron compared to an up spin electron, which is the definition for the exchange energy J. From this data we can determine that J is 2.7 ev, which is in very good agreement with the theoretical [35] or ionic [20] values for the exchange 11

13 integral (about 0.9 ev) since there are 3 t2g electrons to couple to. The similar exchange splitting (2.7 ev) observed for both symmetry states confirms the consistency of the data and the subtraction procedure. The lower spectral weight of the down-spin states is probably due to a reduced Mn-O hybridization since these states are farther in energy from the main portion of the O 2p band (the absorption process at the O 1s edge occurs through a projection onto the O 2p states). Going from d 3 to d 4, the extra electron will occupy the lowest available state (d z 2 up) and therefore the dx2-y2 up (530.2 ev) should be the lowest unoccupied state, followed by the d z 2 down state (531.3 ev). This is exactly what is observed in figure 13b. Although we also expect t 2g down spin states in this energy range, they show up only very weakly, as expected because of the weak hybridization between the O 2p and Mn t 2g states. This is consistent with the model calculations presented by Saitoh et al. [20] and presented in Figure XAS of intermediately doped layered and cubic compounds and the Jahn-Teller energy E J-T Figure 14 shows polarization-dependent XAS data for x=.4 (d 3.6 ) samples as 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 the peak shown near 533 ev is due to states in the (La, Sr)-O plane because it varies with layer number and does not exist in the 3-dim case. The general trend of the data and the polarization effects in the near-edge region are similar to that for the d 3 sample - the lowest energy portion (528.5eV) has principally out-ofplane character (dz 2 ) while the higher energy portion (529.5eV) has principally in-plane character (dx2-y2). While the splitting between the centroids of the two states (as determined by the subtracted spectra) are very similar to that determined from the d 3 sample, the peaks are in general broader and more washed out. We attribute this to an increase in the electron itinerancy energy for the doped samples. From the similarity of the pre-edge structures of the layered and cubic samples in figure 14, it is natural to assume that the two bumps in the pre-edge of all samples are of the same origin, i.e. they are from e g -symmetry states which have had their degeneracy broken by a distortion of the MnO 6 octahedra. For the layered samples this is a static elongation along the z-axis, while for the cubic sample it should be due to a Jahn-Teller distortion (note that the cubic d 3 sample of figure 13 does not show the splitting, as expected since the d 3 ion is not Jahn-Teller active). It is important that this distortion must be short-range and dynamic, because diffraction studies sensitive to the long range order have not indicated a distortion [11]. The XAS should not be limited by the dynamic nature of a lattice distortion since the electronic transitions are much faster than the time scale of a lattice distortion. Structural studies sensitive to the shortrange distortions such as EXAFS [14] and neutron PDF [12,13] have also shown distortions of the octahedra in doped cubic manganites, although there is still a degree of variation in the reported results. 12

14 The Jahn-Teller interpretation of the splitting of the 529 ev XAS peak is different from interpretations made by previous investigators. The splitting was not explicitly addressed by Abbate [32] or Saitoh [20]. J.H. Park et al. [18] and E. Pelligren et. al.[33] assigned the lower of the two peaks to both e g up states and the higher of the two peaks (~ 530 ev) to the t 2g down states. While the t 2g down spin states will likely contribute to the spectra, we expect them to show up more weakly than the e g states due to a reduced hybridization to the oxygen 2p states (see Saitoh's calculation in figure 12). In addition, the doping dependences 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 4E J-T, where E J-T is the energy 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 electronic energy equal to 1/2 of the total splitting of the levels. At the same time there is an energy cost for structurally distorting the lattice. In the harmonic approximation this cost is half the electronic energy gain, meaning the total energy gain is 1/4 of the splitting of the levels. Therefore, since the experimentally observed splitting is near 1 ev, E J-T is estimated to be approximately 0.25 ev. The magnitude of E J-T is mostly important in comparison to other energy scales such as the one-electron bandwidth W. These comparisons and their implications will be discussed in section Low energy k-dependent electronic structure In this section we focus on the momentum dependence of the near-e F states as measured by high energy resolution ARPES. At the time of this writing, the only reported data has been from the Colorado/Stanford/Tokyo collaboration. We will concentrate on measurements from the bilayer material La 1.2 Sr 1.8 Mn 2 O 7. This material has a nominal doping level of.4 holes per Mn site (d 3.6 ) and more than two orders of magnitude decrease in resistivity at the ferromagnetic T c of 130K. The low temperature resistivity is unusually high - greater than 3 x10-3 ohm-cm and even has a slight upturn at the lowest temperatures. 6.1 Low temperature k-dependent data and a large "ghost" Fermi surface Figure 15 shows these near-e F states along various k-space directions, measured at 10K (ferromagnetic phase), after Dessau et. al. [36]. Directions of these 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), we observe a strong feature first visible at (.27π,0) which disperses towards the Fermi energy as we progress towards (π,0). In addition, there is a weak and broad feature at about -.6 ev which is strongest near the (0,0) point (at higher photon energies this feature evolves into a clearly resolvable peak, so we are confident that it is real). Panel c shows a continuation of the dispersion along the (π,0) --> (π,π) direction. In the first part of this cut the peak continues to disperse towards the Fermi energy, but surprisingly never reaches E F. Instead, 13

15 it attains its minimum energy near the angle (π,.27π), at which point it rapidly loses intensity as if weight was transferred above the Fermi energy. Beyond this point, the spectra in addition exhibit some evidence of bending back away from EF in a similar way from what would be expected for the opening of an excitation gap centered at EF. A very similar result is seen for the cut shown in panel 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 in panels 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 density approximation (LSDA+U) band structure calculations [37]. The calculation predicts a set of dispersive bands of e g symmetry mostly separated from a region of many relatively non-dispersive bands (t 2g d and oxygen p states). The band crossing E F near the (0,0) point is predicted to have principally d 3z 2-r2 out-of-plane character, while the two bands crossing between (π,0) and (π,π) are predicted to have primarily d x 2-y2 in-plane character. We find that there is a correspondence between many aspects of the experimental and theoretical data. First, the agreement in both energy position and dispersion rate between the experiment and theory along the (0,0)-(π,0) line is reasonably good, especially considering that we have not rescaled or shifted the energy scales to account for the often observed renormalization effects. Second, by taking advantage of the polarization of the incident photons we have performed a symmetry analysis on the main dispersive features (the ones predicted to cross E F along (π,0) - (π,π)) and found them to have primarily d x 2- y2 character [34], in agreement with the band theory prediction. Third the locations of the experimental minima in binding energy as well as the locations where the spectral weight is rapidly being depleted agree well with the predicted Fermi surface crossings. In other words, there is a locus of points in k-space where critical spectral behavior occurs, and this locus is found to closely resemble the band structure Fermi surface. This indicates that Luttinger's theorem [38] is obeyed for these compounds. Despite these agreements there are clear deviations between the experiment and theory, signaling additional physics not contained in the calculation. These deviations can tell us many of the details of the interactions responsible for the very unusual properties of the manganites. In particular, 1) The width of the ARPES features are anomalously broad, and do not sharpen up as they approach the Fermi momentum k F. This indicates that the dispersive peaks can not be described as single Fermi-Liquid-like quasiparticle (q.p.) excitations. 2) The spectral behavior at the locus of critical k-points discussed above is different from that expected at a real Fermi surface. This is why we call the locus a "ghost" Fermi surface. Specifically, we find a) the centroids of the experimental peaks never approach closer than approximately 0.65 ev to E F, while theoretically they are expected to reach E F. b) There is never more than a vanishingly small spectral weight at E F, even though the measurements were made in the ferromagnetic "metallic" state of the compound. This lack of spectral weight is termed the "pseudogap." To make sure that we simply didn't miss a Fermi crossing, we have made measurements along all the high symmetry directions as well as along many off-symmetry points (not shown), 14

16 have used a variety of photon polarizations and photon energies, and have repeated the measurements on more than 10 samples. 6.2 Bandwidth of the in-plane d x 2-y2 states Experimentally, the occupied part of the d x 2-y2 up-spin band starts approximately 1.5 ev below E F (Fig.15) and the unoccupied part of the d x 2-y2 up-spin band can be seen at least 1.5 ev above E F (Fig. 14). The total bare bandwidth of the d x 2-y2 state is therefore at least 3 ev, which is similar to the predictions of the LSDA calculation of Hamada [38]. This is not surprising since the dispersion rate of the experimental and theoretical bands was found to be similar. For the 3-dimensional compounds with similar doping (e.g. La.6 Sr.4 MnO 3 ) we expect the bare bandwidth to be up to 1.5 times larger due to dimensionality effects, although this will be reduced somewhat due to a distorted O-Mn-O bond-angle. Therefore, to first order we can expect La.6 Sr.4 MnO 3 to have a bare bandwidth of 4 ev. We schematically illustrate the ferromagnetic band structure for the most relevant d x 2-y2 (including d z 2-x2 and d z 2-y2 for the 3-d samples) symmetry states in Figure 16. Assuming J H to be the same for all compounds (it is an Intra-atomic term), the bandwidth W is larger or slightly larger than J H (4.5 ev and 3 ev vs. 2.7 ev), and so we expect that the up and down spin d x 2-y2 bands will not be completely separated but will overlap slightly. This implies that the manganites may not fit completely into the DE limit, in which J H. However, because E F is still far from the bottom of the down-spin states, the near-e F states should still be mostly spin polarized. This is consistent with the full spin polarization of the near-e F states observed by J.H. Park et al. [27] (see section 4.3). The large bandwidths are rather surprising, especially in the context of a system which may be expected to have strong correlations or polaronic effects. However, the quoted bandwidth should only be considered the bare or oneelectron bandwidth, which may be renormalized due to electron-phonon or other effects. Typically, these effects would be expected to change the observed dispersion rate of the ARPES peaks. However, as discussed in section 6.6, if the coupling is very strong, then the weight of the true quasiparticle peak can go to near zero and the dispersive ARPES peaks (consisting only of the incoherent part of the spectrum) may disperse as the bare particle. 6.3 Temperature dependent dispersion of La 1.2 Sr 1.8 Mn 2 O 7 Figure 17 shows the temperature dependence of the near-e F bands of La 1.2 Sr 1.8 Mn 2 O 7 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 are more severe at high temperatures) the sample was cleaved and initially measured at high temperature, after which it was cooled to low temperature and remeasured. Measurements on other samples were made in which the sample was cleaved cold and then warmed, with qualitatively consistent results. It is observed that along the (0,0)-->(π,0) direction where the states are farther from E F, the temperature-dependent effects are rather weak, whereas they are the 15

17 strongest at (π,.27π) which corresponds to the closest approach of the feature to E F, as well as to the k F predicted by the band theory calculation. It is seen that the high temperature spectrum is pushed back to higher energies and the amount of spectral weight near E F is reduced further, i.e. the pseudogap is affecting the high temperature spectra more dramatically than the low temperature spectra. This must be at least partially responsible for the large changes in the conductivity that occur across the phase transition. However, even at (π,.27π) the ARPES peak always remains pulled far back from E F, and the spectral weight reaching E F is vanishingly small. More details of the temperature dependence of the spectra of La 1.2 Sr 1.8 Mn 2 O 7 at (π,.27π) are shown in Fig.18. The triangles indicate the spectral weight found very near E F obtained over two different energy integration windows, and the diamonds show the energy shift of the leading edge (at two different positions on the edge) as a function of temperature. It is seen that both the near-e F weight and the position of the leading edge begin increasing at T c and then rise monotonically without saturation as the temperature is lowered. The onset of the changes at the sample's T c clearly indicate that they are directly associated with or responsible for the very large changes in conductivity at T c. Similar effects have also been observed by Saitoh et al. for the cubic perovskite La.82 Sr.18 MnO 3 (see figure 9). The temperature dependence of the observed changes is qualitatively incompatible with the prediction of double-exchange theory, which predicts a very small change in spectral weight in the opposite direction to that observed experimentally (see figure 2e). The fact that the spectral change saturate much more 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 theory makes predictions about the temperature dependence of the one-electron bandwidth W. As discussed in section 2.2 and shown in figure 2, double exchange tells us that to first order the hopping probability and hence the bandwidth should decrease by about 30% when going from the ferromagnetic to the paramagnetic phases. Considering the d x 2-y2 up-spin states, the band starts at the (0,0) point more than 1.5 ev below E F and extends to at least 1.5 ev above E F (see section 6.2). If the bandwidth was to change due to the double-exchange effect, we expect the change to be centered near the mean value of the band energy. In other words, the states at the extremum of the band near 1.5 ev binding energy should show a significant (30%) energy shift towards E F. 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 of rather large regions of in-plane ferromagnetic order, so that the local hopping probability is barely changed upon going through T c. This idea is consistent with recent transport and neutron scattering studies of the x=.3 bilayer compound, which have been interpreted as having 3D ferromagnetic order below the T c of 90K, and 2D ferromagnetic order between 90K and 300K [39]. Much more work needs to be done to understand this behavior, especially its connection to the pseudogap 16

18 6.4 Discussion of anomalous spectral properties - the photoemission lineshape and pseudogap The ARPES features of the manganites are anomalously broad and do not sharpen appreciably as k F is approached. Broad ARPES features are also observed in the high T c superconductors, and have been taken to indicate very anomalous non Fermi-Liquid like behavior [15,17]. In those materials, the normal-state features obtain a minimum width of a few tenths of a volt, which is much worse than the energy resolution. In the manganites, the features are much broader, with widths approaching 1 ev. The manganites also have a strongly suppressed spectral weight near E F which is termed a pseudogap. ARPES (as well as many other) measurements on the high T c superconductors have likewise observed a pseudogap in the high T c superconductors[40]. In the high T c s, the magnitude of this effect is on the order of 20 mev and is observed to occur primarily near the (π,0) points of the Brillouin zone. In the manganites the pseudogap effect is observed throughout the entire Brillouin zone and has a much larger magnitude of many tenths of an ev (note that the pseudogap is a soft gap, and so does not simply determine the activation energies). It is expected that much work will be needed to fully understand their properties. Here, we will try to give some first order explanations of these anomalous properties. We explore a couple of possible explanations for the anomalous spectral and physical properties of the manganites. Mechanisms that should be considered include gap formation due to static or fluctuating charge, spin, or orbital order; a Mott-Hubbard type gap; a splitting of the levels due to the Jahn-Teller effect; a Coulomb gap; and strong electron-lattice coupling. Although it is expected that correlation effects will play a role in these materials, the Mott-Hubbard type gap is expected to be centered at E F only for samples of integral electron-filling and so can not be responsible for the observed pseudogap. The splitting of the e g symmetry levels due to the Jahn- Teller effect should also only be centered at E F at special doping levels. A Coulomb gap is usually discussed in terms of localized (impurity) states [41]. The large amount of dispersion observed in figure 15 is in opposition with such localized states. On the other hand, the coupling of the electrons to a Boson such as a lattice distortion can give a qualitative explanation for many of the anomalous spectral properties. We begin by discussing the exact solution of the problem of a single electron coupled to a bath of Einstein phonons (or any other Boson) of frequency ω 0 [42]. The electron spectral function for this problem is an envelope of many individual peaks separated by ω 0, as illustrated in figures 19a and b. The multiple peaks indicate that a single electron is not an eigenstate of the system -- therefore the removal of an electron from the system occurs with a probability of shaking off a certain number of phonons. The quasiparticle peak or ``coherent'' part of the spectrum is the one with zero phonons shaken off and is the peak closest to the Fermi energy. In the strong coupling case the envelope function 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 17

19 coupling, the centroid or first moment of the distribution is equal to the energy of the electron in the absence of the coupling [42]. A known example of this type of distribution is the measured photoemission spectrum of gaseous Hydrogen, which shows a clear progression of many peaks, corresponding to the many different vibrational levels [17]. Following this logic, we suggest that the dispersive peaks we have measured should not be considered to be a single quasiparticle peak but should be considered to be an envelope of many individual peaks, in the spirit of the strong coupling arguments above (the individual peaks are probably not resolved due to lifetime, solid-state, and resolution effects). Second, in analogy to the single-electron calculation above, we argue that the centroid of the ARPES spectrum should have an energy equal or similar to the energy in the absence of the coupling, which in this case is the LSDA band energy. While this may not be a rigorous result in general, it does explain the surprisingly good agreement of the experiment and theory through much of the zone (see Fig. 19d). The quasiparticle peak, if it existed, would correspond to the portion of the spectrum nearest E F, and is found to have an almost vanishingly small weight for this material, indicating that the coupling is strong (this is also seen by the large width of the peaks). By Luttinger's theorem [38], we expect the quasiparticle peak to cross E F at the location predicted by the band theory calculation (non-interacting limit). A key point here is that when the quasiparticle peak crosses E F the entire photoemission peak must rapidly lose weight because the excitation can no longer be created (Fig. 19d). The centroid of the envelope therefore always stays well below E F with a minimum binding energy equal to the distance between the centroid of the distribution and the quasiparticle peak. The above scenario can give a first order explanation for both the broad ARPES peaks and the large reduction in spectral weight at E F (pseudogap). An important question within this scenario is then what type of Boson are the electrons coupling to? We gain insight into this question by examining the k- space dependence of the pseudogap. We have found that the pseudogap affects the entire Fermi surface to a similar degree with little or no anisotropy. This general lack of k-space dependence makes it less likely that charge, spin, or orbital ordering should play a dominant role in the gap opening, as these ordering phenomena should occur with a wavevector which will affect certain parts of the Brillouin zone more strongly than others. An example of this is the recently observed pseudogap effect in the high-t c superconductors which has a pronounced k-space dependence [40]. In those materials, the maximal gapping effect is near the (π,0) point of the Brillouin zone, signaling a possible origin from the antiferromagnetic fluctuations with wave vector near (π,π). A local effect, such as a lattice distortion, is more likely to give the isotropic effects observed in the manganites. This is consistent with the temperature-dependent structural distortions observed in the manganites [12-14] as well as the very large isotope effects [43]. However, the collective modes can also derive from degrees of freedom other than phonons. As the correlation effects are quite strong in these materials, which is manifested in the propensity of the material to have charge 18

20 and orbital order and/or inhomogeneity [44], other collective excitations may provide alternative explanation to the photoemission data. 6.5 Franck Condon analysis and lattice relaxation energies The Frank-Condon picture is an essentially equivalent way to discuss the strong coupling to phonons in the photoemission spectra. As illustrated in figure 20, we consider a configurational coordinate diagram where there is a parabola describing the phonon potential energy curve both for the ground state (N electron system) and the final state (N-1 electron system) of the photoemission absorption process. Due to the strong lattice effects, the two parabolas are displaced by an amount Q 1 -Q 0. We consider transitions between the ground state and any of the (vibrational) levels of the excited state, with the photoemission spectrum being a superposition of the possible transitions (due to additional broadening effects in the solid the individual levels may not be separately observable). The lowest energy transition occurs without exciting any phonons and will give rise to the portion of the spectrum closest to the Fermi energy. The vertical transition is the most probable and will correspond to the most intense portion of the spectrum. The difference between these two represents the difference in energy between the relaxed and unrelaxed state, that is, it represents the lattice relaxation energy E L. Looking at the most intense portion of the spectra at (π,.27π) or (.63π,.27π) which roughly correspond to k=k F, we estimate the lattice relaxation energy to be.65 ev in the ferromagnetic case (50K) and.8 ev for the paramagnetic case (200K) (see Fig 17). 6.6 Dimensionless coupling parameters The magnitude of the lattice relaxation energy E L discussed in section 6.5 or the Jahn-Teller energy E J-T discussed in section 5.3 are mostly important in comparison to the electron kinetic energy or hopping parameter t. To first order, we can obtain these quantities by a measurement of the dispersive bandwidth W, as discussed in section 6.2. For instance, in the lattice-electron coupling model proposed by Millis, there is a coupling constant, λ =2E J-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 the ferro or paramagnetic cases (see section 6.2 and 6.3) and following Millis's convention of a t which is 1/4 the bandwidth, we obtain a value for t of about 1 ev. We therefore find a coupling constant λ ~.5 ev/1 ev ~.5 which is less than but on the order of unity. A strict interpretation of this number within Millis model would tell us that the Jahn-Teller distortion is not strong enough to localize the electrons into polarons. Within the same model we can likewise determine the dimensionless coupling parameter λ associated with the lattice relaxation discussed in section 6.5 for the bilayer compound La 1.2 Sr 1.8 Mn 2 O 7. Using a full bandwidth W of 3 ev for the in-plane d x 2-y2 states and lattice relaxation energies E L of.65 ev and.8 ev, we obtain a coupling parameter slightly less than 2 for the ferromagnetic case and near 2.5 for the paramagnetic case. This indicates that these materials are in the strong coupling regime in both the ferromagnetic and 19

21 paramagnetic states. Within the picture outlined in section 6.5, this is consistent with the broad ARPES peaks and the vanishingly small quasiparticle weight (and hence pseudogap). However, because the energy scale for the Jahn-Teller effect is relatively weak, this indicates that some other distortions (such as for instance a breathing mode) or completely different types of collective excitations or local inhomogeneities should be considered. Implicit in the above discussions is that there is primarily one mechanism that competes with the kinetic energy to renormalize the physics. A distinct possibility is that there are two or more mechanisms, neither of which is strong enough on its own to localize an electron, but which can cooperate to have a strong effect. An example of this is the discussion by Emin of the cooperation between large and small polaron physics in localizing an electron [46]. 6.7 Summary of data from different samples and different temperatures Figure 21a shows a compilation of photoemission data from the three different families of the manganites, all with the same doping level of x=.4 holes per Mn site, while Fig. 21b shows the behavior of ρ vs. T for the same samples. The n=infinity sample has a finite N(E F ) and is metallic, the n=1 sample has a clear gap and is insulating, while the n=2 sample has a vanishingly small weight at E F and is barely metallic. As discussed in section 6.5, we can explain the pseudogap to first order within the context of strong coupling of the electrons to the lattice. As discussed in section 6.6, the coupling parameter λ is a dimensionless ratio of the lattice distortion energy over the one electron bandwidth W. Since W is largest (by dimensionality arguments) for the n=infinity sample and smallest for the n=1 sample, we expect that λ and hence the pseudogap effects should be smallest for the n=infinity samples and largest for the n=1 sample, as observed. We also have discussed how λ is observed to change across the ferromagnetic transition temperature. Therefore, the changes in the spectral weight at E F (pseudogap) with changing temperature also can be understood to first order within this simple model. Fig 22 is an attempt to summarize the layer-number and temperature dependent properties for a variety of the compounds into one plot, within the pretext that the coupling of the electrons to some boson (e.g. phonons) dominates the problem. The vertical axis is the density of states at E F, and the horizontal axis is the electron-boson coupling parameter λ. As the coupling is increased, the quasiparticle weight is reduced by the factor 1/Z for the reasons described in Fig 19 a and b. In concert with this reduction in quasiparticle weight, the quasiparticle band should exhibit reduced dispersion, or an effective mass increase by the same factor Z. The net result of this is that in the weak coupling limit N(E F ) is unchanged as a function of λ. In the very strong coupling limit, the system is composed of completely localized small polarons which can transport current only by tunneling from one lattice site to another, i.e. there are 20

22 no free carriers and no spectral weight at E F. Connecting these two limits there must be a region where the spectral weight is of an intermediate value, which is termed the intermediate coupling regime. In figures 8,9 and 18 we have shown that the spectral weight at E F is a strong function of temperature, with the increase starting just as the temperature is lowered through T c. We have also discussed how the coupling parameter λ changes as we change temperature. We illustrate the changing λ with temperature on this plot for the n=1, n=2, and n=infinity. At high temperatures they are all in the strong coupling regime where N(E F ) is zero and they are insulating. As the temperature is lowered double-exchange takes effect, the electron itinerancy energy increases, and λ decreases so that the system enters the intermediate coupling regime and the weight at E F is finite but still drastically reduced. Continued lowering of the temperature increases N(E F ) continuously, as seen in figures 9 and 18. However, as discussed before, N(E F ) is always well reduced from its expected (weak-coupling) value, so we argue that the coupling to the lattice is very significant even at the lowest temperatures. This is in opposition with the usual arguments which state that the strong coupling (e.g. polaronic) effects should only be important in the high temperature state, with the low temperature state consisting of essentially free electrons. The results shown here indicate that for the layered samples the electron-boson coupling critically affects the electronic structure even below T c, and probably is also important below T c for the 3-dimensional manganites. 7.0 Summary, Conclusions and Outlook The colossal magnetoresistive oxides display a large amount of unusual electronic and physical properties. It is therefore not surprising that the electronic structure of these materials is also found to be very unusual. In this chapter we have reviewed the current status of measurements of the electronic structure of the CMR oxides. Angle-integrated photoemission data from the (pseudo) cubic manganites have indicated: 1) A finite but very low spectral intensity at the Fermi energy E F in the low temperature ferromagnetic state, and zero weight at the Fermi energy in the high temperature paramagnetic state. This indicates that the metal-insulator transition is likely due to a change in the effective number of carriers, instead of a change in the carrier mobility. 2) A total spin polarization of the near-e F bands for measurements made in the low temperature ferromagnetic state. 3) The low energy charge fluctuations in the undoped parent insulators are primarily p-d type, i.e. they should be considered charge-transfer insulators. Angle-resolved photoemission (ARPES) measurements have been successfully obtained from cleaved single crystals of the layered manganites. In particular, measurements on the bi-layer sample La 1.2 Sr 1.8 Mn 2 O 7 have shown: 1) A temperature-dependent pseudogap centered at E F, similar in many respects to that seen in the pseudo cubic compounds. This pseudogap kills all 21

23 the weight at E F in the paramagnetic regime and leaves only a vanishingly small weight below T c. 2) Broad yet highly dispersive peaks which can not be interpreted as single quasiparticle excitations. 3) A locus of k-space regions where critical behavior is observed, which roughly matches the large Fermi surfaces predicted by band theory calculations. Since no clear Fermi surface crossing behavior is observed, the locus is described as a "ghost" Fermi surface. 4) Temperature dependent behavior which is qualitatively in contrast to the Double Exchange predictions. In particular, the spectral weight at E F increases continuously without an apparent saturation as the temperature is lowered below T c. Another important aspect of the work has been the determination of some of the key energy scales and coupling parameters for the CMR oxides. In particular, it is seen that: 1) The one-electron bandwidth W is approximately 3 ev for the ferromagnetic state of the bilayer manganites. W is expected to be higher (~ 4 ev) for the most metallic of the pseudocubic manganites. 2) The energy gain for Jahn-Teller distortions in the doped pseudocubic manganites is of order.25 ev or less. 3) The Hund's rule coupling energy J H is of order 2.7 ev (energy difference to add a down spin e g electron vs. an up-spin e g electron). 4) The lattice relaxation energy (Jahn-Teller plus other contributions) for the bilayer manganites of order.65 ev for the ferromagnetic state and.8 ev for the paramagnetic state. In general it is found that the low temperature ferromagnetic state of the CMR oxides can not be described as a normal metal. This is somewhat different from many of the earlier expectations, which considered only the high temperature paramagnetic state to be unusual (and probably controlled by polaronic effects). A discussion based upon strong (but varying) electron-lattice coupling in both the ferro and paramagnetic states appears to be able to qualitatively explain much of the anomalous behavior. Much more work both experimentally and theoretically needs to be done to fully understand and perhaps harness the beautiful and exotic behavior that the CMR oxides display. 8.0 Acknowledgments The 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, and Y. 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 Young Investigator Program for generous support. Most of the experiments were 22

24 performed at the Stanford Synchrotron Radiation Laboratory, which is supported by the Department of Energy. The Stanford work was supported by the 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, (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, (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, (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, (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 (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, (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) 23

25 [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, G.D. Mahan, Plenum Press (1990). [43] G. Zhao et al., Nature 381, 676 (1996) [44] S. Ishihara et al., Phys. Rev. B 55, 8280 (1997); S. Ishihara et al., Phys. Rev. B 56, 686 (1997) [45] A. J. Millis et al., Phys. Rev. B 54, 5389 (1996) [46] D. Emin in Science and Technology of Magnetic Oxides, M. Hundley, J. Nickel, R. Ramesh and Y. Tokura, eds., (Materials Research Society, 1998) [47] Y. Moritomo et al., Nature 380, 141 (1996) 24

26 Figure 1 - a) An MnO 6 octahedron. b) The MnO 2 plane, which is identical in structure to the CuO 2 planes of the high temperature superconductors. c) The crystal structure of the layered and cubic manganites. Figure 2. (a) The d 4 ion. (b) The d 3 ion. (c,d) An illustration of the concept of double exchange - the hopping matrix element as a function of spin alignment. (e) The double-exchange prediction for the bandwidths for the ferromagnetic and paramagnetic cases. Figure 3. An illustration of the Jahn Teller effect for the d 4 ion. Figure 4 a) A schematic of the photoemission process. b) An illustration of angle-resolved photoemission (ARPES) from a band crossing the Fermi energy. Figure 5 An illustration of the X-ray absorption (XAS) process, which gives unoccupied density of states information. Figure 6 Doping dependence of angle-integrated photoemission measurements of (La 1-x Ca x )MnO 3, from J.H. Park et al. [18] (a) Valence band and shallow core levels. The inset shows the doping dependence of the chemical potential shift. (b) Valence band spectra from panel a, after compensating for the chemical potential shifts. Figure 7 Doping dependence of angle-integrated photoemission measurements of (La 1-x Sr x )MnO 3, from Dessau et al [21]. The data is from single crystals cleaved and measured at T=10K. Figure 8 a) Temperature dependent angle-integrated photoemission spectra from J.H. Park et al. [18] from T c =260K La.67 Ca.33MnO3 (left panel) and from T c =330K La.7 Pb.3MnO3 (right panel). Figure 9 A plot of the near-e F spectral weight of pseudo-cubic La.82 Sr.18 MnO 3 (for two energy intervals) as a function of temperature, from Saitoh et al. [24]. The vertical axis is the relative weight compared to what is expected by band theory calculations, i.e. even at the lowest temperature, there is approximately a factor of 10 less spectral weight at E F than expected. The data is compared to the temperature dependent Drude weight measured by Okimoto et al. [25]. Figure 10 - Spin-resolved photoemission spectra by J.H. Park et al. [27] from a T c =350K thin film sample of La.7 Sr.3 MnO 3 at (a) T=40K and (b) T=380K. Figure 11 - Oxygen 1s XAS data of La (1-x) Sr x MnO 3 from M. Abbate et al.[32] Figure 12 - UPS and O 1s XAS of LaMnO 3 and SrMnO 3 and cluster model analysis from Saitoh et al. [20] Figure 13. Oxygen 1s XAS data from a single-layer d 3 (panel a) and d 4 sample (panel b) from C.-H. Park et al. [34]. The solid curves were the measurements at grazing incidence (E field out-of-plane) and the dotted curves were measurements at normal incidence (E field in-plane). The bottom curves of 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 (d 3.6 ) after C.-H. Park et al. [34]. The data includes 3-dimensional samples 25

27 (set C) and layered samples with one (set A) and two (set B) MnO 2 layers per unit cell. Set D shows the subtraction of the dotted from the solid curves from sets A and B. Figure 15. (a)-(d) Low temperature high resolution ARPES spectra from Dessau et al. [36] of La 1.2 Sr 1.8 Mn 2 O 7 along various high symmetry directions, as indicated at the top of each panel and by the arrows along the twodimensional Brillouin zone of panel (e). The 3 curved lines in panel f are the Fermi surfaces for the up-spin bands in LDA+U band theory calculations. The two x's are the experimental locations of closest approach to E F. (f) The upspin bands in an LDA+U band theory calculation [37] vs. experimentally determined peak centroids from panels a and c (tick marks). Figure 16. A schematic illustrating the up and down-spin density of states for both the layered and 3-dimensional manganites. The experimentally observed pseudogap at E F is also indicated. Figure 17 Temperature dependence of the near-e F bandstructure of La 1.2 Sr 1.8 Mn 2 O 7, after Saitoh et al. [24]. Figure 18. A compilation of temperature dependent data of La 1.2 Sr 1.8 Mn 2 O 7 taken at the k-space point (π,.27π), after Saitoh et al. [24]. The triangles indicate the spectral weight found very near E F obtained over two different energy integration windows, and the diamonds show the energy shift of the leading edge (at two different positions on the edge) as a function of temperature. Figure 19. a) Weak and strong coupling lineshapes for the problem of a single electron coupled to a bath of Einstein phonons c) k-dependent dispersion of a weakly coupled electron phonon system. d) extension to dispersion of strongly coupled electron-phonon system. Figure 20. A schematic of photoemission from a strongly coupled electron-phonon system (right panel), where Q is a generalized distortion. In the spirit of the Franck-Condon approximation, the vertical transition is the most 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 the electron-lattice coupling. Figure 21. a) Near-E F ARPES weight (pseudogap strength) vs. layer number n for (La,Sr) n+1 Mn n O 3n+1 (x=.4 holes per Mn site), from Dessau et al. [21] b) ρ vs. T for the same samples, from Moritomo et al.[47]. Figure 22. Schematic diagram showing the spectral weight at E F as a function of electron-boson coupling parameter λ. Included are approximate placements of three-dimensional, bi-layer and single-layer manganites as a function of temperature. 26

28 a) MnO 6 cluster b) MnO 2 plane Mn O c) Fig 1 Cleave -----> -----> -----> layered cub ic a) LaMnO 3 b) SrMnO 3 c) x=0 x=1 e g t 2g Mn 3+ 3d 4 e g t 2g Mn 4+ 3d 3 ~ t = t o cos(θ/2) θ e g electron itinerant t 2g electrons core-like S=3/2 d) Ferro ~ t = t o Para e) Fig 2 ρ(e) E F Para ~ t ~.707 t Ferro o W o J ~0.7W o E

29 MnO6 Mn ion stretch Oxygen ion eg dx2-y2, d3z2-r2 eg dx2-y2 d3z2-r2 Fig 3 t2g dxy, dxz, dyz t2g dxy dxz, dyz d3 e.g. CaMnO3 d4 e.g. LaMnO3 a) b) Energy E Band Structure (metal) ARPES Spectra hν VL E F hν E F k θ 1 θ 2 θ 3 θ 4 θ 5 Fig 4 Density of States k 1 k 2 k 3 k 4 k 5 E F a) Continuum b) E F hν Unoccupied states Valence band Core level DOS 0 Energy above E F Fig 5

30 La 1-x Sr x MnO 3 x=.5 Intensity (Arb Units) x= Energy Relative to E F (ev) d 3.5 d 3.6 d 3.7 d 3.82 d 4 Fig 6 Fig 7 La 0.67 Ca 0.33 MnO 3 T c =260K La 0.7 Pb 0.3 MnO 3 T c =330K Weight Ratio (Exp/Band) ev ev Drude weight Drude Weight (x10-2 ) T/T c Fig 8 Fig 9

31 Fig 10 Fig 11 (a) LaMnO 3 La 5p La 5d (b) SrMnO 3 Sr 4p Sr 4d e g e e g g t 2g e g t 2g t 2g e g e g t 2g Fig 12 d 3 d 5 d 2 d 4 d 4 L d 6 L d 3 L d 5 L d 5 L ENERGY RELATIVE TO E F (ev) d 7 L 2 d 4 L ENERGY RELATIVE TO E F (ev) d 6 L 2