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Soft X-ray investigation of strongly correlated electron systems
Journal of Electron Spectroscopy and Related Phenomena 144–147 (2005) 331–336
Soft X-ray investigation of strongly correlated electron systems D.J. Huang, C.T. Chen∗ National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan Available online 2 March 2005
Abstract Soft X-ray spectroscopy plays an important role for understanding the electronic structure of correlated electron materials. We review two examples of soft X-ray spectroscopic investigation on electron correlations and orbital symmetry in transition-metal oxides. The measurements show the existence of Coulomb correlations in CrO2 and the Mott–Hubbard character of 3d electrons. We conclude that CrO2 has a dualistic electronic nature, in which the states at the Fermi level are bandlike and while those at higher energies are strongly localized of completely different origin and symmetry. In addition, we demonstrate that linear dichroism in Mn 2p X-ray absorption is a powerful method to test the validity of models for orbital ordering in transition-metal oxides. Our linear dichroism measurements indicate that orbital ordering of the Mn eg electrons in La0.5 Sr1.5 MnO4 is dominated by x2 − z2 /y2 − z2 type of ordering. © 2004 Published by Elsevier B.V. Keywords: Strongly electron correlations; Soft X-ray absorption; Spin polarization; Orbital ordering; Magnetic materials
1. Introduction Correlated electron materials such as transition-metal (TM) oxides have recently attracted much attention [1]. These materials are often with interesting physical properties, and are also technologically important. The hottest topics of these materials includes non-conventional superconductivity, colossal maganetoresistance, novel phase transitions, and phase separation. These interesting properties are attributed to the strong coupling between the charge and spin of electrons and the lattice degrees of freedom in transition-metal oxides. Polarization-dependent soft X-ray absorption spectroscopy (XAS) [2] is a well-established technique to determine the orbital and spin characters of the ground state of an ion in transition-metal oxides, because XAS spectra strongly depend on the symmetry of the initial state of transition-metal ions. XAS spectra of O 1s and TM 2p absorptions can be understood straightforward in terms of transitions to final states subjected to the dipole selection rules. O 1s XAS spectra measure transitions from an O 1s core level to unoccupied O 2p states mixed with bands of primary TM character. One
∗
Corresponding author. E-mail address: [email protected] (C.T. Chen).
0368-2048/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.elspec.2005.01.213
can interpret O 1s XAS as a one-electron addition process, e.g., dn → dn+1 , if the influence of the O 1s core is neglected [3,4]. The structure in the measured O 1s XAS spectra near the threshold arise from covalent mixing of TM 3d and O 2p. Moreover, polarization-dependent TM L2,3 -edge XAS can lead us to reveal the spin state and orbital symmetry of transition-metal oxides and also reflect the hybridization between TM 3d and O 2p. For example, several experiments show that linear dichroism in TM 2p XAS provides us with a powerful means to pinpoint the spin state and orbital symmetry of La2−x Srx CuO4 [5,6], V2 O3 [7], and La0.5 Sr1.5 MnO4 [8]. In this paper, we review two of our recent works on orbital symmetry and electron correlations in transition-metal oxides. First, we present a spin-resolved electron spectroscopic experiment to identify the co-existence of band effects and Mott–Hubbard interactions in the electronic structure of CrO2 [9]. Spin-resolved XAS shows that CrO2 is a fine example for a strongly correlated system in which both band formation and strong correlation effects coexist. Then we show measurements of LD in Mn 2p-edge XAS of La1−x Sr1+x MnO4 [8]. The LD measurements are compared with multiplet calculations to unravel the orbital character of eg electrons in La0.5 Sr1.5 MnO4 . Finally, we discuss perspectives of inelastic soft X-ray scattering on correlated electron materials.
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2. Spin and orbital polarization of CrO2 CrO2 is an interesting half-metallic ferromagnet in which the majority spin states cross the Fermi level whereas the minority spin states show a band gap. Several experiments suggest that electron correlations are essential to account for the underlying physics of CrO2 , including photoemission [10], soft X-ray absorption [11], resistivity [12], and optical [13] measurements. The self-doping concept has been proposed to explain the anomalous properties of CrO2 based on bandstructure calculations with on-site Coulomb energy U taken into account (LDA+U), which indicate that Coulomb interactions indeed play an important role [14]. This picture is also proposed in a recent model that includes orbital correlations [15]. The latest LDA calculations, however, conclude that there is no need to include strong correlations of the Hubbard type [16]. Moreover, it is even suggested that the inclusion of a Hubbard U leads to unreasonable Kerr spectra [17]. Fig. 1 displays the O 1s XAS spectra of CrO2 measured with a photon energy resolution of 0.2 eV. The spectra recorded in total electron yield mode (solid line) and in the O KLL Auger partial electron yield mode (open triangles) are essentially identical, despite the fact that the probing depths of the two techniques are different, namely 100–200 and 15– ˚ respectively. This clearly demonstrates that our films 20 A, are of high quality in terms of cleanliness and chemical homogeneity in the sample surface region, and that the Auger mode does probe the bulk properties of CrO2 thin films. This fact is important because the Auger signal is later used to obtain the spin-polarized O 1s XAS spectrum as explained below. The inset in Fig. 1 shows that the main-peak at 529.6 eV photon energy exhibits an extremely strong polarization dependence, fully consistent with other XAS measurements [11], verifying the good quality of our CrO2 samples. In order to determine the electronic structure of CrO2 and to verify the predictions made by the various spin-dependent band structure calculations [18,19,14,16], we have measured
Fig. 1. O 1s XAS spectra of CrO2 measured in the total electron yield mode (solid line) and in the O KLL Auger partial electron yield mode (triangles) with the E vector of the light perpendicular to the c-axis. The inset displays the spectra with E c (dashed line) and E ⊥ c (solid line).
Fig. 2. Upper panel: measured spin-resolved O 1s absorption spectra of CrO2 with E ⊥ c and calculated spectra obtained by CI calculations in the vicinity of the main-peak. Lower panel: spin-polarization of the O 1s spectrum (filled circles), and calculated spin polarization curves obtained by LDA+U (dotted line, after [14]), FLAPW (dashed line) and cluster CI (solid line) calculations.
the spin-polarization of the conduction band using spinpolarized O 1s XAS [9]. Spin-resolved O 1s XAS spectra in the vicinity of the main-peak taken with E ⊥ c and its spin polarization are displayed in the top and the bottom panels of Fig. 2, respectively. The photon energy resolution is set to 0.4 eV. The measurement shows that the states closest to the Fermi level have a spin-polarization of (85 ± 10)%. These states are therefore almost fully spin-polarized, consistent with the predictions of band structure calculations [18,19,14,16]. Strikingly, the spin-polarization of the main-peak at 529.6 eV is only 50%. This is in strong disagreement with all band structure calculations which predict that the polarization of this feature of the conduction band should have been 100%. In fact, the spin polarization from the LSDA+U [14] and also our LDA calculations with full potential linear augmented plane waves show a constant spin polarization of 100% for energies from the Fermi level all the way to (and also beyond) the position of the main peak, as shown in Fig. 2. This discrepancy is an indication that strong correlation effects are present in the system. If we take correlation effects explicitly into account, at the expense of ignoring the band structure, we can reproduce the 50% spin polarization of the main-peak (but not of the states closest to Fermi level). By carrying out configuration–
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interaction (CI) calculations using a CrO6 cluster, we can identify the main peak as due to a transition from a high spin, fully magnetized, 3d2 initial state to a high spin 3d3 final state with 4 A2 symmetry [4]. Based on straight forward fractional parentage arguments, the addition of a spin-up or a spindown electron to the 3d2 state leads to the 3d3 4 A2 final state with a probability ratio of 1 : 13 , making the spin polarization of this main-peak (1 − 13 )/(1 + 13 ) = 21 , as shown in Fig. 2. Including a molecular field of 0.1 eV for the ferromagnetic state, the CI also reproduces the energy splitting between the spin up and spin down peaks as shown in the top panel of Fig. 2. This splitting is the Zeeman splitting between the ms =3/2 (spin-up) and ms =1/2 (spin-down) components of the 4 A electron addition state. It gives rise to a spin polarization 2 higher (lower) than the average of 50% for the low (high) energy side of the main-peak. The maximum value calculated using this CI model is 68%. It is remarkable that the spin polarization of the states near the Fermi level can be reproduced by band theory, but not by the CI cluster calculations, while the spin polarization at higher energies can be explained by CI but not by band theory. These spin-resolved data therefore strongly suggest that the electronic structure of CrO2 is dualistic in nature, in the sense that the states at the Fermi level are bandlike while those at higher energies are localized. We show the breakdown of the conventional idea that either band theory or CI theory should work well for a particular compound. Such an intermediate behavior between band theory and CI theory is the most remarkable and characteristic aspect of strongly correlated systems.
3. Orbital ordering of La0.5 Sr1.5 MnO4 Orbital ordering, which manifests itself in the spatial distribution of the outermost valence electrons, is an important topic in current research of transition-metal oxides, as the magnetic and transport properties are closely related to the orbital and charge degrees of freedom [20]. In particular, charge-orbital ordering of half-doped manganites has attracted much attention [21–27]. The mechanism of chargeorbital ordering is being hotly debated [28–34]. To observe orbital ordering directly is a difficult task. Experimental results of resonant X-ray scattering (RXS) at the Mn K-edge in La0.5 Sr1.5 MnO4 and LaMnO3 show removal of degeneracy between 4px and 4py ; these observations have been argued to be direct evidence of orbital ordering [35,36]. However, the origin of RXS at Mn K-edge is controversial. Orbital ordering in transition-metal oxides is typically accompanied by Jahn-Teller lattice distortion. Calculations in the scheme of LDA+U [37,38] and multiple scattering theory [39] indicate that RXS measurements pertain mainly to Jahn-Teller distortion, instead of directly observing 3d orbital ordering. Multiplet calculations have shown that one can use linear dichroism (LD) in soft X-ray absorption spectroscopy (XAS)
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Fig. 3. (a) LD and polarization-dependent XAS taken with E ⊥ c (solid line) and E c (broken line) of LaSrMnO4 . (b) Calculated LD spectrum of Mn3+ ions with occupied d3z2 −r2 orbitals. The calculated LD is plotted on the same scale as the measured one.
to identify the orbital character of 3d states in orbital-ordered manganites [40]. Half-doped manganites such as La0.5 Sr1.5 MnO4 exhibit CE-type antiferromagnetic (AFM) ordering and chargeorbital ordering [41,42,35]. They have a zigzag magnetic structure in which the magnetic moments of Mn on the chain form a ferromagnetic coupling, but AFM coupling between the zigzag chains. Below the charge-ordering (CO) temperature TCO = 217 K, the valence of La0.5 Sr1.5 MnO4 orders in an alternating pattern with two distinct sites identified as Mn3+ and Mn4+ [41,42]. The eg electrons on the nominal Mn3+ sites of La0.5 Sr1.5 MnO4 are believed to exhibit an orbital ordering of 3x2 − r 2 /3y2 − r 2 , in which occupied d3x2 −r2 and d3y2 −r2 orbitals are alternately arranged at two sublattices in the ab plane [26]. However, d3x2 −r2 and dx2 −z2 (d3y2 −r2 and dy2 −z2 ) orbitals might be mixed, because orbitals of these two types have the same spatial symmetry with respect to the MnO2 plane. To clarify the nature of orbital ordering in La0.5 Sr1.5 MnO4 is essential to reveal the origin of orbital ordering in half-doped manganites. Multiplet calculations have shown that one can use LD in L-edge XAS to characterize the 3d orbital character [40]. LD in XAS is defined as the difference between XAS spectra taken with the E vector of photons perpendicular and parallel to the crystal c-axis. To verify experimentally such a capability of LD, we measured the LD in Mn L2,3 -edge XAS of LaSrMnO4 , which is expected to exhibit 3z2 − r 2 “ferro-orbital” ordering. Fig. 3(a) shows our measurements of polarization-dependent XAS and LD on LaSrMnO4 . Most features in the measured LD at Mn L-edge are reproduced by multiplet calculations for Mn3+ ions with occupied d3z2 −r2 orbitals, as shown in Fig. 3(b), revealing that LD in L-edge XAS is an effective means to examine the orbital character of 3d electronic states in an orbital-ordered compound. We measured LD in XAS on La1−x Sr1+x MnO4 with varied doping to clarify further the origin of the LD signal, as
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shown in Fig. 4(a). Because the Jahn-Teller effect on the Mn4+ ions is insignificant [33,34], the contribution of 3d orbitals of these ions to LD is much smaller than that of Mn3+ ions. With increasing doping, the proportion of Mn3+ ions decreases; the LD magnitude of doped La1−x Sr1+x MnO4 diminishes. Note that the magnitude of LD decreases more rapidly than that from a simple picture of Mn3+ –Mn4+ dilution. In particular, the LD magnitude of La0.5 Sr1.5 MnO4 is ∼ 1/4 that observed for LaSrMnO4 ; its sign at the L2 -edge is the same as that of LaSrMnO4 . To identify the orbital character of the occupied eg states, by using a model of MnO6 cluster based on configuration interaction [4], we calculated LD spectra of Mn3+ with dx2 −z2 /dy2 −z2 and d3x2 −r2 /d3y2 −r2 orbitals occupied, as shown in Fig. 4(b) [43]. Overall the calculated LD of occupied in-plane orbitals such as d3x2 −r2 and d3y2 −r2 is with sign reversed to that of out-of-plane orbitals such as d3z2 −r2 , dx2 −z2 , and dy2 −z2 . Surprisingly the conventional orbital ordering model of 3x2 − r 2 /3y2 − r 2 type is incompatible with LD measurements. The calculated LD of 3x2 − r 2 /3y2 − r 2 -type orbital ordering is with sign reversed to that of measured LD from La0.5 Sr1.5 MnO4 . One might suspect this inconsistency could result from anisotropic eg charge distribution on the Mn4+ sites. If so, only eg charge with d3z2 −r2 or dx2 −z2 /dy2 −z2 polarization transferred from Mn3+ to Mn4+ could give rise to a LD similar to the measurement. However, even in the most unfavorable case, that is, even if the transferred eg charge on the Mn4+ site were maximum (leading to equal charges on both Mn sites) and fully (3z2 − r 2 )-polarized, only half of the observed LD could be accounted for. This anisotropy gives opposite contributions to LD with respect to the measurement; the inconsistency can not be reconciled even if the anisotropic charge distribution of Mn4+ was taken into account. Furthermore, the lineshape of the measured LD spectrum for x = 0.5 is similar to those from calculations for Mn3+ with occupied d3z2 −r2 or dx2 −z2 /dy2 −z2 orbitals, implying that La0.5 Sr1.5 MnO4 has an orbital polarization of strong z character, e.g., d3z2 −r2 or dx2 −z2 /dy2 −z2 . If La0.5 Sr1.5 MnO4 exhibited 3z2 − r 2 orbital ordering, all Mn3+ sites, i.e., half of all Mn atoms, would contribute to LD and its magnitude at Mn L2 -edge would be half of that observed in LaSrMnO4 , in contrast to the measurements. If La0.5 Sr1.5 MnO4 exhibits x2 − z2 /y2 − z2 orbital ordering, by choosing LD as the difference in XAS spectra taken with the E vector parallel to x and z axes, we observe essentially linear dichroism resulting only from the sublattice with occupied dy2 −z2 . In other words, only half of Mn3+ sites contribute to LD; one quarter of Mn atoms contribute to LD, consistent with the measurements. Our LD measurements thus suggest that orbital ordering of the eg states on the Mn site in La0.5 Sr1.5 MnO4 is dominated by x2 − z2 /y2 − z2 type. In fact, LDA+U calculations give rise to an orbital ordering dominated by x2 − z2 /y2 − z2 on the Mn3+ sites of La0.5 Sr1.5 MnO4 . Interestingly we found that La0.5 Sr1.5 MnO4 would exhibit 3x2 − r 2 /3y2 − r 2 orbital ordering if the on-site Coulomb interactions were not
Fig. 4. (a) LD in Mn L2,3 -edge XAS of La1−x Sr1+x MnO4 with varied doping. Linear-dichroism spectra were derived from XAS normalized to the same peak intensity at Mn L3 -edge and measured at 300 K for x ≤ 0.35 and 150 K for x = 0.5. (b) Calculated LD spectra of Mn3+ ions with dx2 −z2 /dy2 −z2 and d3x2 −r2 /d3y2 −r2 orbitals occupied.
explicitly included, in agreement with previous LDA calculations [33]. Such a cross-type orbital ordering results from a combined effect of AFM structure, Jahn-Teller distortion, and the on-site Coulomb interactions of 3d electrons. The existence of orbital ordering of cross-type x2 − 2 z /y2 − z2 can be understood within the framework of crystal field effect with lattice distortion taken into account. On the Mn3+ sites of a cubic perovskite, eg orbitals of 3y2 − r 2 (3x2 − r 2 ) symmetry are preferentially occupied if the Mn–O length is elongated along the y (x) direction; y2 − z2 (x2 − z2 ) orbitals are occupied if the Mn–O length is contracted along the x (y) direction, as shown in Fig. 5. For example, in CEtype charge-orbital-ordered half-doped manganites of cubic perovskite such as La0.5 Ca0.5 MnO3 , the Mn3+ site exhibits a large Jahn-Teller distortion, in which the Mn–O length is elongated alternately along the x and y directions (two long ˚ along the zigzag chain and four short bonds bonds of 2.06 A ˚ [44], producing 3x2 − r 2 /3y2 − r 2 orbital orderof 1.92 A) ing. As for La0.5 Sr1.5 MnO4 , the shear-type distortion leads effectively to alternate contractions of along the x and y directions in La0.5 Sr1.5 MnO4 , because the longer in-plane Mn–O ˚ is close to the out-of-plane Mn–O length length (2.00 A) ˚ (1.98 A), while the shorter in-plane Mn–O length is 1.84 ˚ A. Orbital ordering of x2 − z2 /y2 − z2 is expected to be energetically more favorable than that of 3x2 − r 2 /3y2 − r 2 .
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could lead us to open a new era in the research of low-energy excitations of correlated compounds.
Acknowledgements
Fig. 5. View of d3y2 −r2 and dx2 −z2 orbitals on the Mn3+ sites with different Jahn-Teller distortions. (a and b) Show the Mn–O length elongated along the y direction and contracted along the x direction, respectively. Filled circles denote O atoms in which 2p orbitals are omitted for clarity.
Note that small tetragonal distortions with c/a = 0.98 and c/a = 1.04 in strained thin films of La0.5 Sr0.5 MnO3 can result in ferro-orbital ordering of x2 − y2 and 3z2 − r 2 , respectively [45,46]. In short, we demonstrate that LD in Mn 2p XAS is a powerful method to test the validity of models for orbital ordering in transition-metal oxides. With LD measurements, we inferred that orbital ordering of the Mn eg electrons in La0.5 Sr1.5 MnO4 is dominated by x2 − z2 /y2 − z2 type, as corroborated by our LDA+U calculations. Orbital ordering of Mn eg electrons in La0.5 Sr1.5 MnO4 is derived from a combined effect of antiferromagnetic structure, Jahn-Teller distortion, and on-site Coulomb interactions.
4. Perspective of soft X-ray spectroscopies Recent advances in synchrotron storage ring, soft X-ray beamline technology, and X-ray spectrometers provide us with great opportunities in future scientific research of correlated electron materials using soft X-rays, particularly in the areas of soft X-ray scattering. Inelastic soft-X-ray scattering experiments are powerful bulk-sensitive spectroscopic methods for probing the electronic structure of correlated electron systems, because of the photon-in-photon-out experimental technique. In addition, inelastic soft X-ray scattering spectroscopy is particularly suitable for probing the low energy electron excitations crossing the Fermi level of transition-metal compounds, because the soft X-ray spectral region covers the structure-rich core-level excitations of many important elements, and the spectral broadening due to core-hole lifetime inherited XAS and X-ray fluorescence spectroscopy can be avoided [47]. Furthermore, this technique is free from the interference of electric and magnetic fields; one therefore can employ inelastic soft X-ray scattering to study physical properties under extreme conditions. Taking the concept of energy-compensation in a monochromator-spectrometor set-up, recently Fung et al. have proposed a new design of a high-efficiency monochromator-spectrometor for inelastic soft-X-ray scattering [48]. This new set-up would enable experiments of inelastic soft-X-ray scattering with an efficiency of two orders of magnitudes higher than that of the conventional design and
We thank A. Fujimori, G.Y. Guo, T. Jo, H.-J. Lin, A. Tanaka, and L.H. Tjeng for valuable discussions and collaboration on previously published results reviewed in this work.
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Soft X-ray investigation of strongly correlated electron systems D.J. Huang, C.T. Chen∗ National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan Available online 2 March 2005
Abstract Soft X-ray spectroscopy plays an important role for understanding the electronic structure of correlated electron materials. We review two examples of soft X-ray spectroscopic investigation on electron correlations and orbital symmetry in transition-metal oxides. The measurements show the existence of Coulomb correlations in CrO2 and the Mott–Hubbard character of 3d electrons. We conclude that CrO2 has a dualistic electronic nature, in which the states at the Fermi level are bandlike and while those at higher energies are strongly localized of completely different origin and symmetry. In addition, we demonstrate that linear dichroism in Mn 2p X-ray absorption is a powerful method to test the validity of models for orbital ordering in transition-metal oxides. Our linear dichroism measurements indicate that orbital ordering of the Mn eg electrons in La0.5 Sr1.5 MnO4 is dominated by x2 − z2 /y2 − z2 type of ordering. © 2004 Published by Elsevier B.V. Keywords: Strongly electron correlations; Soft X-ray absorption; Spin polarization; Orbital ordering; Magnetic materials
1. Introduction Correlated electron materials such as transition-metal (TM) oxides have recently attracted much attention [1]. These materials are often with interesting physical properties, and are also technologically important. The hottest topics of these materials includes non-conventional superconductivity, colossal maganetoresistance, novel phase transitions, and phase separation. These interesting properties are attributed to the strong coupling between the charge and spin of electrons and the lattice degrees of freedom in transition-metal oxides. Polarization-dependent soft X-ray absorption spectroscopy (XAS) [2] is a well-established technique to determine the orbital and spin characters of the ground state of an ion in transition-metal oxides, because XAS spectra strongly depend on the symmetry of the initial state of transition-metal ions. XAS spectra of O 1s and TM 2p absorptions can be understood straightforward in terms of transitions to final states subjected to the dipole selection rules. O 1s XAS spectra measure transitions from an O 1s core level to unoccupied O 2p states mixed with bands of primary TM character. One
∗
Corresponding author. E-mail address: [email protected] (C.T. Chen).
0368-2048/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.elspec.2005.01.213
can interpret O 1s XAS as a one-electron addition process, e.g., dn → dn+1 , if the influence of the O 1s core is neglected [3,4]. The structure in the measured O 1s XAS spectra near the threshold arise from covalent mixing of TM 3d and O 2p. Moreover, polarization-dependent TM L2,3 -edge XAS can lead us to reveal the spin state and orbital symmetry of transition-metal oxides and also reflect the hybridization between TM 3d and O 2p. For example, several experiments show that linear dichroism in TM 2p XAS provides us with a powerful means to pinpoint the spin state and orbital symmetry of La2−x Srx CuO4 [5,6], V2 O3 [7], and La0.5 Sr1.5 MnO4 [8]. In this paper, we review two of our recent works on orbital symmetry and electron correlations in transition-metal oxides. First, we present a spin-resolved electron spectroscopic experiment to identify the co-existence of band effects and Mott–Hubbard interactions in the electronic structure of CrO2 [9]. Spin-resolved XAS shows that CrO2 is a fine example for a strongly correlated system in which both band formation and strong correlation effects coexist. Then we show measurements of LD in Mn 2p-edge XAS of La1−x Sr1+x MnO4 [8]. The LD measurements are compared with multiplet calculations to unravel the orbital character of eg electrons in La0.5 Sr1.5 MnO4 . Finally, we discuss perspectives of inelastic soft X-ray scattering on correlated electron materials.
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2. Spin and orbital polarization of CrO2 CrO2 is an interesting half-metallic ferromagnet in which the majority spin states cross the Fermi level whereas the minority spin states show a band gap. Several experiments suggest that electron correlations are essential to account for the underlying physics of CrO2 , including photoemission [10], soft X-ray absorption [11], resistivity [12], and optical [13] measurements. The self-doping concept has been proposed to explain the anomalous properties of CrO2 based on bandstructure calculations with on-site Coulomb energy U taken into account (LDA+U), which indicate that Coulomb interactions indeed play an important role [14]. This picture is also proposed in a recent model that includes orbital correlations [15]. The latest LDA calculations, however, conclude that there is no need to include strong correlations of the Hubbard type [16]. Moreover, it is even suggested that the inclusion of a Hubbard U leads to unreasonable Kerr spectra [17]. Fig. 1 displays the O 1s XAS spectra of CrO2 measured with a photon energy resolution of 0.2 eV. The spectra recorded in total electron yield mode (solid line) and in the O KLL Auger partial electron yield mode (open triangles) are essentially identical, despite the fact that the probing depths of the two techniques are different, namely 100–200 and 15– ˚ respectively. This clearly demonstrates that our films 20 A, are of high quality in terms of cleanliness and chemical homogeneity in the sample surface region, and that the Auger mode does probe the bulk properties of CrO2 thin films. This fact is important because the Auger signal is later used to obtain the spin-polarized O 1s XAS spectrum as explained below. The inset in Fig. 1 shows that the main-peak at 529.6 eV photon energy exhibits an extremely strong polarization dependence, fully consistent with other XAS measurements [11], verifying the good quality of our CrO2 samples. In order to determine the electronic structure of CrO2 and to verify the predictions made by the various spin-dependent band structure calculations [18,19,14,16], we have measured
Fig. 1. O 1s XAS spectra of CrO2 measured in the total electron yield mode (solid line) and in the O KLL Auger partial electron yield mode (triangles) with the E vector of the light perpendicular to the c-axis. The inset displays the spectra with E c (dashed line) and E ⊥ c (solid line).
Fig. 2. Upper panel: measured spin-resolved O 1s absorption spectra of CrO2 with E ⊥ c and calculated spectra obtained by CI calculations in the vicinity of the main-peak. Lower panel: spin-polarization of the O 1s spectrum (filled circles), and calculated spin polarization curves obtained by LDA+U (dotted line, after [14]), FLAPW (dashed line) and cluster CI (solid line) calculations.
the spin-polarization of the conduction band using spinpolarized O 1s XAS [9]. Spin-resolved O 1s XAS spectra in the vicinity of the main-peak taken with E ⊥ c and its spin polarization are displayed in the top and the bottom panels of Fig. 2, respectively. The photon energy resolution is set to 0.4 eV. The measurement shows that the states closest to the Fermi level have a spin-polarization of (85 ± 10)%. These states are therefore almost fully spin-polarized, consistent with the predictions of band structure calculations [18,19,14,16]. Strikingly, the spin-polarization of the main-peak at 529.6 eV is only 50%. This is in strong disagreement with all band structure calculations which predict that the polarization of this feature of the conduction band should have been 100%. In fact, the spin polarization from the LSDA+U [14] and also our LDA calculations with full potential linear augmented plane waves show a constant spin polarization of 100% for energies from the Fermi level all the way to (and also beyond) the position of the main peak, as shown in Fig. 2. This discrepancy is an indication that strong correlation effects are present in the system. If we take correlation effects explicitly into account, at the expense of ignoring the band structure, we can reproduce the 50% spin polarization of the main-peak (but not of the states closest to Fermi level). By carrying out configuration–
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interaction (CI) calculations using a CrO6 cluster, we can identify the main peak as due to a transition from a high spin, fully magnetized, 3d2 initial state to a high spin 3d3 final state with 4 A2 symmetry [4]. Based on straight forward fractional parentage arguments, the addition of a spin-up or a spindown electron to the 3d2 state leads to the 3d3 4 A2 final state with a probability ratio of 1 : 13 , making the spin polarization of this main-peak (1 − 13 )/(1 + 13 ) = 21 , as shown in Fig. 2. Including a molecular field of 0.1 eV for the ferromagnetic state, the CI also reproduces the energy splitting between the spin up and spin down peaks as shown in the top panel of Fig. 2. This splitting is the Zeeman splitting between the ms =3/2 (spin-up) and ms =1/2 (spin-down) components of the 4 A electron addition state. It gives rise to a spin polarization 2 higher (lower) than the average of 50% for the low (high) energy side of the main-peak. The maximum value calculated using this CI model is 68%. It is remarkable that the spin polarization of the states near the Fermi level can be reproduced by band theory, but not by the CI cluster calculations, while the spin polarization at higher energies can be explained by CI but not by band theory. These spin-resolved data therefore strongly suggest that the electronic structure of CrO2 is dualistic in nature, in the sense that the states at the Fermi level are bandlike while those at higher energies are localized. We show the breakdown of the conventional idea that either band theory or CI theory should work well for a particular compound. Such an intermediate behavior between band theory and CI theory is the most remarkable and characteristic aspect of strongly correlated systems.
3. Orbital ordering of La0.5 Sr1.5 MnO4 Orbital ordering, which manifests itself in the spatial distribution of the outermost valence electrons, is an important topic in current research of transition-metal oxides, as the magnetic and transport properties are closely related to the orbital and charge degrees of freedom [20]. In particular, charge-orbital ordering of half-doped manganites has attracted much attention [21–27]. The mechanism of chargeorbital ordering is being hotly debated [28–34]. To observe orbital ordering directly is a difficult task. Experimental results of resonant X-ray scattering (RXS) at the Mn K-edge in La0.5 Sr1.5 MnO4 and LaMnO3 show removal of degeneracy between 4px and 4py ; these observations have been argued to be direct evidence of orbital ordering [35,36]. However, the origin of RXS at Mn K-edge is controversial. Orbital ordering in transition-metal oxides is typically accompanied by Jahn-Teller lattice distortion. Calculations in the scheme of LDA+U [37,38] and multiple scattering theory [39] indicate that RXS measurements pertain mainly to Jahn-Teller distortion, instead of directly observing 3d orbital ordering. Multiplet calculations have shown that one can use linear dichroism (LD) in soft X-ray absorption spectroscopy (XAS)
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Fig. 3. (a) LD and polarization-dependent XAS taken with E ⊥ c (solid line) and E c (broken line) of LaSrMnO4 . (b) Calculated LD spectrum of Mn3+ ions with occupied d3z2 −r2 orbitals. The calculated LD is plotted on the same scale as the measured one.
to identify the orbital character of 3d states in orbital-ordered manganites [40]. Half-doped manganites such as La0.5 Sr1.5 MnO4 exhibit CE-type antiferromagnetic (AFM) ordering and chargeorbital ordering [41,42,35]. They have a zigzag magnetic structure in which the magnetic moments of Mn on the chain form a ferromagnetic coupling, but AFM coupling between the zigzag chains. Below the charge-ordering (CO) temperature TCO = 217 K, the valence of La0.5 Sr1.5 MnO4 orders in an alternating pattern with two distinct sites identified as Mn3+ and Mn4+ [41,42]. The eg electrons on the nominal Mn3+ sites of La0.5 Sr1.5 MnO4 are believed to exhibit an orbital ordering of 3x2 − r 2 /3y2 − r 2 , in which occupied d3x2 −r2 and d3y2 −r2 orbitals are alternately arranged at two sublattices in the ab plane [26]. However, d3x2 −r2 and dx2 −z2 (d3y2 −r2 and dy2 −z2 ) orbitals might be mixed, because orbitals of these two types have the same spatial symmetry with respect to the MnO2 plane. To clarify the nature of orbital ordering in La0.5 Sr1.5 MnO4 is essential to reveal the origin of orbital ordering in half-doped manganites. Multiplet calculations have shown that one can use LD in L-edge XAS to characterize the 3d orbital character [40]. LD in XAS is defined as the difference between XAS spectra taken with the E vector of photons perpendicular and parallel to the crystal c-axis. To verify experimentally such a capability of LD, we measured the LD in Mn L2,3 -edge XAS of LaSrMnO4 , which is expected to exhibit 3z2 − r 2 “ferro-orbital” ordering. Fig. 3(a) shows our measurements of polarization-dependent XAS and LD on LaSrMnO4 . Most features in the measured LD at Mn L-edge are reproduced by multiplet calculations for Mn3+ ions with occupied d3z2 −r2 orbitals, as shown in Fig. 3(b), revealing that LD in L-edge XAS is an effective means to examine the orbital character of 3d electronic states in an orbital-ordered compound. We measured LD in XAS on La1−x Sr1+x MnO4 with varied doping to clarify further the origin of the LD signal, as
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shown in Fig. 4(a). Because the Jahn-Teller effect on the Mn4+ ions is insignificant [33,34], the contribution of 3d orbitals of these ions to LD is much smaller than that of Mn3+ ions. With increasing doping, the proportion of Mn3+ ions decreases; the LD magnitude of doped La1−x Sr1+x MnO4 diminishes. Note that the magnitude of LD decreases more rapidly than that from a simple picture of Mn3+ –Mn4+ dilution. In particular, the LD magnitude of La0.5 Sr1.5 MnO4 is ∼ 1/4 that observed for LaSrMnO4 ; its sign at the L2 -edge is the same as that of LaSrMnO4 . To identify the orbital character of the occupied eg states, by using a model of MnO6 cluster based on configuration interaction [4], we calculated LD spectra of Mn3+ with dx2 −z2 /dy2 −z2 and d3x2 −r2 /d3y2 −r2 orbitals occupied, as shown in Fig. 4(b) [43]. Overall the calculated LD of occupied in-plane orbitals such as d3x2 −r2 and d3y2 −r2 is with sign reversed to that of out-of-plane orbitals such as d3z2 −r2 , dx2 −z2 , and dy2 −z2 . Surprisingly the conventional orbital ordering model of 3x2 − r 2 /3y2 − r 2 type is incompatible with LD measurements. The calculated LD of 3x2 − r 2 /3y2 − r 2 -type orbital ordering is with sign reversed to that of measured LD from La0.5 Sr1.5 MnO4 . One might suspect this inconsistency could result from anisotropic eg charge distribution on the Mn4+ sites. If so, only eg charge with d3z2 −r2 or dx2 −z2 /dy2 −z2 polarization transferred from Mn3+ to Mn4+ could give rise to a LD similar to the measurement. However, even in the most unfavorable case, that is, even if the transferred eg charge on the Mn4+ site were maximum (leading to equal charges on both Mn sites) and fully (3z2 − r 2 )-polarized, only half of the observed LD could be accounted for. This anisotropy gives opposite contributions to LD with respect to the measurement; the inconsistency can not be reconciled even if the anisotropic charge distribution of Mn4+ was taken into account. Furthermore, the lineshape of the measured LD spectrum for x = 0.5 is similar to those from calculations for Mn3+ with occupied d3z2 −r2 or dx2 −z2 /dy2 −z2 orbitals, implying that La0.5 Sr1.5 MnO4 has an orbital polarization of strong z character, e.g., d3z2 −r2 or dx2 −z2 /dy2 −z2 . If La0.5 Sr1.5 MnO4 exhibited 3z2 − r 2 orbital ordering, all Mn3+ sites, i.e., half of all Mn atoms, would contribute to LD and its magnitude at Mn L2 -edge would be half of that observed in LaSrMnO4 , in contrast to the measurements. If La0.5 Sr1.5 MnO4 exhibits x2 − z2 /y2 − z2 orbital ordering, by choosing LD as the difference in XAS spectra taken with the E vector parallel to x and z axes, we observe essentially linear dichroism resulting only from the sublattice with occupied dy2 −z2 . In other words, only half of Mn3+ sites contribute to LD; one quarter of Mn atoms contribute to LD, consistent with the measurements. Our LD measurements thus suggest that orbital ordering of the eg states on the Mn site in La0.5 Sr1.5 MnO4 is dominated by x2 − z2 /y2 − z2 type. In fact, LDA+U calculations give rise to an orbital ordering dominated by x2 − z2 /y2 − z2 on the Mn3+ sites of La0.5 Sr1.5 MnO4 . Interestingly we found that La0.5 Sr1.5 MnO4 would exhibit 3x2 − r 2 /3y2 − r 2 orbital ordering if the on-site Coulomb interactions were not
Fig. 4. (a) LD in Mn L2,3 -edge XAS of La1−x Sr1+x MnO4 with varied doping. Linear-dichroism spectra were derived from XAS normalized to the same peak intensity at Mn L3 -edge and measured at 300 K for x ≤ 0.35 and 150 K for x = 0.5. (b) Calculated LD spectra of Mn3+ ions with dx2 −z2 /dy2 −z2 and d3x2 −r2 /d3y2 −r2 orbitals occupied.
explicitly included, in agreement with previous LDA calculations [33]. Such a cross-type orbital ordering results from a combined effect of AFM structure, Jahn-Teller distortion, and the on-site Coulomb interactions of 3d electrons. The existence of orbital ordering of cross-type x2 − 2 z /y2 − z2 can be understood within the framework of crystal field effect with lattice distortion taken into account. On the Mn3+ sites of a cubic perovskite, eg orbitals of 3y2 − r 2 (3x2 − r 2 ) symmetry are preferentially occupied if the Mn–O length is elongated along the y (x) direction; y2 − z2 (x2 − z2 ) orbitals are occupied if the Mn–O length is contracted along the x (y) direction, as shown in Fig. 5. For example, in CEtype charge-orbital-ordered half-doped manganites of cubic perovskite such as La0.5 Ca0.5 MnO3 , the Mn3+ site exhibits a large Jahn-Teller distortion, in which the Mn–O length is elongated alternately along the x and y directions (two long ˚ along the zigzag chain and four short bonds bonds of 2.06 A ˚ [44], producing 3x2 − r 2 /3y2 − r 2 orbital orderof 1.92 A) ing. As for La0.5 Sr1.5 MnO4 , the shear-type distortion leads effectively to alternate contractions of along the x and y directions in La0.5 Sr1.5 MnO4 , because the longer in-plane Mn–O ˚ is close to the out-of-plane Mn–O length length (2.00 A) ˚ (1.98 A), while the shorter in-plane Mn–O length is 1.84 ˚ A. Orbital ordering of x2 − z2 /y2 − z2 is expected to be energetically more favorable than that of 3x2 − r 2 /3y2 − r 2 .
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could lead us to open a new era in the research of low-energy excitations of correlated compounds.
Acknowledgements
Fig. 5. View of d3y2 −r2 and dx2 −z2 orbitals on the Mn3+ sites with different Jahn-Teller distortions. (a and b) Show the Mn–O length elongated along the y direction and contracted along the x direction, respectively. Filled circles denote O atoms in which 2p orbitals are omitted for clarity.
Note that small tetragonal distortions with c/a = 0.98 and c/a = 1.04 in strained thin films of La0.5 Sr0.5 MnO3 can result in ferro-orbital ordering of x2 − y2 and 3z2 − r 2 , respectively [45,46]. In short, we demonstrate that LD in Mn 2p XAS is a powerful method to test the validity of models for orbital ordering in transition-metal oxides. With LD measurements, we inferred that orbital ordering of the Mn eg electrons in La0.5 Sr1.5 MnO4 is dominated by x2 − z2 /y2 − z2 type, as corroborated by our LDA+U calculations. Orbital ordering of Mn eg electrons in La0.5 Sr1.5 MnO4 is derived from a combined effect of antiferromagnetic structure, Jahn-Teller distortion, and on-site Coulomb interactions.
4. Perspective of soft X-ray spectroscopies Recent advances in synchrotron storage ring, soft X-ray beamline technology, and X-ray spectrometers provide us with great opportunities in future scientific research of correlated electron materials using soft X-rays, particularly in the areas of soft X-ray scattering. Inelastic soft-X-ray scattering experiments are powerful bulk-sensitive spectroscopic methods for probing the electronic structure of correlated electron systems, because of the photon-in-photon-out experimental technique. In addition, inelastic soft X-ray scattering spectroscopy is particularly suitable for probing the low energy electron excitations crossing the Fermi level of transition-metal compounds, because the soft X-ray spectral region covers the structure-rich core-level excitations of many important elements, and the spectral broadening due to core-hole lifetime inherited XAS and X-ray fluorescence spectroscopy can be avoided [47]. Furthermore, this technique is free from the interference of electric and magnetic fields; one therefore can employ inelastic soft X-ray scattering to study physical properties under extreme conditions. Taking the concept of energy-compensation in a monochromator-spectrometor set-up, recently Fung et al. have proposed a new design of a high-efficiency monochromator-spectrometor for inelastic soft-X-ray scattering [48]. This new set-up would enable experiments of inelastic soft-X-ray scattering with an efficiency of two orders of magnitudes higher than that of the conventional design and
We thank A. Fujimori, G.Y. Guo, T. Jo, H.-J. Lin, A. Tanaka, and L.H. Tjeng for valuable discussions and collaboration on previously published results reviewed in this work.
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