We present resonant x-ray Raman scattering results on Sr2CuO2Cl2, a model compound for high-Tc
superconductors. We demonstrate that the dd excitations can be observed and show that the polarization
dependence can be used to identify the dd excitations. We find the transition from the dx²-y² ground
state to the dxy excited state at 1.35 eV and to the degenerate dxz and dyz excited states at 1.7 eV. From
analysis of the polarization dependence we conclude that the d3z²-r² orbital energy is at 1.5 eV and not
in the midinfrared (0.5 eV) as recently suggested. We use recent theoretical arguments to show that
the d3z22r2 excitation is accompanied by a local spin flip resulting in a shift upwards of 0.2 eV due to
the exchange interaction with the neighboring spins

Duda, L.-C.

Guo, J.-H.

Kuiper, Pieter

Nordgren, Joseph

Sâthe, Conny

We present resonant x-ray Raman scattering results on Sr2CuO2Cl2, a model compound for high-Tc

superconductors. We demonstrate that the dd excitations can be observed and show that the polarization

dependence can be used to identify the dd excitations. We find the transition from the dx²-y² ground

state to the dxy excited state at 1.35 eV and to the degenerate dxz and dyz excited states at 1.7 eV. From

analysis of the polarization dependence we conclude that the d3z²-r² orbital energy is at 1.5 eV and not

in the midinfrared (0.5 eV) as recently suggested. We use recent theoretical arguments to show that

the d3z22r2 excitation is accompanied by a local spin flip resulting in a shift upwards of 0.2 eV due to

the exchange interaction with the neighboring spins

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Resonant X-Ray Raman Spectra of Cu dd Excitations in Sr2CuO2Cl2

Utrecht University Repository

VOLUME 80, NUMBER 23 P HY S I CA L REV I EW LE T T ER S 8 JUNE 19985Resonant X-Ray Raman Spectra of Cu dd Excitations in Sr2CuO2Cl2Pieter Kuiper,* J.-H. Guo, Conny Såthe, L.-C. Duda,† and Joseph NordgrenDepartment of Physics, Uppsala University, Box 530, S-751 21 Uppsala, SwedenJ. J.M. Pothuizen, F.M. F. de Groot, and G. A. SawatzkyLaboratory of Solid State Physics, Materials Science Center, University of Groningen, Nijenborgh 4, 9747 AG Groningen, TheNetherlands(Received 20 November 1997)We present resonant x-ray Raman scattering results on Sr2CuO2Cl2, a model compound for high-Tcsuperconductors. We demonstrate that the dd excitations can be observed and show that the polarizationdependence can be used to identify the dd excitations. We find the transition from the dx22y2 groundstate to the dxy excited state at 1.35 eV and to the degenerate dxz and dyz excited states at 1.7 eV. Fromanalysis of the polarization dependence we conclude that the d3z22r2 orbital energy is at 1.5 eV and notin the midinfrared (0.5 eV) as recently suggested. We use recent theoretical arguments to show thatthe d3z22r2 excitation is accompanied by a local spin flip resulting in a shift upwards of 0.2 eV due tothe exchange interaction with the neighboring spins. [S0031-9007(98)06273-5]PACS numbers: 78.70.En, 71.70.Ch, 74.72.–hResonant x-ray Raman (RXR) spectroscopy has themakings of a powerful technique to study the elementaryexcitations in solids. Using excitation energies at specificcore-level thresholds one can identify the excitations anddetermine their atomic origin. As was shown recently,one can even observe local spin flip excitations (andthus measure superexchange interactions) by choosingcore-level resonances with strong spin-orbit coupling[1]. In this Letter we present the first RXR results onSr2CuO2Cl2, an insulating model compound for the high-Tc’s, to determine the dd and accompanying spin flipexcitations.The energies of the lowest excitations in the Cu-basedsuperconductors are basic quantities of interest in theongoing struggle to determine the underlying electronicstructure and elementary excitations. The energies of thelocal on-site dd excitations have been a topic of debaterecently. The suggestion that some of these might occurat energies as low as 0.5 eV [2] reopens the questionas to their importance in the so-called midinfrared partof the optical spectrum which is believed by someto be directly involved in the mechanism for high-Tc superconductors [3,4]. These dd excitations are notdipole allowed and therefore are rather weak in opticalabsorption spectroscopies. Recently, however, the highlystoichiometric and pure Sr2CuO2Cl2 has provided thepossibility to study also these weak transitions. It isgenerally accepted that in the ground state the 3d holeon Cu is in a dx22y2 orbital allowing for three local ddexcitations in the local square-planar D4h symmetry tothe dxy , the degenerate dxz , dyz , and the d3z22r2 states.The optical studies revealed a sharp feature starting at0.4 eV followed by a rather wide absorption region whichwas suggested to be due to transitions to d3z22r2 localstates [2]. Lorenzana et al. objected to this assignmentand suggested that the very sharp structure at 0.4 eV204 0031-9007y98y80(23)y5204(4)$15.00was due to a phonon assisted two magnon absorptionand supported this claim with theoretical calculations [5].They, however, were unable to explain the intensity of therather broad higher energy shoulder, which left open thepossibility that this structure could be the transitions tod3z22r2 states. Also recent detailed Raman studies havebeen unable to find the d3z22r2 states at energies above1 eV finding only the dxy states at 1.35 eV [6,7]. Usingresonant x-ray Raman spectroscopy we locate the dxy anddxz,yz states and present strong evidence that the d3z22r2excitation is around 1.7 eV.By choosing x-ray energies at the Cu 3p resonances(around 75 eV) we achieve elemental specificity for localexcitations on copper. We probe specifically the dd exci-tations by the transition sequence 3p63d9 ! 3p53d10 !3p63d9. These dd excitations are fully allowed, and theirintensities can be calculated. The x-rays in this energyregion have a penetration depth of about 1000 Å, so thatthe method is bulk sensitive. Only recently has the reso-lution of RXR spectroscopy become sufficiently high tostudy valence-valence excitations. Molecules and wide-band solids have attracted considerable interest [8], butthe method has also been used to study charge-transferexcitations in correlated systems [9] and dd excitations inMnO [10].Tanaka and Kotani were the first to study resonant x-ray Raman spectroscopy on cuprates theoretically [11].They calculated the x-ray emission spectrum of CuO andLa2CuO4 at the Cu L3 resonance, and concluded thatthe energies of dd excitations can be measured by thismethod. Ichikawa et al. [12] measured the predicted dif-ference for these two copper compounds. A polarization-dependent resonant study was done by Duda et al. [13],also at the L3 (2p3y2) resonance. But at these high ener-gies (930 eV), it is difficult to achieve a combined reso-lution of monochromator and spectrometer better than© 1998 The American Physical SocietyVOLUME 80, NUMBER 23 P HY S I CA L REV I EW LE T T ER S 8 JUNE 19981 eV, which is necessary to resolve low-energy excita-tions. That is much easier at the Cu M2,3 (3p) resonancearound 75 eV, where we achieved a combined resolutionof 0.2 eV in this first experiment. Theoretically, there islittle difference between the Raman spectra at the L2,3 andthe M2,3 edges. The nonresonant M2,3 emission spectra ofcuprates in Ref. [14] are affected by the 1.5 eV core-holelifetime broadening, but the lifetime does not affect theresolution of resonant x-ray Raman spectroscopy for thesame reasons it does not affect the resolution of resonantphotoemission.The experiment was performed at beam line 7 ofthe Advanced Light Source (ALS) at Berkeley. Thesynchrotron was running at an electron beam energy of1.5 GeV. At this setting the undulator can go downin energy to approximately 70 eV. The undulatorand monochromator combination produced a smallintense spot of x-ray with an energy resolution ofabout 0.1 eV. The Raman spectra were recorded bya grazing-incidence grating spectrometer. We used agrating with 300 linesymm with a radius of 3 m. A slitwidth of 30 mm gave a resolution of 0.2 eV, which alsodetermined the resolution of this experiment (the width ofthe elastic peak).The growth of the Sr2CuO2Cl2 samples by the travelingsolvent floating zone technique is described elsewhere[15]. As the experiments are not surface sensitive, thesamples were cleaved in situ or just before introductioninto vacuum. The sample quality was checked by theoxygen 1s x-ray absorption spectra. The polarizationdependence of the total photoelectric current (surfacesensitive) was similar to that of the x-ray fluorescent yield.The spectra were recorded in two different geometries.In both cases the detector was placed in a directionperpendicular to the incident beam, either in the planeof the synchrotron orbit or perpendicular to it. The firstgeometry (horizontal position of the detector) has theadvantage that the elastic peak is minimized (no Rayleighscattering in the direction of the electrical field vector ofthe incident radiation). But the second geometry (vertical)is more suitable for determining the polarization of thescattered radiation from our two-dimensional sample. Asinelastic scattering at the Cu p edges occurs only viaexcitation to the unoccupied 3dx22y2 , we want to keep theCuO2 planes parallel with the polarization of the incidentradiation. This is done by rotating the sample’s normalfrom near perpendicular incidence (so that the verticaldetector measures radiation at grazing exit angles withboth x, y and with z polarizations) to nearly vertical(so that the detector measures only emission with x, ypolarization). The rotations in this second (vertical)geometry are shown in the insets of Fig. 1.Figure 1 shows the x-ray Raman spectra with theexcitation energy at 74 eV, which is the Cu 3p3y2 (M3)resonance. The spectra are normalized to the elastic peak,which is also shown reduced by a factor of 200. Thiselastic peak has a full width at half maximum of 0.2 eV,which is the resolution of this experiment. However,the tail of the strong elastic peak makes it impossible toobserve excitations at energies smaller than about 0.5 eV.We observe clear sharp features between 1 and 2 eVenergy loss, features that can be assigned to dd excitationson Cu21. Tanaka and Kotani predicted also charge-transfer peaks around 5 eV [11], but those are hardly seenat the L3 resonance either [12,13], and must be weakerthan predicted.The intensity of the Raman spectrum is highest neargrazing incidence (normal emission), and decreases whenthe sample is turned towards normal incidence. The de-crease is caused by the combined effect of increasingpenetration depth closer to normal incidence and in-creased absorption of emission towards the spectrometer.Clearly, it would be desirable to have samples with facesparallel to the c axis, to measure a stronger z-polarizedsignal. A very smooth surface is needed to avoid an ex-cessively strong elastic peak.Two inelastic peaks are resolved in Fig. 1, one around1.35 eV and the other around 1.8 eV. The relativeintensity of these peaks changes with angle. The peakat 1.35 eV becomes strongest closer to normal emission.Clearly this peak is polarized in the Cu-O plane, andthe assignment to transitions to the xy orbital seemsunavoidable. The peak at 1.8 eV must then be assignedto the xz and yz orbitals. This leaves one dd excitationunaccounted for, namely, the 3z2 2 r2 transition. OfFIG. 1. Polarization-dependent x-ray resonant Raman spectraat the Cu M3 resonance (74 eV). The angle between theemission direction and the sample normal is 30±, 40±, and 60±,from top to bottom. The last spectrum is also shown reducedby a factor of 200.5205VOLUME 80, NUMBER 23 P HY S I CA L REV I EW LE T T ER S 8 JUNE 1998course, it might be hidden at low energies under thetail of the elastic peak. But if the splitting of the xyand xz, yz orbitals is 0.4 eV as in our assignment, onewould expect the splitting between the x2 2 y2 and the3z2 2 r2 orbitals to be several times larger.A calculation of relative intensities is necessary to un-derstand why the 3z2 2 r2 peak is not seen in our spec-tra. The procedure is straightforward. As in the case ofMnO [10], we use the Kramers-Heisenberg formula forinelastic scattering. In the present case of Cu21, the in-termediate states have a filled 3d shell so that only sixintermediate states need to be considered: four with a3p3y2 hole (mj › 3y2, 1y2, 21y2, 23y2) and two with a3p1y2 hole (mj › 1y2, 21y2). Interference plays a rolebecause the 3p spin-orbit separation is comparable tothe lifetime width. Selection rules and angular-overlapintegrals determine the relative intensities of the finalstates. Unlike the case of MnO, the crystal field needsto be taken into account. The eigenfunctions in a crys-tal field are linear combinations of the atomic 3d Ylmorbitals with well-known ratios, which are independentof the strength of the crystal field. Model calculationshave been done on a Cu21 atom in tetragonal symme-try with an exchange field along the z axis [1]. The re-sults show that the 3z2 2 r2 peak is weak and that itis only allowed for spin flipped final states, so that thisweak peak is spread out and shifted to higher energy bythe exchange interaction and the excitation of magnons.But even with its calculated low intensity this peakcannot be hidden under the peak at 1.35 eV. The strongangle dependence of the relative intensities can only bereproduced by assuming that the 3z2 2 r2 transition con-tributes to the peak at 1.7 eV. Figure 2 shows spec-tra calculated with the following parameters: 10Dqxy ›1.35 eV, Esxz, yzd › Es3z2 2 r2d1.7 eV, and a spin flipenergy of 0.2 eV.The low Raman intensity made it difficult to investigateits energy dependence in detail, but a first result is clearenough to be presented. Figure 3 shows two spectra takenat the M3 and at the M2 edges in the horizontal positionFIG. 2. Model calculation of the angle dependence at the M3resonance.5206of the detector. The x-ray emission was measured in thedirection of the E vector of the incident x rays, at an angleof 40± to the sample normal. The M3 spectrum agreeswith the middle trace of Fig. 1, but the M2 spectrumis rather different. The intensity at 1.7 eV is relativelymuch lower, and there is extra intensity around 2 eV.Theory indicates that the intensities near the M2 edgeare sensitive to the exact excitation energy, because ofinterference with the M3 path. The calculations reproducethis difference. The extra intensity around 2 eV at the M2resonance is due to spin flip states. They have a relativelylarger intensity at the 3p1y2 than at the 3p3y2 intermediatestate because of the DJ › 0, 61 selection rule. Thismakes sure that the mj › 3y2 intermediate state ofopposite spin cannot be reached from the ground state.But at 3p1y2, both intermediate states (mj › 1y2, 21y2)are populated, and there are relatively more spin flips inthe excitation step [1].Our observation of an in-plane polarized Cu dd ex-citation at 1.35 eV matches perfectly with a large-shiftRaman peak observed by laser spectroscopy. Using pho-ton energies around 3.5 eV, Salamon et al. [6,7] observea loss peak with a polarization dependence characteristicfor excitation to 3dxy final states. Its energy dependenceon the Cu-O bond length would predict a dxy transitionat 1.35 eV for 1.986 Å, the in-plane Cu-O bond length inSr2CuO2Cl2 [16]. We can also compare with data of 3dorbital energies in K2CuF4 [17] and in the square-planarCuCl224 ion [18]. Table I shows that the oxychloride isintermediate between these two other cases. One can alsocompare with the optically observed dd excitations inLa2NiO4, where the tetragonal distortion is smaller [19].In the controversy over the assignment of features inthe optical spectra of high-Tc cuprates and the energyof the lowest electronic excitations, our results support adifferent assignment than that given by Perkins et al. [2].FIG. 3. X-ray resonant Raman spectra at the Cu M3 and M2resonances (74 and 76.3 eV). The emission direction is in thedirection of the incident polarization and makes an angle of 40±with the sample normal.VOLUME 80, NUMBER 23 P HY S I CA L REV I EW LE T T ER S 8 JUNE 1998TABLE I. Energies in eV of the 3d orbitals of differentsquare-planar coordinated Cu21 ions.Orbital K2CuF4 a Sr2CuO2Cl2 b sCuCl4d22 cxy 1.17 1.35 1.55xz, yz 1.51 1.7 1.773z2 2 r2 1.03 1.5 2.1aRef. [17]. bThis work. cRef. [18].They assign a strong shoulder at 1.5 eV in the optical ab-sorption of Sr2CuO2Cl2 to dx22y2 ! dxy transitions, butour x-ray and Salamon’s laser Raman spectra [6,7] estab-lish 1.35 eV as the energy for this excitation. Maybe thistransition is responsible for the weak structure just below1.4 eV in the optical spectrum [2]. Perkins et al. [2,20]assign a feature around 0.5 eV to dx22y2 ! d3z22r2 tran-sitions. Although we do not directly observe this transi-tion (calculations indicate that it is relatively weak), sucha low value would be inconsistent with a separation of0.4 eV between the 3dxzsyzd transitions and the 3dxy peak.The splitting between the dx22y2 and the d3z22r2 shouldbe at least 2 or 3 times as large in crystal or ligand fieldtheory.In conclusion, the new method of resonant x-rayRaman spectroscopy was used to study Cu dd excitations,using the Cu M23 resonance at 75 eV, with a resolutionof 0.2 eV. We observe a peak at 1.35 eV, whichon the basis of polarization dependence is assignedto the xy transition. At higher energies (1.8 eV onthe M3 resonance, 2.0 eV at the M2 resonance) wefind peaks which are assigned to xz, yz orbitals. Thedifference is due to different probabilities of magnonexcitation. The controversial 3z2 2 r2 transition is notresolved, which can be explained by its low intensityaccording to theory. By comparing with calculations ofthe polarization dependence, we conclude that it is hiddenunder the dxz,yz structure at 1.8 eV, shifted 0.2 eV upwardby a spin flip excitation.We thank the staff of the Advanced Light Source fortheir help. We thank Per Skytt for help with the earlymeasurements.*Present address: ITN, Halmstad University College, Box823, S-301 18 Halmstad, Sweden.Electronic address: Pieter.Kuiper@itn.hh.se†Present address: Department of Physics, BostonUniversity, 590 Commonwealth Avenue, Boston, MA02215.[1] F.M. F. de Groot, P. Kuiper, and G.A. Sawatzky, Phys.Rev. B (to be published).[2] J. D. Perkins, J.M. Graybeal, M.A. Kastner, R. J. Birge-nau, J. P. Falck, and M. Greven, Phys. Rev. Lett. 71, 1621(1993).[3] W. Weber, A. L. Shelankov, and X. Zotos, Physica(Amsterdam) 162-164C, 307 (1989).[4] W. Weber, in Electronic Properties of High-Tc Supercon-ductors and Related Compounds (Springer-Verlag, Berlin,1990), p. 352.[5] J. Lorenzana and G.A. Sawatzky, Phys. Rev. Lett. 74,1867 (1995).[6] R. Liu, D. Salamon, M.V. Klein, S. L. Cooper, W.C. Lee,S.-W. Cheong, and D.M. Ginsberg, Phys. Rev. Lett. 71,3709 (1993).[7] D. Salamon, R. Liu, M.V. Klein, M.A. Karlow, S. L.Cooper, S.-W. Cheong, W.C. Lee, and D.M. Ginsberg,Phys. Rev. B 51, 6617 (1995).[8] J. Nordgren and N. Wassdahl, J. Electron Spectrosc. Relat.Phenom. 72, 273 (1995).[9] S.M. Butorin, D. C. Mancini, J.-H. Guo, N. Wassdahl,M. Nakazawa, S. Tanaka, T. Uozumi, A. Kotani, Y. Ma,K. E. Myano, B.A. Karlin, and D.K. Shuh, Phys. Rev.Lett. 77, 574 (1996).[10] S.M. Butorin, J.-H. Guo, M. Magnuson, P. Kuiper, andJ. Nordgren, Phys. Rev. B 54, 4405 (1996).[11] S. Tanaka and A. Kotani, J. Phys. Soc. Jpn. 62, 464(1993).[12] K. Ichikawa, K. Jouda, S. Tanaka, K. Soda, M. Mat-sumoto, Y. Taguchi, T. Katsumi, O. Aita, H. Maezawa,Y. Azuma, and H. Kitazawa, J. Electron Spectrosc. Relat.Phenom. 78, 183 (1996).[13] L.-C. Duda, Ph.D. thesis, Uppsala University, 1996;L.-C. Duda, G. Dräger, S. Tanaka, A. Kotani, J.-H. Guo,D. Heumann, S. Bocharov, N. Wassdahl, and J. Nordgren(unpublished).[14] D.W. Mueller, J. Wallace, D. L. Ederer, J. J. Jia, W. L.O’Brien, Q. Y. Dong, and T.A. Callcott, Phys. Rev. B 46,11 069 (1992).[15] N. T. Hien, J. J.M. Franse, J. J.M. Pothuizen, T.W. Li,and A.A. Menovsky, J. Cryst. Growth 171, 102 (1997).[16] L. L. Miller, X. L. Wang, S. X. Wang, C. Stassis, D. C.Johnston, J. Faber, Jr., and C.-K. Loong, Phys. Rev. B 41,1921 (1990).[17] M. J. Riley, L. Dubicki, G. Moran, E. R. Krausz, andI. Yamada, Inorg. Chem. 29, 1614 (1990).[18] M.A. Hitchman and P. J. Cassidy, Inorg. Chem. 18, 1745(1979).[19] P. Kuiper, J. van Elp, D. E. Rice, D. J. Buttrey, H.-J. Lin,and C. T. Chen, Phys. Rev. B 57, 1552 (1998).[20] J. D. Perkins, D. S. Kleinberg, M.A. Kastner, R. J. Birge-nau, Y. Endoh, K. Yamada, and S. Hosoya, Phys. Rev. B52, R9863 (1995).5207

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Resonant X-Ray Raman Spectra of Cu dd Excitations in Sr2CuO2Cl2

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