- Email: [email protected]
Charge excitations in a quantum antiferromagnet
Physica C 364±365 (2001) 618±621
www.elsevier.com/locate/physc
Charge excitations in a quantum antiferromagnet M.Z. Hasan a,*, E.D. Isaacs b, Z.-X. Shen a, L.L. Miller c a
Department of Applied Physics and Physics, Stanford University and Stanford Synchrotron Radiation Laboratory (SSRL), Stanford Linear Accelerator Center (SLAC), Stanford, CA 94305-4045, USA b Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA c Department of Physics, Ames Laboratory, Iowa State University, Ames, IA 50011, USA
Abstract We brie¯y report momentum-resolved charge excitations in a cuprate antiferromagnetic insulator in the intermediate regimes of momentum transfers using high energy resonant X-ray scattering near the Cu K-edge. The excitation spectra show dispersive features near the insulating gap edge which can be understood in terms of antiferromagnetic correlation of the underlying lattice. Details of the experiment will be reported elsewhere. Ó 2001 Published by Elsevier Science B.V. Keywords: Resonant scattering; HTSC; Antiferromagnetic insulator
Even after several decades of extensive research, electronic structure of late transition metal oxides lacks comprehensive understanding. The existence of exotic transport properties such as high Tc superconductivity in cuprates or colossal magnetoresistance in manganites are believed to be related to the strong electron±electron Coulomb correlations in these systems. This suggests the necessity of studying their correlated charge dynamics and magnetism [1±4]. Much is known about their magnetism from studies based on neutron scattering [3,4] and angle-resolved photoemission has shed much light on the occupied electronic states of these systems [5,6]. But any bulk study of the momentum-resolved electronic structure specially
* Corresponding author. Address: LAM, 476 Lomita Mall, # 434, Stanford University, Stanford, CA 94305, USA. Tel.: +1650-723-8654; fax: +1-650-725-5457. E-mail address: [email protected] (M.Z. Hasan).
the unoccupied bands and particle±hole pair excitations are absent for these complex electron systems. Such information can be provided by the inelastic X-ray scattering as it measures the charge ¯uctuation spectrum in a momentum resolved manner. Recent experimental and theoretical investigations have shown that by tuning the incident energy near an X-ray absorption edge a large enhancement can be achieved making such experiments feasible to perform [7±14]. The observation of a low-energy charge-transfer gap has been reported recently with nonzero-q, (q being the scattering vector) in a parent cuprate using inelastic X-ray scattering [10,12,14] and has been studied by optical spectroscopies (with q 0) [15] and electron energy-loss spectroscopy [16]. We have performed high resolution inelastic X-ray scattering near Cu K-edge on Ca2 CuO2 Cl2 and Sr2 CuO2 Cl2 to study charge ¯uctuations at intermediate q's expanding on our earlier work [12] using the high ¯ux X21A3 wiggler beamline at the
0921-4534/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 8 6 4 - 4
M.Z. Hasan et al. / Physica C 364±365 (2001) 618±621
National Synchrotron Light Source of Brookhaven National Laboratory. With an overall energy resolution of 435 meV, the inelastic count rates from the sample were about 20 counts per minute at energy losses of several electron volts. The scattered beam was re¯ected from a diced analyzer and focused onto a solid-state detector. For qscans, incident energy was kept ®xed near the Cu K-edge. Background was measured by keeping track of scattering intensities on the energy gain side which was about 2±3 counts per minute. The Ca2 CuO2 Cl2 and Sr2 CuO2 Cl2 crystals used for this experiment were grown and characterized by techniques described elsewhere [17]. Fig. 1(A) shows inelastic X-ray scattering spectra near the Cu K-edge with varying momentum transfers along the h1 0i direction (the Cu±O bond direction) and Fig. 1(B) shows spectra with momentum transfers along the h1 1i direction (45° to the Cu±O bond direction). All the spectra in each panel were normalized near 8 eV energy-loss and quasielastic scattering was removed by ®tting. Each spectrum shows two features, one around 5.8 eV and another, lower in energy, appear in the range of 2.5±3.8 eV depending on dierent values of q. Based on electronic structure calculations, the 5.8-eV feature is believed to be a charge transfer excitation from an occupied state with b1g symmetry to an empty state with a1g symmetry [18]. The lower energy feature, on the other hand, has a signi®cant movement in changing q along the h1 1i direction as seen in Fig. 1(B). The feature disperses upward about 1.4 eV monotonically in this direction. Where as if the momentum transfer is along the bond direction it does not show much dispersion in going from (2.1p, 0) to (2.5p, 0). But in going from (2.5p, 0) to (3.1p, 0) (®rst three spectra from bottom to top in Fig. 1(B)) it disperses upward by about 0.5 eV as seen in Fig. 1(A). Fig. 1(C) shows the magnitude of resonant enhancement of the inelastic scattering as a function of incident energies in the region near the Cu K-edge. For the q-scans incident energy was set ®xed at 8.996 keV where enhancement was measured to be largest. (A model for interpreting the shape of the enhancement curve would be published elsewhere.) Dispersion behavior in two directions are summarized in Fig. 2(A) where we plotted the center of
619
Fig. 1. Inelastic X-ray scattering spectra near the Cu K-edge are shown along two directions in the Cu±O plane: (A) scattering with q along the h1 0i-direction. The values of q for the spectra from bottom to top are (2.1p, 0), (2.2p, 0), (2.5p, 0), (2.7p, 0), (3.1p, 0) respectively. (B) Scattering with q along the h1 1i-direction. The values of q for the spectra from bottom to top are (1.9p, 1.9p), (1.7p, 1.7p), (1.5p, 1.5p), (1.2p, 1.2p), (1.1p, 1.1p) respectively. Incident photon energy E0 8:996 keV. Panel (C) shows the location of the energy where best resonance enhancement was found. (The enhancement is not corrected for changes in eective scattering volume due to absorption. Detailed analysis will be reported elsewhere.)
gravity of the spectral weights of the inelastic features. Overall dispersion along the bond direction
620
M.Z. Hasan et al. / Physica C 364±365 (2001) 618±621
Fig. 2. The momentum dependence of the center of gravity of the inelastic features are compared along the h1 0i-direction and the h1 1i-direction and shown in (A). (B) shows a schematic of particle±hole pair excitations in a CuO2 square lattice with long-range antiferromagnetic correlation. The arrows denote the spins of holes. The `®lled' and `empty' circles denote Cuand O-sites respectively. The empty site in the middle is the electron (particle) and the big complex containing four oxygen sites is the Zhang±Rice singlet (hole). The propagation of particle±hole excitations is strongly anisotropic in this antiferromagnetically ordered lattice. The long dotted arrows denote two propagation directions (along the bond h1 0i and 45° to the bond h1 1i for the particle±hole pair created by the IXS process).
is much smaller than dispersion along the diagonal direction.
Inelastic X-ray scattering measures the dynamical correlation function (charge ¯uctuations) which can be interpreted as particle±hole pair excitations in the range of momentum-transfers comparable to the size of the Brillouin zone of the system. Near an absorption edge the measured dynamical response function gets modi®ed but it can still be interpreted as composites of pair excitations [11±14]. In the scattering process, the core±hole created by the X-ray photon near the absorption edge causes electronic excitations in the valence band which creates a hole in the occupied band and promotes an electron to the unoccupied band across the gap in an insulator. The parent high Tc cuprates (such as Ca2 CuO2 Cl2 and Sr2 CuO2 Cl2 ) are believed to be 2-D quantum antiferromagnets whose spin correlations are well described within 2-D quantum Heisenberg antiferromagnet as known from neutron scattering studies [19]. It is known that in such an antiferromagnetic lattice a hole forms a Zhang±Rice singlet state [20]. We interpret the dispersion of the low energy feature seen in our data as the dispersion of the particle±hole pair created across the eective Mott gap in the system. The particle±hole pair formed in the process absorbs the energy and momentum lost from the incident X-ray beam and propagates in the direction of q. Because of the antiferromagnetic order of the lattice, the pair would have dierent propagation probabilities along the Cu-O bond and 45° to the Cu±O bond as its propagation would break dierent number of bonds [14,16,20]. Fig. 2(B) shows an schematic of the pair formation and the antiferromagnetic correlation of the lattice which suggests that the propagation probabilities for the pair along the bond and 45°s to the bond are dierent. Along the diagonal direction pair propagation is relatively easy and consequently dispersion is larger than the bond direction [16]. These results are further consistent with numerical studies of Hubbard hamiltonian [13,14]. We postpone the extraction of quantitative details for higher resolution experiments in future. These results suggest that inelastic X-ray scattering near a core resonance can be used to study electronic structure in complex insulators and correlated electron systems in general. Particle±
M.Z. Hasan et al. / Physica C 364±365 (2001) 618±621
hole excitations are fundamental to the transport phenomena so it is of importance to use two-particle spectroscopies (such as inelastic X-ray scattering) in a momentum-resolved mode so that an understanding of the nonlocal and anisotropic interaction potentials can be obtained which determine various ground states of a correlated system. Higher resolution experiments would be necessary to extract quantitative details about the fundamental electronic parameters using such spectroscopies. Acknowledgements We gratefully acknowledge C. Kao, W. Lenner and P. Abbamonte. This work performed at the National Synchrotron Light Source was jointly supported by the Department of Energy through Stanford Synchrotron Radiation Lab of Stanford Linear Accelerator Center, Stanford, California and independently by Bell-Laboratories of Lucent Technologies, New Jersey.
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References [1] J. Hubbard, Proc. Phys. Soc. London A 277 (1964) 237. [2] J. Zaanen, G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 55 (1985) 418. [3] H.A. Mook et al., Nature 395 (1998) 580. [4] J.M. Tranquada et al., Nature 375 (1995) 561. [5] B.O. Wells et al., Phys. Rev. Lett. 74 (1995) 964. [6] F. Ronning et al., Science 282 (1998) 2067. [7] C.C. Kao, W.A.L. Caliebe, J.B. Hastings, J.M. Gillet, Phys. Rev. B 54 (1996) 16361. [8] E.D. Isaacs, P.M. Platzman, P. Metcalf, J.M. Honig, Phys. Rev. Lett. 76 (1996) 4211. [9] J.P. Hill et al., Phys. Rev. Lett. 80 (1998) 4967. [10] P. Abbamonte et al., Phys. Rev. Lett. 83 (1999) 860. [11] P.M. Platzman, E.D. Isaacs, Phys. Rev. B 57 (1998) 11107. [12] M.Z. Hasan et al., Physica C 341±348 (2000) 781. [13] K. Tsutsui, T. Tohyama, S. Maekawa, Phys. Rev. Lett. 83 (1999) 3705. [14] M.Z. Hasan et al., Science 288 (2000) 1811. [15] S.L. Cooper et al., Phys. Rev. B 47 (1993) 8233. [16] Y.Y. Wang et al., Phys. Rev. Lett. 77 (1997) 1809. [17] L.L. Miller et al., Phys. Rev. B 41 (1990) 1921. [18] M.E. Simon et al., Phys. Rev. B 54 (1996) R3780. [19] M. Greven et al., Phys. Rev. Lett. 72 (1994) 1096. [20] F.C. Zhang, T.M. Rice, Phys. Rev. B 37 (1988) 3759.
www.elsevier.com/locate/physc
Charge excitations in a quantum antiferromagnet M.Z. Hasan a,*, E.D. Isaacs b, Z.-X. Shen a, L.L. Miller c a
Department of Applied Physics and Physics, Stanford University and Stanford Synchrotron Radiation Laboratory (SSRL), Stanford Linear Accelerator Center (SLAC), Stanford, CA 94305-4045, USA b Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA c Department of Physics, Ames Laboratory, Iowa State University, Ames, IA 50011, USA
Abstract We brie¯y report momentum-resolved charge excitations in a cuprate antiferromagnetic insulator in the intermediate regimes of momentum transfers using high energy resonant X-ray scattering near the Cu K-edge. The excitation spectra show dispersive features near the insulating gap edge which can be understood in terms of antiferromagnetic correlation of the underlying lattice. Details of the experiment will be reported elsewhere. Ó 2001 Published by Elsevier Science B.V. Keywords: Resonant scattering; HTSC; Antiferromagnetic insulator
Even after several decades of extensive research, electronic structure of late transition metal oxides lacks comprehensive understanding. The existence of exotic transport properties such as high Tc superconductivity in cuprates or colossal magnetoresistance in manganites are believed to be related to the strong electron±electron Coulomb correlations in these systems. This suggests the necessity of studying their correlated charge dynamics and magnetism [1±4]. Much is known about their magnetism from studies based on neutron scattering [3,4] and angle-resolved photoemission has shed much light on the occupied electronic states of these systems [5,6]. But any bulk study of the momentum-resolved electronic structure specially
* Corresponding author. Address: LAM, 476 Lomita Mall, # 434, Stanford University, Stanford, CA 94305, USA. Tel.: +1650-723-8654; fax: +1-650-725-5457. E-mail address: [email protected] (M.Z. Hasan).
the unoccupied bands and particle±hole pair excitations are absent for these complex electron systems. Such information can be provided by the inelastic X-ray scattering as it measures the charge ¯uctuation spectrum in a momentum resolved manner. Recent experimental and theoretical investigations have shown that by tuning the incident energy near an X-ray absorption edge a large enhancement can be achieved making such experiments feasible to perform [7±14]. The observation of a low-energy charge-transfer gap has been reported recently with nonzero-q, (q being the scattering vector) in a parent cuprate using inelastic X-ray scattering [10,12,14] and has been studied by optical spectroscopies (with q 0) [15] and electron energy-loss spectroscopy [16]. We have performed high resolution inelastic X-ray scattering near Cu K-edge on Ca2 CuO2 Cl2 and Sr2 CuO2 Cl2 to study charge ¯uctuations at intermediate q's expanding on our earlier work [12] using the high ¯ux X21A3 wiggler beamline at the
0921-4534/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 8 6 4 - 4
M.Z. Hasan et al. / Physica C 364±365 (2001) 618±621
National Synchrotron Light Source of Brookhaven National Laboratory. With an overall energy resolution of 435 meV, the inelastic count rates from the sample were about 20 counts per minute at energy losses of several electron volts. The scattered beam was re¯ected from a diced analyzer and focused onto a solid-state detector. For qscans, incident energy was kept ®xed near the Cu K-edge. Background was measured by keeping track of scattering intensities on the energy gain side which was about 2±3 counts per minute. The Ca2 CuO2 Cl2 and Sr2 CuO2 Cl2 crystals used for this experiment were grown and characterized by techniques described elsewhere [17]. Fig. 1(A) shows inelastic X-ray scattering spectra near the Cu K-edge with varying momentum transfers along the h1 0i direction (the Cu±O bond direction) and Fig. 1(B) shows spectra with momentum transfers along the h1 1i direction (45° to the Cu±O bond direction). All the spectra in each panel were normalized near 8 eV energy-loss and quasielastic scattering was removed by ®tting. Each spectrum shows two features, one around 5.8 eV and another, lower in energy, appear in the range of 2.5±3.8 eV depending on dierent values of q. Based on electronic structure calculations, the 5.8-eV feature is believed to be a charge transfer excitation from an occupied state with b1g symmetry to an empty state with a1g symmetry [18]. The lower energy feature, on the other hand, has a signi®cant movement in changing q along the h1 1i direction as seen in Fig. 1(B). The feature disperses upward about 1.4 eV monotonically in this direction. Where as if the momentum transfer is along the bond direction it does not show much dispersion in going from (2.1p, 0) to (2.5p, 0). But in going from (2.5p, 0) to (3.1p, 0) (®rst three spectra from bottom to top in Fig. 1(B)) it disperses upward by about 0.5 eV as seen in Fig. 1(A). Fig. 1(C) shows the magnitude of resonant enhancement of the inelastic scattering as a function of incident energies in the region near the Cu K-edge. For the q-scans incident energy was set ®xed at 8.996 keV where enhancement was measured to be largest. (A model for interpreting the shape of the enhancement curve would be published elsewhere.) Dispersion behavior in two directions are summarized in Fig. 2(A) where we plotted the center of
619
Fig. 1. Inelastic X-ray scattering spectra near the Cu K-edge are shown along two directions in the Cu±O plane: (A) scattering with q along the h1 0i-direction. The values of q for the spectra from bottom to top are (2.1p, 0), (2.2p, 0), (2.5p, 0), (2.7p, 0), (3.1p, 0) respectively. (B) Scattering with q along the h1 1i-direction. The values of q for the spectra from bottom to top are (1.9p, 1.9p), (1.7p, 1.7p), (1.5p, 1.5p), (1.2p, 1.2p), (1.1p, 1.1p) respectively. Incident photon energy E0 8:996 keV. Panel (C) shows the location of the energy where best resonance enhancement was found. (The enhancement is not corrected for changes in eective scattering volume due to absorption. Detailed analysis will be reported elsewhere.)
gravity of the spectral weights of the inelastic features. Overall dispersion along the bond direction
620
M.Z. Hasan et al. / Physica C 364±365 (2001) 618±621
Fig. 2. The momentum dependence of the center of gravity of the inelastic features are compared along the h1 0i-direction and the h1 1i-direction and shown in (A). (B) shows a schematic of particle±hole pair excitations in a CuO2 square lattice with long-range antiferromagnetic correlation. The arrows denote the spins of holes. The `®lled' and `empty' circles denote Cuand O-sites respectively. The empty site in the middle is the electron (particle) and the big complex containing four oxygen sites is the Zhang±Rice singlet (hole). The propagation of particle±hole excitations is strongly anisotropic in this antiferromagnetically ordered lattice. The long dotted arrows denote two propagation directions (along the bond h1 0i and 45° to the bond h1 1i for the particle±hole pair created by the IXS process).
is much smaller than dispersion along the diagonal direction.
Inelastic X-ray scattering measures the dynamical correlation function (charge ¯uctuations) which can be interpreted as particle±hole pair excitations in the range of momentum-transfers comparable to the size of the Brillouin zone of the system. Near an absorption edge the measured dynamical response function gets modi®ed but it can still be interpreted as composites of pair excitations [11±14]. In the scattering process, the core±hole created by the X-ray photon near the absorption edge causes electronic excitations in the valence band which creates a hole in the occupied band and promotes an electron to the unoccupied band across the gap in an insulator. The parent high Tc cuprates (such as Ca2 CuO2 Cl2 and Sr2 CuO2 Cl2 ) are believed to be 2-D quantum antiferromagnets whose spin correlations are well described within 2-D quantum Heisenberg antiferromagnet as known from neutron scattering studies [19]. It is known that in such an antiferromagnetic lattice a hole forms a Zhang±Rice singlet state [20]. We interpret the dispersion of the low energy feature seen in our data as the dispersion of the particle±hole pair created across the eective Mott gap in the system. The particle±hole pair formed in the process absorbs the energy and momentum lost from the incident X-ray beam and propagates in the direction of q. Because of the antiferromagnetic order of the lattice, the pair would have dierent propagation probabilities along the Cu-O bond and 45° to the Cu±O bond as its propagation would break dierent number of bonds [14,16,20]. Fig. 2(B) shows an schematic of the pair formation and the antiferromagnetic correlation of the lattice which suggests that the propagation probabilities for the pair along the bond and 45°s to the bond are dierent. Along the diagonal direction pair propagation is relatively easy and consequently dispersion is larger than the bond direction [16]. These results are further consistent with numerical studies of Hubbard hamiltonian [13,14]. We postpone the extraction of quantitative details for higher resolution experiments in future. These results suggest that inelastic X-ray scattering near a core resonance can be used to study electronic structure in complex insulators and correlated electron systems in general. Particle±
M.Z. Hasan et al. / Physica C 364±365 (2001) 618±621
hole excitations are fundamental to the transport phenomena so it is of importance to use two-particle spectroscopies (such as inelastic X-ray scattering) in a momentum-resolved mode so that an understanding of the nonlocal and anisotropic interaction potentials can be obtained which determine various ground states of a correlated system. Higher resolution experiments would be necessary to extract quantitative details about the fundamental electronic parameters using such spectroscopies. Acknowledgements We gratefully acknowledge C. Kao, W. Lenner and P. Abbamonte. This work performed at the National Synchrotron Light Source was jointly supported by the Department of Energy through Stanford Synchrotron Radiation Lab of Stanford Linear Accelerator Center, Stanford, California and independently by Bell-Laboratories of Lucent Technologies, New Jersey.
621
References [1] J. Hubbard, Proc. Phys. Soc. London A 277 (1964) 237. [2] J. Zaanen, G.A. Sawatzky, J.W. Allen, Phys. Rev. Lett. 55 (1985) 418. [3] H.A. Mook et al., Nature 395 (1998) 580. [4] J.M. Tranquada et al., Nature 375 (1995) 561. [5] B.O. Wells et al., Phys. Rev. Lett. 74 (1995) 964. [6] F. Ronning et al., Science 282 (1998) 2067. [7] C.C. Kao, W.A.L. Caliebe, J.B. Hastings, J.M. Gillet, Phys. Rev. B 54 (1996) 16361. [8] E.D. Isaacs, P.M. Platzman, P. Metcalf, J.M. Honig, Phys. Rev. Lett. 76 (1996) 4211. [9] J.P. Hill et al., Phys. Rev. Lett. 80 (1998) 4967. [10] P. Abbamonte et al., Phys. Rev. Lett. 83 (1999) 860. [11] P.M. Platzman, E.D. Isaacs, Phys. Rev. B 57 (1998) 11107. [12] M.Z. Hasan et al., Physica C 341±348 (2000) 781. [13] K. Tsutsui, T. Tohyama, S. Maekawa, Phys. Rev. Lett. 83 (1999) 3705. [14] M.Z. Hasan et al., Science 288 (2000) 1811. [15] S.L. Cooper et al., Phys. Rev. B 47 (1993) 8233. [16] Y.Y. Wang et al., Phys. Rev. Lett. 77 (1997) 1809. [17] L.L. Miller et al., Phys. Rev. B 41 (1990) 1921. [18] M.E. Simon et al., Phys. Rev. B 54 (1996) R3780. [19] M. Greven et al., Phys. Rev. Lett. 72 (1994) 1096. [20] F.C. Zhang, T.M. Rice, Phys. Rev. B 37 (1988) 3759.