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Spin dynamics of the spin ladder system Sr14Cu24O41
Physica B 259—261 (1999) 1038—1039
Spin dynamics of the spin ladder system Sr Cu O L.P. Regnault *, A.H. Moudden, J.P. Boucher, E. Lorenzo, A. Hiess, A. Vietkin, A. Revcolevschi Department de Recherche Fondamentale, sur la Matiere Condensee, Centre d’Etudes Nucleaires Grenoble, 17 Rue des Martyrs, DRFMC/MDN CEA Grenoble, F-38054 Grenoble Cedex 9, France Laboratoire Le& on Brillouin, CEA-CNRS, Saclay, F-91191 Gif-sur-Yvette, France Laboratoire de Spectrometrie Physique, UJF F-38042 Saint Martin d’Heres, France Laboratoire de Cristallographie, CNRS, F-38042 Grenoble, France Institut Laue Langevin, F-38042 Grenoble, France Laboratoire de Chimie des Solides, CNRS, UPS F-91405 Orsay, France
Abstract Detailed inelastic neutron scattering studies of the spin dynamics in the spin ladder system Sr Cu O has been performed. We confirm the existence of a spin gap in the ladders as reported earlier in NMR and pulsed neutron work on polycrystalline samples. Using large single crystals, we studied separately the spin excitations of the chain and the ladder subsystems. For the ladders, we clearly show that the inter-ladder coupling is extremely weak and the dispersion relation of the spin dynamics is essentially quasi-1D and remarkably steep. 1999 Elsevier Science B.V. All rights reserved. Keywords: Spin ladders; Inelastic neutron scattering; Spin dynamics
A considerable amount of theoretical effort is actually devoted to the study of spin ladders and more generally to spin gap systems which, when slightly doped, could exhibit high-¹ superconductivity [1,2]. It is generally accepted that two antiferromagnetic Heisenberg chains of spin coupled with an arbitrary small exchange coup ling J , exhibit a spin gap. The ground state should be , a collection of pairs along the rungs of the ladder in singlet state. The gap being of the order of J , corre, sponds to a singlet—triplet excitation energy. Sr Cu O is actually the most promising experi mental realization of spin ladders, to study in some detail the interplay between the spin correlations and superconductivity recently discovered in this material by Uehara et al. [4]. This compound has a composite structure [3] made of alternating layers of Cu O ladders and layers of CuO chains separated by layers of Sr atoms. The chains
* Corresponding author. Tel.: 33-76-88-3137; fax: 33-76-885109; e-mail: [email protected].
subsystem is intrinsically doped while the ladders are only progressively doped via an internal charge transfer from the chains subsystem, induced by Sr/Ca substitution and presumably also by applying a hydrostatic pressure as well. Previous NMR [5] and pulsed neutron studies on polycrystalline samples [6] have reported the existence of a spin gap of about 33 meV in the ladder subsystem, whereas Matsuda et al. [7] using standard neutron triple-axis studies on single crystals, reported magnetic scattering at about 11 meV which they attributed to inter-ladder coupling. In view of these results we felt that more inelastic neutron scattering work is still needed to first explore the dispersion relation of the magnetic excitations in the pure system and extract the relevant exchange couplings. And next study the effects of doping. In this report we present our results obtained on IN8 and 1T triple-axis spectrometers at ILL and LLB using a large undoped single crystal of Sr Cu O grown by the travelling solvent floating zone technique. In Figs. 1 and 2, we show representative inelastic scans through the AF scattering vector (4.5, 0, 0.5) when
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 8 7 4 - 6
L.P. Regnault et al. / Physica B 259—261 (1999) 1038—1039
Fig. 1. Representative energy scans showing the magnetic signal above 32 meV. The inset shows the Q -dependence distinctive of V the ladder.
Fig. 2. Q-scans at different constant energies across the gap, illustrating the steepness of the dispersion relation.
referring to the orthorhombic cell of the ladder subsystem with the lattice parameters a"11.47 As , b"13.37 As and c"3.93 As . In Fig. 1, we compare at 1.5 K, the spectrum we have measured right at the AF scattering vector (filled circles) with the corresponding energy scan (open circles) at a slightly shifted scattering vector (4.5, 0, 0.65) along the legs of the ladder. Using various momentum and energy scans in different Brillouin zones, we were able to map out the structure factor and show that the inelastic signal observed above 32 meV with an asymmetrical profile, is unambiguously magnetic. Moreover at
1039
given energy and perpendicular to the legs of the ladders, the Q-dependence of the intensity shown in the inset of Fig. 1, is remarkably well accounted for by the structure factor of the single ladder (solid line in the inset) given by [ f (Q)sin(Q p/3)], where f (Q) is the copper magnetic ! V ! form factor. The slight discrepancy observed at Q &7 is V due to a phonon contamination. This behaviour clearly indicates that the inter-ladders magnetic coupling is extremely weak. Various constant energy scans reported on Fig. 2, show that the energy gap below which the magnetic signal from the ladders vanishes, is reasonably well defined at about 32 meV. Further, the dispersion relation of this signal is essentially quasi-1D and considerably steep, suggesting a strong magnetic coupling along the ladders. Assuming a simple model of AF dispersion u(q )"*#[p/2 J sin(q )], where * is the spin gap X X related to J through a universal function determined , numerically [8], the related neutron scattering crosssection convolved with the instrumental resolution is used to fit the data. Our best fit is represented by the solid line in Fig. 1. The agreement is remarkably good. Qualitatively, we understand from this model that the asymmetry of the profile could be due to the steepness of the dispersion relation combined with the finite instrumental resolution. Quantitatively however, we find for the exchange couplings, J &80 meV and J &160 meV. The , later is surprisingly larger than the observed exchange coupling in the 2-D cuprates. To get a clearer understanding of this result, we think that more studies at higher energies including the search for the continuum of excitations, is necessary.
References [1] [2] [3] [4] [5] [6] [7] [8]
E. Dagotto et al., Phys. Rev. B 45 (1992) 5744. T.M. Rice et al., Europhys. Lett. 23 (1993). E.M. Carron et al., Mater. Res. B. 23 (1988) 1355. M. Uehara et al., J. Phys. Soc. Japan 65 (1996) 2764. Kumagai et al., Phys. Rev. Lett. 78 (1997). R.S. Eccleston et al., Phys. Rev. B 53 (1996) R14 721. M. Matsuda et al., Phys. Rev. B 53 (1996) 12 201. T. Barnes et al., Phys. Rev. B 47 (1993) 3196.
Spin dynamics of the spin ladder system Sr Cu O L.P. Regnault *, A.H. Moudden, J.P. Boucher, E. Lorenzo, A. Hiess, A. Vietkin, A. Revcolevschi Department de Recherche Fondamentale, sur la Matiere Condensee, Centre d’Etudes Nucleaires Grenoble, 17 Rue des Martyrs, DRFMC/MDN CEA Grenoble, F-38054 Grenoble Cedex 9, France Laboratoire Le& on Brillouin, CEA-CNRS, Saclay, F-91191 Gif-sur-Yvette, France Laboratoire de Spectrometrie Physique, UJF F-38042 Saint Martin d’Heres, France Laboratoire de Cristallographie, CNRS, F-38042 Grenoble, France Institut Laue Langevin, F-38042 Grenoble, France Laboratoire de Chimie des Solides, CNRS, UPS F-91405 Orsay, France
Abstract Detailed inelastic neutron scattering studies of the spin dynamics in the spin ladder system Sr Cu O has been performed. We confirm the existence of a spin gap in the ladders as reported earlier in NMR and pulsed neutron work on polycrystalline samples. Using large single crystals, we studied separately the spin excitations of the chain and the ladder subsystems. For the ladders, we clearly show that the inter-ladder coupling is extremely weak and the dispersion relation of the spin dynamics is essentially quasi-1D and remarkably steep. 1999 Elsevier Science B.V. All rights reserved. Keywords: Spin ladders; Inelastic neutron scattering; Spin dynamics
A considerable amount of theoretical effort is actually devoted to the study of spin ladders and more generally to spin gap systems which, when slightly doped, could exhibit high-¹ superconductivity [1,2]. It is generally accepted that two antiferromagnetic Heisenberg chains of spin coupled with an arbitrary small exchange coup ling J , exhibit a spin gap. The ground state should be , a collection of pairs along the rungs of the ladder in singlet state. The gap being of the order of J , corre, sponds to a singlet—triplet excitation energy. Sr Cu O is actually the most promising experi mental realization of spin ladders, to study in some detail the interplay between the spin correlations and superconductivity recently discovered in this material by Uehara et al. [4]. This compound has a composite structure [3] made of alternating layers of Cu O ladders and layers of CuO chains separated by layers of Sr atoms. The chains
* Corresponding author. Tel.: 33-76-88-3137; fax: 33-76-885109; e-mail: [email protected].
subsystem is intrinsically doped while the ladders are only progressively doped via an internal charge transfer from the chains subsystem, induced by Sr/Ca substitution and presumably also by applying a hydrostatic pressure as well. Previous NMR [5] and pulsed neutron studies on polycrystalline samples [6] have reported the existence of a spin gap of about 33 meV in the ladder subsystem, whereas Matsuda et al. [7] using standard neutron triple-axis studies on single crystals, reported magnetic scattering at about 11 meV which they attributed to inter-ladder coupling. In view of these results we felt that more inelastic neutron scattering work is still needed to first explore the dispersion relation of the magnetic excitations in the pure system and extract the relevant exchange couplings. And next study the effects of doping. In this report we present our results obtained on IN8 and 1T triple-axis spectrometers at ILL and LLB using a large undoped single crystal of Sr Cu O grown by the travelling solvent floating zone technique. In Figs. 1 and 2, we show representative inelastic scans through the AF scattering vector (4.5, 0, 0.5) when
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 8 7 4 - 6
L.P. Regnault et al. / Physica B 259—261 (1999) 1038—1039
Fig. 1. Representative energy scans showing the magnetic signal above 32 meV. The inset shows the Q -dependence distinctive of V the ladder.
Fig. 2. Q-scans at different constant energies across the gap, illustrating the steepness of the dispersion relation.
referring to the orthorhombic cell of the ladder subsystem with the lattice parameters a"11.47 As , b"13.37 As and c"3.93 As . In Fig. 1, we compare at 1.5 K, the spectrum we have measured right at the AF scattering vector (filled circles) with the corresponding energy scan (open circles) at a slightly shifted scattering vector (4.5, 0, 0.65) along the legs of the ladder. Using various momentum and energy scans in different Brillouin zones, we were able to map out the structure factor and show that the inelastic signal observed above 32 meV with an asymmetrical profile, is unambiguously magnetic. Moreover at
1039
given energy and perpendicular to the legs of the ladders, the Q-dependence of the intensity shown in the inset of Fig. 1, is remarkably well accounted for by the structure factor of the single ladder (solid line in the inset) given by [ f (Q)sin(Q p/3)], where f (Q) is the copper magnetic ! V ! form factor. The slight discrepancy observed at Q &7 is V due to a phonon contamination. This behaviour clearly indicates that the inter-ladders magnetic coupling is extremely weak. Various constant energy scans reported on Fig. 2, show that the energy gap below which the magnetic signal from the ladders vanishes, is reasonably well defined at about 32 meV. Further, the dispersion relation of this signal is essentially quasi-1D and considerably steep, suggesting a strong magnetic coupling along the ladders. Assuming a simple model of AF dispersion u(q )"*#[p/2 J sin(q )], where * is the spin gap X X related to J through a universal function determined , numerically [8], the related neutron scattering crosssection convolved with the instrumental resolution is used to fit the data. Our best fit is represented by the solid line in Fig. 1. The agreement is remarkably good. Qualitatively, we understand from this model that the asymmetry of the profile could be due to the steepness of the dispersion relation combined with the finite instrumental resolution. Quantitatively however, we find for the exchange couplings, J &80 meV and J &160 meV. The , later is surprisingly larger than the observed exchange coupling in the 2-D cuprates. To get a clearer understanding of this result, we think that more studies at higher energies including the search for the continuum of excitations, is necessary.
References [1] [2] [3] [4] [5] [6] [7] [8]
E. Dagotto et al., Phys. Rev. B 45 (1992) 5744. T.M. Rice et al., Europhys. Lett. 23 (1993). E.M. Carron et al., Mater. Res. B. 23 (1988) 1355. M. Uehara et al., J. Phys. Soc. Japan 65 (1996) 2764. Kumagai et al., Phys. Rev. Lett. 78 (1997). R.S. Eccleston et al., Phys. Rev. B 53 (1996) R14 721. M. Matsuda et al., Phys. Rev. B 53 (1996) 12 201. T. Barnes et al., Phys. Rev. B 47 (1993) 3196.