Resonant inelastic x-ray scattering study of spin-wave excitations in the cuprate parent compound ${\mathrm{Ca}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$

Resonant inelastic x-ray scattering study of spin-wave excitations in the cuprate parent compound ${Ca}_{2} {CuO}_{2} {Cl}_{2}$

B. W. Lebert, M. P. M. Dean, A. Nicolaou, J. Pelliciari, M. Dantz, T. Schmitt, R. Yu, M. Azuma, J.-P. Castellan, H. Miao, A. Gauzzi, B. Baptiste, and M. d'Astuto

Phys. Rev. B 95, 155110 – Published 7 April 2017

Abstract

By means of resonant inelastic x-ray scattering at the Cu $L_{3}$ edge, we measured the spin-wave dispersion along $〈 100 〉$ and $〈 110 〉$ in the undoped cuprate ${Ca}_{2} {CuO}_{2} {Cl}_{2}$ . The data yield a reliable estimate of the superexchange parameter $J = 135 \pm 4$ meV using a classical spin-1/2 two-dimensional Heisenberg model with nearest-neighbor interactions and including quantum fluctuations. Including further exchange interactions increases the estimate to $J = 141$ meV. The 40 meV dispersion between the magnetic Brillouin zone boundary points (1/2, 0) and (1/4, 1/4) indicates that next-nearest-neighbor interactions in this compound are intermediate between the values found in ${La}_{2} {CuO}_{4}$ and ${Sr}_{2} {CuO}_{2} {Cl}_{2}$ . Due to the low- $Z$ elements composing ${Ca}_{2} {CuO}_{2} {Cl}_{2}$ , the present results may enable a reliable comparison with the predictions of quantum many-body calculations, which would improve our understanding of the role of magnetic excitations and of electronic correlations in cuprates.

Received 28 October 2016
Revised 7 March 2017

DOI:https://doi.org/10.1103/PhysRevB.95.155110

Physics Subject Headings (PhySH)

Spin waves

Antiferromagnets Charge-transfer insulators High-temperature superconductors

Neutron scattering Resonant inelastic x-ray scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

B. W. Lebert^1,2, M. P. M. Dean³, A. Nicolaou², J. Pelliciari⁴, M. Dantz⁴, T. Schmitt⁴, R. Yu⁵, M. Azuma⁵, J.-P. Castellan^6,7, H. Miao³, A. Gauzzi¹, B. Baptiste¹, and M. d'Astuto^1,*

¹IMPMC-Sorbonne Universités, Université Pierre et Marie Curie, CNRS, IRD, MNHN 4, place Jussieu, 75252 Paris, France
²Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin, 91192 Gif-sur-Yvette Cedex, France
³Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973, USA
⁴Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
⁵Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori, Yokohama 226-8503, Japan
⁶Laboratoire Léon Brillouin (CEA-CNRS), CEA-Saclay, F-91911 Gif-sur-Yvette, France
⁷Institute for Solid State Physics, Karlsruhe Institute of Technology, D-76021 Karlsruhe, Germany

^*matteo.dastuto@impmc.upmc.fr

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Vol. 95, Iss. 15 — 15 April 2017

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Figure 1
Top left: Tetragonal crystal structure [17] of ${Ca}_{2} {CuO}_{2} {Cl}_{2}$ [11]. The square coordination of copper with its four nearest-neighbor oxygen ions in the ${CuO}_{2}$ planes is shown. The chlorine ions are located in the apical site above and below the copper. Black arrows indicate one of the possible magnetic structures consistent with neutron-diffraction data [18]. Bottom right: Temperature dependence of the fitted intensity of the averaged Bragg reflections $(\frac{1}{2}, \frac{1}{2}, \frac{5}{2})$ and $(\frac{1}{2}, \frac{1}{2}, \frac{7}{2})$ and a power-law fit (red).
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Figure 2
RIXS geometry for measuring along $〈 100 〉$ with $π$ -polarization and grazing out emission (modified from Ref. [20]). The scattering angle $2 θ$ is defined between the photon momentum of the incoming beam k and the direction where the analyzer collects the scattered beam $k^{'}$ . $2 θ$ and the azimuthal angles are fixed, whereas the incident angle can be changed by a rotation, $θ$ , around the $b$ axis. The incident angle defines $δ$ , which is the angle between the sample normal c and the transferred momentum q (red arrow), so that $δ = 0$ in specular reflection. The projection of q onto the sample's ab plane is denoted $q_{∥}$ , which is 0 for $δ = 0$ and maximal for grazing geometries. Measurements along $〈 110 〉$ are done with the sample rotated $45^{\circ}$ around the $c$ axis.
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Figure 3
RIXS map at $q_{∥} = (0.34, 0)$ with $π$ incidence polarization showing the resonant behavior of the magnetic excitations, dd excitations, and charge-transfer excitations. Weak fluorescence is seen at high energy when the system is excited above the Cu $L_{3}$ edge threshold. The color map is a logarithmic scale in arbitrary intensity units.
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Figure 4
RIXS spectra showing the dispersion of the magnetic excitations along $〈 100 〉$ (top) and $〈 110 〉$ (bottom). Spectra are normalized by their dd excitations.
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Figure 5
Cu $L_{3}$ RIXS spectra of ${Ca}_{2} {CuO}_{2} {Cl}_{2}$ at different in-plane transferred momentum, $q_{∥}$ , expressed as $(h$ , $k)$ in reciprocal-lattice units. (a) Representative RIXS spectra along $〈 100 〉$ (red) and $〈 110 〉$ (black). All spectra have been normalized to the area of the dd excitations. The midinfrared regions of these spectra are shown in (c,d), where vertical bars represent the energy of a single magnon found by fitting. The inset shows TEY-XAS (solid) and TFY-XAS (dashed), with an arrow indicating incident energy for our RIXS measurements. (b) Example of the fitting procedure at $q_{∥} = (0.21, 0.21)$ shown as a black curve through data points. The elastic $(E$ , magenta), phonon $(P$ , green), and single magnon $(M$ , red) peaks were resolution-limited, and the multimagnon $(M M$ , blue) peak fitting is described in the text.
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Figure 6
Dispersion of ${Ca}_{2} {CuO}_{2} {Cl}_{2}$ measured using Cu $L_{3}$ RIXS. The red, continuous line is a calculation for a classical spin-1/2 2D Heisenberg model with nearest-neighbor exchange, and the blue, dashed line is a calculation including further exchange terms that is described in the text. Inset: 2D Brillouin zone showing high-symmetry points. The first Brillouin zone boundary is represented by a thick black square, while the magnetic Brillouin zone boundary is represented by a dashed line. The region where we measured is shown as two thick red lines along $Γ − X$ and $Γ − M$ .
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Physical Review B

covering condensed matter and materials physics

Resonant inelastic x-ray scattering study of spin-wave excitations in the cuprate parent compound ${Ca}_{2} {CuO}_{2} {Cl}_{2}$

B. W. Lebert, M. P. M. Dean, A. Nicolaou, J. Pelliciari, M. Dantz, T. Schmitt, R. Yu, M. Azuma, J.-P. Castellan, H. Miao, A. Gauzzi, B. Baptiste, and M. d'Astuto

Phys. Rev. B 95, 155110 – Published 7 April 2017

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Physical Review B

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Resonant inelastic x-ray scattering study of spin-wave excitations in the cuprate parent compound Ca2CuO2Cl2

B. W. Lebert, M. P. M. Dean, A. Nicolaou, J. Pelliciari, M. Dantz, T. Schmitt, R. Yu, M. Azuma, J.-P. Castellan, H. Miao, A. Gauzzi, B. Baptiste, and M. d'Astuto

Phys. Rev. B 95, 155110 – Published 7 April 2017

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Resonant inelastic x-ray scattering study of spin-wave excitations in the cuprate parent compound ${Ca}_{2} {CuO}_{2} {Cl}_{2}$