Spin wave excitations in the tetragonal double perovskite ${\mathrm{Sr}}_{2}{\mathrm{CuWO}}_{6}$

Spin wave excitations in the tetragonal double perovskite ${Sr}_{2} {CuWO}_{6}$

H. C. Walker, O. Mustonen, S. Vasala, D. J. Voneshen, M. D. Le, D. T. Adroja, and M. Karppinen

Phys. Rev. B 94, 064411 – Published 9 August 2016

Abstract

${Sr}_{2} {CuWO}_{6}$ is a double perovskite proposed to be at the border between two- and three-dimensional magnetism, with a square lattice of $S = \frac{1}{2} {Cu}^{2 +}$ ions. We have used inelastic neutron scattering to investigate the spin wave excitations of the system, to find out how they evolve as a function of temperature, as well as to obtain information about the magnetic exchange interactions. We observed well defined dispersive spin wave modes at 6 K, which partially survive above the magnetic ordering temperature $T_{N} = 24$ K. Linear spin wave theory is used to determine the exchange interactions revealing them to be highly two dimensional in nature. Density functional theory calculations are presented supporting this experimental finding, which is in contrast to a previous ab initio study of the magnetic interactions. Our analysis confirms that not the nearest neighbor, but the next nearest neighbor interactions in the tetragonal $a b$ plane are the strongest. Low incident energy measurements reveal the opening of a 0.6(1) meV gap below $T_{N}$ , which suggests the presence of a very weak single ion anisotropy term in the form of an easy axis along $\hat{a}$ .

Received 10 February 2016
Revised 29 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.064411

Physics Subject Headings (PhySH)

Antiferromagnetism Exchange interaction Spin waves

Oxides Perovskites

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. C. Walker¹, O. Mustonen², S. Vasala^2,3, D. J. Voneshen¹, M. D. Le¹, D. T. Adroja^1,4, and M. Karppinen²

¹ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, United Kingdom
²Department of Chemistry, Aalto University, FI-00076 Aalto, Finland
³Laboratory of Photonics and Interfaces, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
⁴Highly Correlated Matter Research Group, Physics Department, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa

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Vol. 94, Iss. 6 — 1 August 2016

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Figure 1
Schematic view of the magnetic structure and exchange constants $J_{1}$ to $J_{4}$ between Cu ions in double perovskite ${Sr}_{2} {CuWO}_{6}$ . Large dark spheres are Cu, smaller spheres are W, and the smallest palest spheres are O. Sr has been omitted for clarity.
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Figure 2
Schematic of the four AFM orderings used in calculating the magnetic exchange constants of ${Sr}_{2} {CuWO}_{6}$ . Black and cyan spheres correspond to the two spin states on the Cu ions. Other ions and long bonds along the $c$ axis are omitted for clarity.
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Figure 3
Color coded inelastic neutron scattering intensity maps in arbitrary units, energy transfer vs momentum transfer $Q$ of ${Sr}_{2} {CuWO}_{6}$ measured with an incident energy of $E_{i} = 45$ meV on MERLIN.
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Figure 4
The measured magnetic scattering in arbitrary units at 6 K after phonon scattering subtraction for (a) $E_{i} = 10$ and (e) $E_{i} = 45$ meV; compared with the spin wave scattering at 6 K simulated using the SpinW program with exchange parameters (b) and (f) optimized for the experimental data: $J_{1} = - 1.2$ meV, $J_{2} = - 9.5$ meV, $J_{3} = 0$ meV, and $J_{4} = - 0.01$ meV, (c) and (g) from a previous DFT study [8]: $J_{1} = - 1.20$ meV, $J_{2} = - 7.47$ meV, $J_{3} = - 0.03$ meV, and $J_{4} = - 4.21$ meV, and (d) and (h) from the DFT study presented in Sec. V: $J_{1} = - 2.45$ meV, $J_{2} = - 8.83$ meV, $J_{3} = 0$ meV, and $J_{4} = - 0.01$ meV.
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Figure 5
One-dimensional cuts of the magnetic scattering from ${Sr}_{2} {CuWO}_{6}$ at 6 K (a) intergrated between $1 < | Q | < 1.7 Å^{- 1}$ compared with the simulated powder average spin waves for the original DFT-determined exchange parameters (dashed red line) and for the more two-dimensional INS obtained exchange parameters (solid green line), and for the best revised DFT exchange parameters (dot-dash cyan line), (b) a $q$ cut through the $\sim 18$ meV feature, showing that it follows the magnetic form factor for ${Cu}^{2 +}$ , and (c) a $q$ cut through the data integrated between $4 < E < 6$ meV compared with simulations for the original DFT-determined exchange parameters (dashed red line), for the more two-dimensional INS obtained exchange parameters (solid green line), and for the best revised DFT exchange parameters (dot-dash cyan line).
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Figure 6
The magnetic scattering data in arbitrary units for $E_{i} = 3.51$ meV at (a) 5 K, (b) 30 K, and (c) 100 K. (d) A SpinW simulation for the low temperature data, reproducing a gap with the addition of single ion anisotropy term. One-dimensional cuts through the data at 5 K (blue), 30 K (green), and 100 K (red) for (e) $0.1 < E < 0.6$ meV and (f) $0.8 < E < 2$ meV are compared with cuts through the simulation (black line).
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Physical Review B

covering condensed matter and materials physics

Spin wave excitations in the tetragonal double perovskite ${Sr}_{2} {CuWO}_{6}$

H. C. Walker, O. Mustonen, S. Vasala, D. J. Voneshen, M. D. Le, D. T. Adroja, and M. Karppinen

Phys. Rev. B 94, 064411 – Published 9 August 2016

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Physical Review B

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Spin wave excitations in the tetragonal double perovskite Sr2CuWO6

H. C. Walker, O. Mustonen, S. Vasala, D. J. Voneshen, M. D. Le, D. T. Adroja, and M. Karppinen

Phys. Rev. B 94, 064411 – Published 9 August 2016

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Spin wave excitations in the tetragonal double perovskite ${Sr}_{2} {CuWO}_{6}$