Magnetic Excitations of the Classical Spin Liquid ${\mathrm{MgCr}}_{2}{\mathrm{O}}_{4}$

Magnetic Excitations of the Classical Spin Liquid ${MgCr}_{2} O_{4}$

X. Bai, J. A. M. Paddison, E. Kapit, S. M. Koohpayeh, J.-J. Wen, S. E. Dutton, A. T. Savici, A. I. Kolesnikov, G. E. Granroth, C. L. Broholm, J. T. Chalker, and M. Mourigal

Phys. Rev. Lett. 122, 097201 – Published 5 March 2019

Abstract

We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet ${MgCr}_{2} O_{4}$ in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all of the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic ${MgCr}_{2} O_{4}$ are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly correlated paramagnetic background. Our results also suggest that ${MgCr}_{2} O_{4}$ is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magnetostructural phase transition in ${MgCr}_{2} O_{4}$ .

Received 28 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.097201

Physics Subject Headings (PhySH)

Frustrated magnetism Quasiparticles & collective excitations Spin dynamics Spin liquid

Pyrochlores

Inelastic neutron scattering Monte Carlo methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

X. Bai¹, J. A. M. Paddison^1,2, E. Kapit^3,4, S. M. Koohpayeh⁵, J.-J. Wen^5,*, S. E. Dutton^6,†, A. T. Savici⁷, A. I. Kolesnikov⁷, G. E. Granroth⁷, C. L. Broholm^5,7, J. T. Chalker³, and M. Mourigal^1,5,‡

¹School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
²Churchill College, University of Cambridge, Storey’s Way, Cambridge CB3 0DS, United Kingdom
³Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3NP, United Kingdom
⁴Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
⁵Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
⁶Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
⁷Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*Present address: Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA.
^†Present address: Cavendish Laboratory, Department of Physics, University of Cambridge, JJ Thomson Ave., Cambridge CB3 0HE, UK.
^‡mourigal@gatech.edu

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Vol. 122, Iss. 9 — 8 March 2019

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Figure 1
(a) The pyrochlore lattice of ${Cr}^{3 +}$ ions (red spheres) in ${MgCr}_{2} O_{4}$ and definition of exchange interactions up to third neighbors. Note that $J_{3 a}$ and $J_{3 b}$ span the same distance but are not equivalent by symmetry. (b) Contour plot of the goodness of fit $χ^{2}$ between calculations and neutron (blue solid lines) and bulk susceptibility (green dashed lines) measurements. FN exchange interactions $J_{2}$ and $J_{3 a}$ are fixed on a grid with $J_{1}$ and $J_{3 b}$ fitted at each grid point. The choice of $J_{2} \pm J_{3 a}$ as plotting axes highlights the nearly equivalent spin structure factors obtained for $J_{2} = J_{3 a}$ . Spin correlations are calculated using the self-consistent Gaussian approximation (SCGA) at $T = 20 K$ . The red star is the best overall fit. (c) Momentum dependence of $I_{0} (Q) = F (| Q |) S (Q)$ and $I_{1} (Q) = F (| Q |) K (Q)$ along several paths of the Brillouin zone (BZ) at $T = 20 K$ , and comparisons with SCGA predictions for NN (dashed black line) and FN (solid red line) models. For the NN model, $J_{1} = 38 K$ . (d)–(e) Selected reciprocal-space planes showing $I_{0} (Q)$ and $I_{1} (Q)$ , as labeled in the figure, and comparison between NN and FN models calculated using the SCGA. Throughout, white rings are masked aluminum background lines. In (c)–(e), only $E_{i} = 80 meV$ data are shown, but both 40 meV and 80 meV data were included in fits.
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Figure 2
Magnetic excitation spectra of ${MgCr}_{2} O_{4}$ at $T = 20 K$ measured with incident neutron energy $E_{i} = 40 meV$ , and comparison with linear spin-wave theory (LSWT) calculations for our FN model. (a) Momentum-energy slices through $g^{2} S (Q, E)$ along different paths, comparing data (left column) and FN model (right column). (b) Cuts at constant energies $\bar{E} \pm 0.2 meV$ through the data (gray circles) and FN model (red lines), where $\bar{E}$ is labeled on each plot. The intensity is multiplied by $\bar{E}$ and offset by $4 {sr}^{- 1} {Cr}^{- 1}$ for clarity. (c) Energy dependence of the experimental (colored circles) and modeled (colored lines) dynamical structure factor at selected momenta, normalized to the energy transfer $E_{0} = 2 meV$ . (d) Slices at constant energies $\bar{E} \pm 0.2 meV$ through the data (left column) and the FN model (right column) in the $(h, k, k)$ plane. Throughout, blank space is due to kinematic constraints on the scattering, and the extra intensity at (4,0,0) arises from a strong nuclear Bragg peak and its associated acoustic phonon.
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Figure 3
(a) Sets of ordering wave vectors $κ$ with nearly-degenerate energies represented in the Brillouin zone as colored surfaces. The pink surface shows wave vectors with energies within $\sim 0.5 %$ of the global energy minimum for the FN interaction parameters of ${MgCr}_{2} O_{4}$ . The blue lines show wave vectors with energy equal to the global energy minimum for the macroscopically-degenerate phases represented by a blue dashed line in the phase diagram. (b) Mean-field phase diagrams of our FN Heisenberg model as a function of $J_{2}$ and $J_{3 a}$ , showing results for $J_{3 b} = 0$ (left) and $J_{3 b} = 0.0085 J_{1}$ (right). Phases with different ordering wave vectors $κ$ are shown in different colors. Special phases (dashed lines) correspond to a macroscopic number of ordering wave vectors with degenerate energies. They emerge from $J_{3 a} - J_{2} = 0$ (yellow line), which corresponds to the NN model, to form two half-planes corresponding to $J_{3 a} - J_{2} = \mp J_{3 b}$ (green and blue lines).
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Physical Review Letters

Magnetic Excitations of the Classical Spin Liquid MgCr2O4

X. Bai, J. A. M. Paddison, E. Kapit, S. M. Koohpayeh, J.-J. Wen, S. E. Dutton, A. T. Savici, A. I. Kolesnikov, G. E. Granroth, C. L. Broholm, J. T. Chalker, and M. Mourigal

Phys. Rev. Lett. 122, 097201 – Published 5 March 2019

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Magnetic Excitations of the Classical Spin Liquid ${MgCr}_{2} O_{4}$