Spin-wave and electromagnon dispersions in multiferroic ${\mathrm{MnWO}}_{4}$ as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction

Spin-wave and electromagnon dispersions in multiferroic ${MnWO}_{4}$ as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction

Y. Xiao (肖荫果), C. M. N. Kumar, S. Nandi, Y. Su (苏夷希), W. T. Jin (金文涛), Z. Fu (付振东), E. Faulhaber, A. Schneidewind, and Th. Brückel

Phys. Rev. B 93, 214428 – Published 21 June 2016

Abstract

High-resolution inelastic neutron scattering reveals that the elementary magnetic excitations in multiferroic ${MnWO}_{4}$ consist of low-energy dispersive electromagnons in addition to the well-known spin-wave excitations. The latter can well be modeled by a Heisenberg Hamiltonian with magnetic exchange coupling extending to the 12th nearest neighbor. They exhibit a spin-wave gap of 0.61(1) meV. Two electromagnon branches appear at lower energies of 0.07(1) and 0.45(1) meV at the zone center. They reflect the dynamic magnetoelectric coupling and persist in both the collinear magnetic and paraelectric AF1 phase and the spin spiral ferroelectric AF2 phase. These excitations are associated with the Dzyaloshinskii-Moriya exchange interaction, which is significant due to the rather large spin-orbit coupling.

Received 19 January 2016
Revised 18 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.214428

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Spin waves

Multiferroics

Heisenberg model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Xiao (肖荫果)^1,*, C. M. N. Kumar^2,3,†, S. Nandi^1,4,5, Y. Su (苏夷希)⁴, W. T. Jin (金文涛)^1,4, Z. Fu (付振东)⁴, E. Faulhaber^6,7, A. Schneidewind^4,7, and Th. Brückel^1,4

¹Jülich Centre for Neutron Science and Peter Grünberg Institut, JARA-FIT, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
²Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at SNS, POB 2008, 1 Bethel Valley Road, Oak Ridge, Tennessee 37831-6473, USA
³Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Jülich Centre for Neutron Science at Heinz Maier-Leibnitz Zentrum, Forschungszentrum Jülich GmbH, Lichtenbergstraße 1, 85747 Garching, Germany
⁵Department of Physics, Indian Institute of Technology, Kanpur 208016, India
⁶Heinz Maier-Leibnitz Zentrum, Technische Universität München, Lichtenbergstraße 1, 85748 Garching, Germany
⁷Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany

^*y.xiao@fz-juelich.de
^†n.kumar@fz-juelich.de

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Vol. 93, Iss. 21 — 1 June 2016

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Figure 1
(a) Schematic drawing of the crystal and magnetic structure of the AF1 phase of ${MnWO}_{4}$ showing the magnetic ${Mn}^{2 +}$ ions only. Solid lines highlight the monoclinic unit cell. The arrows on the Mn atoms denote the directions of their spins and the dashed lines denote the paths of Heisenberg exchange interactions. (b) Evolution of magnetic modulation (1/4, 1/2, 1/2) with increasing temperature. The dots denote the temperature dependence of the molar specific-heat measurement. Four distinct phases labeled as AF1, AF2, AF3, and paramagnetic are revealed. Comm. and IC. denote commensurate and incommensurate modulation, respectively.
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Figure 2
The measured spin-wave spectrum compared to calculations based on a Heisenberg model that describes the antiferromagnetic ground state of ${MnWO}_{4}$ . (a) and (c) Experimental low-energy excitations along [1 0 2] and [0 1 0] directions at temperature of 1.5 K. The spectrum is composed of 16 constant- $Q$ scans at various wave vectors. The solid lines demonstrated the spin-wave dispersion relationship resulting from a fit of the dispersion relations employing a Heisenberg Hamiltonian as described in the text. (b) and (d) Calculated spin-wave excitations of ${MnWO}_{4}$ in comparison with measured ones. The color code represents the intensity of inelastic scattered neutrons.
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Figure 3
Distance dependence of exchange interaction parameters. The parameters are obtained by considering Mn-Mn spin-exchange interaction up to the 9th, 11th, and 12th nearest neighbor, respectively.
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Figure 4
(a) and (b) Calculated spin-wave excitation spectra of the AF1 phase along the [1 0 2] direction with $K = 0.5$ and 1, respectively. (c) and (d) Calculated spin-wave excitation spectra of the AF1 phase along the [ $1 0 - 2]$ direction with $K = 0.5$ and 1, respectively.
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Figure 5
(a) Representative magnetic excitation spectra around zone center (1/4, 1/2, 1/2) at 1.5 K. The dashed lines are the estimated line shape for spin-wave excitations, while the spectral weights arising from electromagnon excitations are highlighted as the shaded areas under the curves. The dash-dotted line corresponds to the instrumental resolution. The inset illustrates the $↑ ↑ ↓ ↓$ spin configuration along the $a$ axis, which can be treated as a special case of a modulated spin structure. (b) and (c) Dispersion relation and spectral weight of electromagnon excitation $ω_{2}$ along the [1 0 2] direction. The solid lines are guides to the eye. (d) and (e) Dispersion relation and spectral weight of electromagnon excitation $ω_{2}$ along the [0 1 0] direction.
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Figure 6
(a) Selected energy scans at various wave vectors in the incommensurate AF2 phase at 10 K. The curves are shifted vertically for comparison. The inset shows the measured excitations in the AF2 phase around the zone center Q = (0.26, 0.5, 0.52) as a color plot.
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Physical Review B

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Spin-wave and electromagnon dispersions in multiferroic ${MnWO}_{4}$ as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction

Y. Xiao (肖荫果), C. M. N. Kumar, S. Nandi, Y. Su (苏夷希), W. T. Jin (金文涛), Z. Fu (付振东), E. Faulhaber, A. Schneidewind, and Th. Brückel

Phys. Rev. B 93, 214428 – Published 21 June 2016

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Physical Review B

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Spin-wave and electromagnon dispersions in multiferroic MnWO4 as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction

Y. Xiao (肖荫果), C. M. N. Kumar, S. Nandi, Y. Su (苏夷希), W. T. Jin (金文涛), Z. Fu (付振东), E. Faulhaber, A. Schneidewind, and Th. Brückel

Phys. Rev. B 93, 214428 – Published 21 June 2016

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Spin-wave and electromagnon dispersions in multiferroic ${MnWO}_{4}$ as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction