Nontrivial temperature dependence of magnetic anisotropy in multiferroic ${\mathrm{Ba}}_{2}{\mathrm{MnGe}}_{2}{\mathrm{O}}_{7}$

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Nontrivial temperature dependence of magnetic anisotropy in multiferroic ${Ba}_{2} {MnGe}_{2} O_{7}$

Shunsuke Hasegawa, Shohei Hayashida, Shinichiro Asai, Masato Matsuura, Zaliznyak Igor, and Takatsugu Masuda

Phys. Rev. Research 3, L032023 – Published 28 July 2021

Abstract

We measured the temperature dependences of the static magnetization and the spin excitation in the square-lattice multiferroic ${Ba}_{2} {MnGe}_{2} O_{7}$ . An anisotropy gap of the observed low-energy mode is scaled by electric polarization rather than a power of the sublattice moment. Spin-nematic interaction in the effective spin Hamiltonian, which is equivalent to interaction of the electric polarization, is responsible for the easy-axis anisotropy. The nontrivial behavior of the anisotropy gap can be rationalized as change in the hybridized $d − p$ orbital with temperature, leading to the temperature dependence of the spin-nematic interaction.

Received 29 April 2021
Accepted 8 July 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.L032023

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Dipolar interaction Magnetic anisotropy Magnons Spin dynamics

Multiferroics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shunsuke Hasegawa ¹, Shohei Hayashida ¹, Shinichiro Asai¹, Masato Matsuura ², Zaliznyak Igor³, and Takatsugu Masuda ^1,4,5

¹Institute for Solid State Physics, The University of Tokyo, Chiba 277-8581, Japan
²Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society, Ibaraki 319-1106, Japan
³Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
⁴Institute of Materials Structure Science, High Energy Accelerator Research Organization, Ibaraki 305-0801, Japan
⁵Trans-scale Quantum Science Institute, The University of Tokyo, Tokyo 113-0033, Japan

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Vol. 3, Iss. 3 — July - September 2021

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Figure 1
(a) Crystal structure of ${Ba}_{2} {MnGe}_{2} O_{7}$ . ${MnO}_{4}$ tetrahedra are alternatively tilted by the characteristic angle of $κ$ . (b) Magnetic structure of ${Ba}_{2} {MnGe}_{2} O_{7}$ and the exchange pathways.
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Figure 2
Field derivative of magnetization ( $d M / d H$ ). (a) False color plot of $d M / d H$ measured in the field applied in the $a b$ plane at 1.8 K. The horizontal axis is the angle between [100] and the field directions. (b) False color plot of calculated $d M / d H$ in the $a b$ plane. (c) Measured $H − T$ map of $d M / d H$ for $H ∥$ [110]. $d M / d H$ curves measured at typical temperatures are shown in Supplemental Fig. S3. Black circles indicate $H_{SF}$ determined by the peak tops of $d M / d H$ . A circle at 0.5 K indicates $H_{SF}$ reported in a previous study [20]. Triangles indicate Néel temperatures evaluated from the $T$ dependence of the magnetization. The representative descriptions of the magnetic structures below and above $H_{SF}$ are inserted.
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Figure 3
Inelastic neutron scattering (INS) spectra. (a) False color plot of the INS spectrum measured at 0.05 K projected onto the $ℏ ω − (1, k, 1 / 2)$ plane. The spectrum is integrated in the range of 0.9 $\leq h \leq$ 1.1 and 0.45 $\leq l \leq$ 0.55. (b)–(e) The INS spectra focused on the low-energy range measured at (b) 0.05 K, (c) 0.9 K, (d) 1.8 K, and (e) 2.5 K. White solid curves are calculated dispersions. (f) Temperature evolution of constant- $q$ cuts at $Q = (1, 0, 1 / 2)$ ; data at different temperature are vertically offset. Coherent elastic scattering is subtracted for each temperature. The spectra are integrated in the range of $- 0.035 \leq k \leq$ 0.035. The asymmetric peak shape results from the wave vector resolution. Black solid curves are the calculated magnon cross section.
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Figure 4
The temperature dependences of gap energies observed in INS spectra, anisotropy energies, sublattice moment, and electric polarization. (a) $T$ dependences of $E_{g 2}$ (red circles), $Δ_{2}^{SWT}$ (black circles), $Δ^{HF}$ (blue circles), and sublattice moment (light green triangles from a previous [20] study and dark green ones from the present study). $E_{g 2}, Δ_{2}^{SWT}$ , and the sublattice moment are superimposed. The light green curve is a guide to the eye. (b) $T$ dependences of $E_{g 1}$ (red circles), $Δ_{1}^{SWT}$ (black circles), and $Δ^{HF}$ (blue circles). (c) $T$ dependences of $Δ_{1}^{SWT}$ (black circles), electric polarization $P$ (orange curve from Ref. [9]), and the second power of the sublattice moment (green triangles). The sublattice moment in this panel is a combination of measurements from the present and previous [20] studies in (a). Vertical error bars for $E_{g 1}, E_{g 2}$ , and $Δ^{HF}$ in (a) and (b) indicate the experimental resolution of the spectrometer estimated at an elastic condition.
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Nontrivial temperature dependence of magnetic anisotropy in multiferroic Ba2MnGe2O7

Shunsuke Hasegawa, Shohei Hayashida, Shinichiro Asai, Masato Matsuura, Zaliznyak Igor, and Takatsugu Masuda

Phys. Rev. Research 3, L032023 – Published 28 July 2021

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Nontrivial temperature dependence of magnetic anisotropy in multiferroic ${Ba}_{2} {MnGe}_{2} O_{7}$