Magnetoelastic phenomena and mechanisms of magnetic skyrmion crystal

Hu Yang-Fan; Wan Xue-Jin; Wang Biao

doi:10.7498/aps.67.20180251

Abstract

Recently, a novel two-dimensional spin structure with non-trivial topological properties, called magnetic skyrmion, has been found in many chiral magnets. In most cases, magnetic skyrmions assemble spontaneously and form a lattice structure, called magnetic skyrmion crystal (SkX). SkX, as a novel macroscopic magnetic phase, may interact with different types of external fields through the intrinsic multi-field coupling of the material, resulting in many peculiar physical phenomena. It is found that due to the intrinsic magnetoelastic coupling of chiral magnets, SkX not only influences the mechanical properties of the materials, but also has emergent elastic properties when subjected to external forces. In this review, we first introduce and categorize various types of SkX-related magnetoelastic phenomena, and then introduce a unified theoretical framework to analyze these magnetoelastic phenomena. Specifically, we establish the Landau-Ginzburg free energy functional with a comprehensive description of the magnetoelastic effect for B20 chiral magnets obtained through symmetry analysis, and prove that SkX should be described by a Fourier series due to its wave nature. We show quantitative agreement between theoretical results and experimental results for three types of phenomena:1) the temperature-magnetic field phase diagrams of MnSi suffering uniaxial compression, it is found that uniaxial compression in the direction[0, 0, 1]T constricts the stable region of the skyrmion phase in the phase diagram, while uniaxial compression in the direction[1, 1, 0]T extends the stable region of the skyrmion phase in the phase diagram; 2) the emergent elastic behavior of SkX, it is found that this property derives from the magnetoelastic effect of the underlying material, and the linear constitutive equation (with coefficient matrix ) which determines the emergent deformation of SkX, is briefly introduced; 3) the variations of elastic coefficients C11, C33, C44, and C66 with the external magnetic field for MnSi, and the predictions of the variation of C12 and C13 are provided by the theory. Based on the theoretical framework, the analytical solutions of the eigenstrain problems for chiral magnets hosting SkX and the surface configuration of SkX in a half-space magnet are introduced. In this process, we show how to use the theoretical framework to deal with different problems. Finally, we make a summary and suggest several directions for the future development of this field.

Keywords:

Authors and contacts

1.
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China

Corresponding author: Hu Yang-Fan, huyf3@mail.sysu.edu.cn;wangbiao@mail.sysu.edu.cn ; Wang Biao, huyf3@mail.sysu.edu.cn;wangbiao@mail.sysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11772360, 11302267, 11472313, 11572355) and Pearl River Nova Program of Guangzhou, China (Grant No. 201806010134).

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Cited By

[1]	Skyrme T H R 1961 Proc. R. Soc. Lond. A 260 127
[2]	Skyrme T H R 1962 Nucl. Phys. 31 556
[3]	Buerle C, Bunkov Y M, Fisher S N, Godfrin H, Pickett G R 1996 Nature 382 332
[4]	Durrer R, Kunz M, Melchiorri A 2002 Phys. Rep. 364 1
[5]	Brey L, Fertig H A, Ct R, MacDonald A H 1995 Phys. Rev. Lett. 75 2562
[6]	Al Khawaja U, Stoof H 2001 Nature 411 918
[7]	Roessler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 797
[8]	Dzyaloshinskii I E 1957 JETP 5 1259
[9]	Moriya T 1960 Phys. Rev. 120 91
[10]	Dzyaloshinskii I 1964 JETP 19 960
[11]	Fert A, Levy P M 1980 Phys. Rev. Lett. 44 1538
[12]	Muehlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Boeni P 2009 Science 323 915
[13]	Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 465 901
[14]	Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2011 Nat. Mater. 10 106
[15]	Seki S, Yu X Z, Ishiwata S, Tokura Y 2012 Science 336 198
[16]	Bogdanov A N, Rler U K 2001 Phys. Rev. Lett. 87 037203
[17]	Bode M, Heide M, von Bergmann K, Ferriani P, Heinze S, Bihlmayer G, Kubetzka A, Pietzsch O, Blgel S, Wiesendanger R 2007 Nature 447 190
[18]	Schulz T, Ritz R, Bauer A, Halder M, Wagner M, Franz C, Pfleiderer C, Everschor K, Garst M, Rosch A 2012 Nat. Phys. 8 301
[19]	Onose Y, Okamura Y, Seki S, Ishiwata S, Tokura Y 2012 Phys. Rev. Lett. 109 037603
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