磁性斯格明子晶格的磁弹现象与机理

胡杨凡; 万学进; 王彪

doi:10.7498/aps.67.20180251

摘要

近年来，人们在一些具有手性相互作用的磁性体材料及薄膜中成功观测到具有非平凡拓扑性质的二维自旋结构，称作磁性斯格明子.在大部分情况下，磁性斯格明子自发地聚集成一种晶格结构，称作斯格明子晶格.孤立的斯格明子由于其奇特的拓扑性质以及优异的电流驱动性质等局域化特征受到人们的广泛关注.与此相对，斯格明子晶格作为一种新颖的宏观磁性相，可能与材料固有的多场耦合性质发生相互作用进而引发许多奇特的宏观物理现象乃至新性质.在此范畴内，人们发现由于手征磁体内禀的磁弹耦合，斯格明子晶格不但对材料的力学性质产生影响，而且在外力作用下自身具备层展的弹性性质.本文对相关现象进行梳理，并基于一种针对B20族手征磁体磁弹耦合效应普遍适用的热力学唯象模型，逐一简述对于不同类型的磁弹现象如何建模分析，进而给出其中一部分现象的实验与理论结果比对.最后，对这一领域的发展提出几个可供进一步探索的方向.

关键词:

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:

作者及机构信息

1.
中山大学中法核工程与技术学院, 珠海 519082

通信作者: 胡杨凡, huyf3@mail.sysu.edu.cn;wangbiao@mail.sysu.edu.cn ; 王彪, huyf3@mail.sysu.edu.cn;wangbiao@mail.sysu.edu.cn

基金项目: 国家自然科学基金（批准号：11772360，11302267，11472313，11572355）和广州市珠江科技新星专题（批准号：201806010134）资助的课题.

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).

参考文献

[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
[20]	Buettner F, Moutafis C, Schneider M, Krueger B, Guenther C M, Geilhufe J, von Schmising C K, Mohanty J, Pfau B, Schaffert S, Bisig A, Foerster M, Schulz T, Vaz C A F, Franken J H, Swagten H J M, Klaeui M, Eisebitt S 2015 Nat. Phys. 11 225
[21]	Jonietz F, Muehlbauer S, Pfleiderer C, Neubauer A, Muenzer W, Bauer A, Adams T, Georgii R, Boeni P, Duine R A, Everschor K, Garst M, Rosch A 2010 Science 330 1648
[22]	Zang J, Mostovoy M, Han J H, Nagaosa N 2011 Phys. Rev. Lett. 107 136804
[23]	Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Boeni P 2009 Phys. Rev. Lett. 102 186602
[24]	Franz C, Freimuth F, Bauer A, Ritz R, Schnarr C, Duvinage C, Adams T, Bluegel S, Rosch A, Mokrousov Y, Pfleiderer C 2014 Phys. Rev. Lett. 112 186601
[25]	Litzius K, Lemesh I, Krueger B, Bassirian P, Caretta L, Richter K, Buettner F, Sato K, Tretiakov O A, Foerster J, Reeve R M, Weigand M, Bykova L, Stoll H, Schuetz G, Beach G S D, Klaeui M 2017 Nat. Phys. 13 170
[26]	Chen G 2017 Nat. Phys. 13 112
[27]	Jiang W, Zhang X, Yu G, Zhang W, Wang X, Jungfleisch M B, Pearson J E, Cheng X, Heinonen O, Wang K L, Zhou Y, Hoffmann A, te Velthuis S G E 2017 Nat. Phys. 13 162
[28]	Shibata K, Iwasaki J, Kanazawa N, Aizawa S, Tanigaki T, Shirai M, Nakajima T, Kubota M, Kawasaki M, Park H S, Shindo D, Nagaosa N, Tokura Y 2015 Nat. Nanotechnol. 10 589
[29]	Karube K, White J S, Reynolds N, Gavilano J L, Oike H, Kikkawa A, Kagawa F, Tokunaga Y, Ronnow H M, Tokura Y, Taguchi Y 2016 Nat. Mater. 15 1237
[30]	Heinze S, von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Bluegel S 2011 Nat. Phys. 7 713
[31]	Huang S X, Chien C L 2012 Phys. Rev. Lett. 108 267201
[32]	Jiang W, Chen G, Liu K, Zang J, te Velthuis S G E, Hoffmann A 2017 Phys. Rep.: Rev. Sect. Phys. Lett. 704 1
[33]	Yu X, DeGrave J P, Hara Y, Hara T, Jin S, Tokura Y 2013 Nano Lett. 13 3755
[34]	Du H, DeGrave J P, Xue F, Liang D, Ning W, Yang J, Tian M, Zhang Y, Jin S 2014 Nano Lett. 14 2026
[35]	Du H, Ning W, Tian M, Zhang Y 2013 Phys. Rev. B 87 014401
[36]	Du H, Che R, Kong L, Zhao X, Jin C, Wang C, Yang J, Ning W, Li R, Jin C, Chen X, Zang J, Zhang Y, Tian M 2015 Nat. Commun. 6 8504
[37]	Adams T, Muehlbauer S, Pfleiderer C, Jonietz F, Bauer A, Neubauer A, Georgii R, Boeni P, Keiderling U, Everschor K, Garst M, Rosch A 2011 Phys. Rev. Lett. 107 217206
[38]	Hu Y 2017 arXiv:1702.01059v2
[39]	Nii Y, Kikkawa A, Taguchi Y, Tokura Y, Iwasa Y 2014 Phys. Rev. Lett. 113 267203
[40]	Cevey L, Wilhelm H, Schmidt M, Lortz R 2013 Phys. Status Solidi B: Basic Solid State Phys. 250 650
[41]	Lobanova I I, Glushkov V V, Sluchanko N E, Demishev S V 2016 Sci. Rep. 6 22101
[42]	Nakajima T, Oike H, Kikkawa A, Gilbert E P, Booth N, Kakurai K, Taguchi Y, Tokura Y, Kagawa F, Arima T H 2017 Sci. Adv. 3 e1602562
[43]	Butenko A B, Leonov A A, Roessler U K, Bogdanov A N 2010 Phys. Rev. B 82 052403
[44]	Wilson M N, Butenko A B, Bogdanov A N, Monchesky T L 2014 Phys. Rev. B 89 094411
[45]	Zhang S S L, Phatak C, Petford-Long A K, Heinonen O G 2017 Appl. Phys. Lett. 111 242405
[46]	Chen J, Cai W P, Qin M H, Dong S, Lu X B, Gao X S, Liu J M 2017 Sci. Rep. 7 7392
[47]	Fobes D M, Luo Y, Leon-Brito N, Bauer E D, Fanelli V R, Taylor M A, DeBeer-Schmitt L M, Janoschek M 2017 Appl. Phys. Lett. 110 192409
[48]	Nii Y, Nakajima T, Kikkawa A, Yamasaki Y, Ohishi K, Suzuki J, Taguchi Y, Arima T, Tokura Y, Iwasa Y 2015 Nat. Commun. 6 8539
[49]	Chacon A, Bauer A, Adams T, Rucker F, Brandl G, Georgii R, Garst M, Pfleiderer C 2015 Phys. Rev. Lett. 115 267202
[50]	Deutsch M, Makarova O L, Hansen T C, Fernandez-Diaz M T, Sidorov V A, Tsvyashchenko A V, Fomicheva L N, Porcher F, Petit S, Koepernik K, Rler U K, Mirebeau I 2014 Phys. Rev. B 89 180407
[51]	Deutsch M, Bonville P, Tsvyashchenko A V, Fomicheva L N, Porcher F, Damay F, Petit S, Mirebeau I 2014 Phys. Rev. B 90 144401
[52]	Wu H C, Chandrasekhar K D, Wei T Y, Hsieh K J, Chen T Y, Berger H, Yang H D 2015 J. Phys. Appl. Phys. 48 475001
[53]	Ritz R, Halder M, Franz C, Bauer A, Wagner M, Bamler R, Rosch A, Pfleiderer C 2013 Phys. Rev. B 87 134424
[54]	Levatic I, Popcevic P, Surija V, Kruchkov A, Berger H, Magrez A, White J S, Ronnow H M, Zivkovic I 2016 Sci. Rep. 6 21347
[55]	Karhu E, Kahwaji S, Monchesky T L, Parsons C, Robertson M D, Maunders C 2010 Phys. Rev. B 82 184417
[56]	Karhu E A, Roessler U K, Bogdanov A N, Kahwaji S, Kirby B J, Fritzsche H, Robertson M D, Majkrzak C F, Monchesky T L 2012 Phys. Rev. B 85 094429
[57]	Ghimire N J, McGuire M A, Parker D S, Sales B C, Yan J Q, Keppens V, Koehler M, Latture R M, Mandrus D 2012 Phys. Rev. B 85 224405
[58]	Liu Y, Lei N, Zhao W, Liu W, Ruotolo A, Braun H B, Zhou Y 2017 Appl. Phys. Lett. 111 022406
[59]	Chen G, N'Diaye A T, Kang S P, Kwon H Y, Won C, Wu Y, Qiu Z Q, Schmid A K 2015 Nat. Commun. 6 6598
[60]	Li Z, Zhang Y, Huang Y, Wang C, Zhang X, Liu Y, Zhou Y, Kang W, Koli S C, Lei N 2017 J. Magn. Magn. Mater. 455 19
[61]	Kang S P, Kwon H Y, Won C 2017 J. Appl. Phys. 121 203902
[62]	Hu Y, Wang B 2017 ArXiv:1608.04840v4
[63]	Hu Y, Wang B 2016 Sci. Rep. 6 30200
[64]	Wan X, Hu Y, Wang B 2018 J. Phys.: Condens. Matter 30 245001
[65]	Petrova A E, Stishov S M 2009 J. Phys. Condens. Matter 21 196001
[66]	Petrova A E, Stishov S M 2015 Phys. Rev. B 91 214402
[67]	Luo Y, Lin S, Leroux M, Wakeham N, Fobes D M, Bauer E D, Betts J B, Thompson J D, Migliori A, Janoschek M, Maiorov B 2017 ArXiv:1711.08873
[68]	Zhang X X, Nagaosa N 2017 New J. Phys. 19 043012
[69]	Ivanov A, Lamago D, Goering E, Weber F, Lhneysen H v, Mignot J M, Wang L, Steffens P, Heid R, Krannich S, Keller T, Sidis Y 2015 Nat. Commun. 6 8961
[70]	Watanabe H, Parameswaran S A, Raghu S, Vishwanath A 2014 Phys. Rev. B 90 045145
[71]	Hu Y, Wang B 2017 New J. Phys. 19 123002
[72]	Kittel C 1949 Rev. Mod. Phys. 21 541
[73]	Plumer M L, Walker M B 1982 J. Phys. C: Solid State Phys. 15 7181
[74]	Bak P, Jensen M H 1980 J. Phys. C: Solid State Phys. 13 L881
[75]	Schuette C, Iwasaki J, Rosch A, Nagaosa N 2014 Phys. Rev. B 90 174434
[76]	Yu X Z, Tokunaga Y, Kaneko Y, Zhang W Z, Kimoto K, Matsui Y, Taguchi Y, Tokura Y 2014 Nat. Commun. 5 3198
[77]	Wang W, Zhang Y, Xu G, Peng L, Ding B, Wang Y, Hou Z, Zhang X, Li X, Liu E, Wang S, Cai J, Wang F, Li J, Hu F, Wu G, Shen B, Zhang X X 2016 Adv. Mater. 28 6887
[78]	Nayak A K, Kumar V, Ma T, Werner P, Pippel E, Sahoo R, Damay F, Rler U K, Felser C, Parkin S 2017 Nature 548 561
[79]	Johnson M T, Bloemen P J H, den Broeder F J A, de Vries J J 1996 Rep. Prog. Phys. 59 1409
[80]	Born M, Huang K 1998 Dynamical Theory of Crystal Lattices (Oxford: Oxford University Press)
[81]	Walker M B 1980 Phys. Rev. Lett. 44 1261
[82]	Mura T 1982 Micromechanics of Defects in Solids (Netherlands: Springer)
[83]	Schulz T, Ritz R, Bauer A, Halder M, Wagner M, Franz C, Pfleiderer C, Everschor K, Garst M, Rosch A 2012 Nat. Phys. 8 2231
[84]	Kong L, Zang J 2013 Phys. Rev. Lett. 111 067203
[85]	Seki S, Ishiwata S, Tokura Y 2012 Phys. Rev. B 86 060403
[86]	Line M E, Glass A M 1977 Principles and Applications of Ferroelectrics and Related Materials (Oxford: Clarendon Press)
[87]	Landau L D, Lifshitz E M 1980 Statistical Physics (Part 1) (Oxford: Butterworth-Heinemann)
[88]	Wiesendanger R 2016 Nat. Rev. Mater. 1 16044
[89]	Hellman F, Hoffmann A, Tserkovnyak Y, Beach G S D, Fullerton E E, Leighton C, MacDonald A H, Ralph D C, Arena D A, Drr H A, Fischer P, Grollier J, Heremans J P, Jungwirth T, Kimel A V, Koopmans B, Krivorotov I N, May S J, Petford-Long A K, Rondinelli J M, Samarth N, Schuller I K, Slavin A N, Stiles M D, Tchernyshyov O, Thiaville A, Zink B L 2017 Rev. Mod. Phys. 89 025006
[90]	Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031
[91]	Kang W, Huang Y, Zhang X, Zhou Y, Zhao W 2016 Proc. IEEE 104 2040
[92]	Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[93]	Zhang X, Ezawa M, Zhou Y 2016 Phys. Rev. B 94 064406
[94]	Gbel B, Mook A, Henk J, Mertig I 2017 Phys. Rev. B 96 060406
[95]	Zhang X, Zhou Y, Ezawa M 2016 Sci. Rep. 6 24795
[96]	Kim S K, Lee K J, Tserkovnyak Y 2017 Phys. Rev. B 95 140404
[97]	Tanaka M, Sumitomo S, Adachi N, Honda S, Awano H, Mibu K 2017 AIP Adv. 7 055916
[98]	Hanneken C, Kubetzka A, von Bergmann K, Wiesendanger R 2016 New J. Phys. 18 055009
[99]	Rybakov F N, Borisov A B, Bluegel S, Kiselev N S 2015 Phys. Rev. Lett. 115 117201
[100]	Milde P, Koehler D, Seidel J, Eng L M, Bauer A, Chacon A, Kindervater J, Muehlbauer S, Pfleiderer C, Buhrandt S, Schuette C, Rosch A 2013 Science 340 1076
[101]	Ogawa N, Koshibae W, Beekman A J, Nagaosa N, Kubota M, Kawasaki M, Tokura Y 2015 Proc. Natl. Acad. Sci. USA 112 8977
[102]	Nepal R, Gngrd U, Kovalev A A 2017 ArXiv:1711.03041

施引文献

[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
[20]	Buettner F, Moutafis C, Schneider M, Krueger B, Guenther C M, Geilhufe J, von Schmising C K, Mohanty J, Pfau B, Schaffert S, Bisig A, Foerster M, Schulz T, Vaz C A F, Franken J H, Swagten H J M, Klaeui M, Eisebitt S 2015 Nat. Phys. 11 225
[21]	Jonietz F, Muehlbauer S, Pfleiderer C, Neubauer A, Muenzer W, Bauer A, Adams T, Georgii R, Boeni P, Duine R A, Everschor K, Garst M, Rosch A 2010 Science 330 1648
[22]	Zang J, Mostovoy M, Han J H, Nagaosa N 2011 Phys. Rev. Lett. 107 136804
[23]	Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Boeni P 2009 Phys. Rev. Lett. 102 186602
[24]	Franz C, Freimuth F, Bauer A, Ritz R, Schnarr C, Duvinage C, Adams T, Bluegel S, Rosch A, Mokrousov Y, Pfleiderer C 2014 Phys. Rev. Lett. 112 186601
[25]	Litzius K, Lemesh I, Krueger B, Bassirian P, Caretta L, Richter K, Buettner F, Sato K, Tretiakov O A, Foerster J, Reeve R M, Weigand M, Bykova L, Stoll H, Schuetz G, Beach G S D, Klaeui M 2017 Nat. Phys. 13 170
[26]	Chen G 2017 Nat. Phys. 13 112
[27]	Jiang W, Zhang X, Yu G, Zhang W, Wang X, Jungfleisch M B, Pearson J E, Cheng X, Heinonen O, Wang K L, Zhou Y, Hoffmann A, te Velthuis S G E 2017 Nat. Phys. 13 162
[28]	Shibata K, Iwasaki J, Kanazawa N, Aizawa S, Tanigaki T, Shirai M, Nakajima T, Kubota M, Kawasaki M, Park H S, Shindo D, Nagaosa N, Tokura Y 2015 Nat. Nanotechnol. 10 589
[29]	Karube K, White J S, Reynolds N, Gavilano J L, Oike H, Kikkawa A, Kagawa F, Tokunaga Y, Ronnow H M, Tokura Y, Taguchi Y 2016 Nat. Mater. 15 1237
[30]	Heinze S, von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Bluegel S 2011 Nat. Phys. 7 713
[31]	Huang S X, Chien C L 2012 Phys. Rev. Lett. 108 267201
[32]	Jiang W, Chen G, Liu K, Zang J, te Velthuis S G E, Hoffmann A 2017 Phys. Rep.: Rev. Sect. Phys. Lett. 704 1
[33]	Yu X, DeGrave J P, Hara Y, Hara T, Jin S, Tokura Y 2013 Nano Lett. 13 3755
[34]	Du H, DeGrave J P, Xue F, Liang D, Ning W, Yang J, Tian M, Zhang Y, Jin S 2014 Nano Lett. 14 2026
[35]	Du H, Ning W, Tian M, Zhang Y 2013 Phys. Rev. B 87 014401
[36]	Du H, Che R, Kong L, Zhao X, Jin C, Wang C, Yang J, Ning W, Li R, Jin C, Chen X, Zang J, Zhang Y, Tian M 2015 Nat. Commun. 6 8504
[37]	Adams T, Muehlbauer S, Pfleiderer C, Jonietz F, Bauer A, Neubauer A, Georgii R, Boeni P, Keiderling U, Everschor K, Garst M, Rosch A 2011 Phys. Rev. Lett. 107 217206
[38]	Hu Y 2017 arXiv:1702.01059v2
[39]	Nii Y, Kikkawa A, Taguchi Y, Tokura Y, Iwasa Y 2014 Phys. Rev. Lett. 113 267203
[40]	Cevey L, Wilhelm H, Schmidt M, Lortz R 2013 Phys. Status Solidi B: Basic Solid State Phys. 250 650
[41]	Lobanova I I, Glushkov V V, Sluchanko N E, Demishev S V 2016 Sci. Rep. 6 22101
[42]	Nakajima T, Oike H, Kikkawa A, Gilbert E P, Booth N, Kakurai K, Taguchi Y, Tokura Y, Kagawa F, Arima T H 2017 Sci. Adv. 3 e1602562
[43]	Butenko A B, Leonov A A, Roessler U K, Bogdanov A N 2010 Phys. Rev. B 82 052403
[44]	Wilson M N, Butenko A B, Bogdanov A N, Monchesky T L 2014 Phys. Rev. B 89 094411
[45]	Zhang S S L, Phatak C, Petford-Long A K, Heinonen O G 2017 Appl. Phys. Lett. 111 242405
[46]	Chen J, Cai W P, Qin M H, Dong S, Lu X B, Gao X S, Liu J M 2017 Sci. Rep. 7 7392
[47]	Fobes D M, Luo Y, Leon-Brito N, Bauer E D, Fanelli V R, Taylor M A, DeBeer-Schmitt L M, Janoschek M 2017 Appl. Phys. Lett. 110 192409
[48]	Nii Y, Nakajima T, Kikkawa A, Yamasaki Y, Ohishi K, Suzuki J, Taguchi Y, Arima T, Tokura Y, Iwasa Y 2015 Nat. Commun. 6 8539
[49]	Chacon A, Bauer A, Adams T, Rucker F, Brandl G, Georgii R, Garst M, Pfleiderer C 2015 Phys. Rev. Lett. 115 267202
[50]	Deutsch M, Makarova O L, Hansen T C, Fernandez-Diaz M T, Sidorov V A, Tsvyashchenko A V, Fomicheva L N, Porcher F, Petit S, Koepernik K, Rler U K, Mirebeau I 2014 Phys. Rev. B 89 180407
[51]	Deutsch M, Bonville P, Tsvyashchenko A V, Fomicheva L N, Porcher F, Damay F, Petit S, Mirebeau I 2014 Phys. Rev. B 90 144401
[52]	Wu H C, Chandrasekhar K D, Wei T Y, Hsieh K J, Chen T Y, Berger H, Yang H D 2015 J. Phys. Appl. Phys. 48 475001
[53]	Ritz R, Halder M, Franz C, Bauer A, Wagner M, Bamler R, Rosch A, Pfleiderer C 2013 Phys. Rev. B 87 134424
[54]	Levatic I, Popcevic P, Surija V, Kruchkov A, Berger H, Magrez A, White J S, Ronnow H M, Zivkovic I 2016 Sci. Rep. 6 21347
[55]	Karhu E, Kahwaji S, Monchesky T L, Parsons C, Robertson M D, Maunders C 2010 Phys. Rev. B 82 184417
[56]	Karhu E A, Roessler U K, Bogdanov A N, Kahwaji S, Kirby B J, Fritzsche H, Robertson M D, Majkrzak C F, Monchesky T L 2012 Phys. Rev. B 85 094429
[57]	Ghimire N J, McGuire M A, Parker D S, Sales B C, Yan J Q, Keppens V, Koehler M, Latture R M, Mandrus D 2012 Phys. Rev. B 85 224405
[58]	Liu Y, Lei N, Zhao W, Liu W, Ruotolo A, Braun H B, Zhou Y 2017 Appl. Phys. Lett. 111 022406
[59]	Chen G, N'Diaye A T, Kang S P, Kwon H Y, Won C, Wu Y, Qiu Z Q, Schmid A K 2015 Nat. Commun. 6 6598
[60]	Li Z, Zhang Y, Huang Y, Wang C, Zhang X, Liu Y, Zhou Y, Kang W, Koli S C, Lei N 2017 J. Magn. Magn. Mater. 455 19
[61]	Kang S P, Kwon H Y, Won C 2017 J. Appl. Phys. 121 203902
[62]	Hu Y, Wang B 2017 ArXiv:1608.04840v4
[63]	Hu Y, Wang B 2016 Sci. Rep. 6 30200
[64]	Wan X, Hu Y, Wang B 2018 J. Phys.: Condens. Matter 30 245001
[65]	Petrova A E, Stishov S M 2009 J. Phys. Condens. Matter 21 196001
[66]	Petrova A E, Stishov S M 2015 Phys. Rev. B 91 214402
[67]	Luo Y, Lin S, Leroux M, Wakeham N, Fobes D M, Bauer E D, Betts J B, Thompson J D, Migliori A, Janoschek M, Maiorov B 2017 ArXiv:1711.08873
[68]	Zhang X X, Nagaosa N 2017 New J. Phys. 19 043012
[69]	Ivanov A, Lamago D, Goering E, Weber F, Lhneysen H v, Mignot J M, Wang L, Steffens P, Heid R, Krannich S, Keller T, Sidis Y 2015 Nat. Commun. 6 8961
[70]	Watanabe H, Parameswaran S A, Raghu S, Vishwanath A 2014 Phys. Rev. B 90 045145
[71]	Hu Y, Wang B 2017 New J. Phys. 19 123002
[72]	Kittel C 1949 Rev. Mod. Phys. 21 541
[73]	Plumer M L, Walker M B 1982 J. Phys. C: Solid State Phys. 15 7181
[74]	Bak P, Jensen M H 1980 J. Phys. C: Solid State Phys. 13 L881
[75]	Schuette C, Iwasaki J, Rosch A, Nagaosa N 2014 Phys. Rev. B 90 174434
[76]	Yu X Z, Tokunaga Y, Kaneko Y, Zhang W Z, Kimoto K, Matsui Y, Taguchi Y, Tokura Y 2014 Nat. Commun. 5 3198
[77]	Wang W, Zhang Y, Xu G, Peng L, Ding B, Wang Y, Hou Z, Zhang X, Li X, Liu E, Wang S, Cai J, Wang F, Li J, Hu F, Wu G, Shen B, Zhang X X 2016 Adv. Mater. 28 6887
[78]	Nayak A K, Kumar V, Ma T, Werner P, Pippel E, Sahoo R, Damay F, Rler U K, Felser C, Parkin S 2017 Nature 548 561
[79]	Johnson M T, Bloemen P J H, den Broeder F J A, de Vries J J 1996 Rep. Prog. Phys. 59 1409
[80]	Born M, Huang K 1998 Dynamical Theory of Crystal Lattices (Oxford: Oxford University Press)
[81]	Walker M B 1980 Phys. Rev. Lett. 44 1261
[82]	Mura T 1982 Micromechanics of Defects in Solids (Netherlands: Springer)
[83]	Schulz T, Ritz R, Bauer A, Halder M, Wagner M, Franz C, Pfleiderer C, Everschor K, Garst M, Rosch A 2012 Nat. Phys. 8 2231
[84]	Kong L, Zang J 2013 Phys. Rev. Lett. 111 067203
[85]	Seki S, Ishiwata S, Tokura Y 2012 Phys. Rev. B 86 060403
[86]	Line M E, Glass A M 1977 Principles and Applications of Ferroelectrics and Related Materials (Oxford: Clarendon Press)
[87]	Landau L D, Lifshitz E M 1980 Statistical Physics (Part 1) (Oxford: Butterworth-Heinemann)
[88]	Wiesendanger R 2016 Nat. Rev. Mater. 1 16044
[89]	Hellman F, Hoffmann A, Tserkovnyak Y, Beach G S D, Fullerton E E, Leighton C, MacDonald A H, Ralph D C, Arena D A, Drr H A, Fischer P, Grollier J, Heremans J P, Jungwirth T, Kimel A V, Koopmans B, Krivorotov I N, May S J, Petford-Long A K, Rondinelli J M, Samarth N, Schuller I K, Slavin A N, Stiles M D, Tchernyshyov O, Thiaville A, Zink B L 2017 Rev. Mod. Phys. 89 025006
[90]	Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031
[91]	Kang W, Huang Y, Zhang X, Zhou Y, Zhao W 2016 Proc. IEEE 104 2040
[92]	Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[93]	Zhang X, Ezawa M, Zhou Y 2016 Phys. Rev. B 94 064406
[94]	Gbel B, Mook A, Henk J, Mertig I 2017 Phys. Rev. B 96 060406
[95]	Zhang X, Zhou Y, Ezawa M 2016 Sci. Rep. 6 24795
[96]	Kim S K, Lee K J, Tserkovnyak Y 2017 Phys. Rev. B 95 140404
[97]	Tanaka M, Sumitomo S, Adachi N, Honda S, Awano H, Mibu K 2017 AIP Adv. 7 055916
[98]	Hanneken C, Kubetzka A, von Bergmann K, Wiesendanger R 2016 New J. Phys. 18 055009
[99]	Rybakov F N, Borisov A B, Bluegel S, Kiselev N S 2015 Phys. Rev. Lett. 115 117201
[100]	Milde P, Koehler D, Seidel J, Eng L M, Bauer A, Chacon A, Kindervater J, Muehlbauer S, Pfleiderer C, Buhrandt S, Schuette C, Rosch A 2013 Science 340 1076
[101]	Ogawa N, Koshibae W, Beekman A J, Nagaosa N, Kubota M, Kawasaki M, Tokura Y 2015 Proc. Natl. Acad. Sci. USA 112 8977
[102]	Nepal R, Gngrd U, Kovalev A A 2017 ArXiv:1711.03041

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