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).

References

[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

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
[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

[1]	Shi Meng, Wang Wei-Wei, Du Hai-Feng. Exploring approximate analytical expression for magnetic skyrmion structure based on symbolic regression method. Acta Physica Sinica, 2024, 73(1): 011201. doi: 10.7498/aps.73.20231473
[2]	Chen Chong, Ma Ming-Yuan, Pan Feng, Song Cheng. Magneto-acoustic coupling: Physics, materials, and devices. Acta Physica Sinica, 2024, 73(5): 058502. doi: 10.7498/aps.73.20231908
[3]	Gao Jin-Wei, Chen Lu, Li Xu-Hong, Shi Jun-Qin, Cao Teng-Fei, Fan Xiao-Li. Intrinsic multiferroic semiconductors with magnetoelastic coupling: two-dimensional MoTeX (X = F, Cl, Br, I) monolayers. Acta Physica Sinica, 2024, 73(19): 197501. doi: 10.7498/aps.73.20240829
[4]	Liu Yi, Qian Zheng-Hong, Zhu Jian-Guo. Research progress of room temperature magnetic skyrmion and its application. Acta Physica Sinica, 2020, 69(23): 231201. doi: 10.7498/aps.69.20200984
[5]	Xuan Sheng-Jie, Liu Yan. Control of skyrmion movement in nanotrack by using periodic strain. Acta Physica Sinica, 2018, 67(13): 137503. doi: 10.7498/aps.67.20180031
[6]	Dong Bo-Wen, Zhang Jing-Yan, Peng Li-Cong, He Min, Zhang Ying, Zhao Yun-Chi, Wang Chao, Sun Yang, Cai Jian-Wang, Wang Wen-Hong, Wei Hong-Xiang, Shen Bao-Gen, Jiang Yong, Wang Shou-Guo. Multi-field control on magnetic skyrmions. Acta Physica Sinica, 2018, 67(13): 137507. doi: 10.7498/aps.67.20180931
[7]	Liu Yi-Zhou, Zang Jiadong. Overview and outlook of magnetic skyrmions. Acta Physica Sinica, 2018, 67(13): 131201. doi: 10.7498/aps.67.20180619
[8]	Li Wen-Jing, Guang Yao, Yu Guo-Qiang, Wan Cai-Hua, Feng Jia-Feng, Han Xiu-Feng. Skyrmions in magnetic thin film heterostructures. Acta Physica Sinica, 2018, 67(13): 131204. doi: 10.7498/aps.67.20180549
[9]	Zhao Wei-Sheng, Huang Yang-Qi, Zhang Xue-Ying, Kang Wang, Lei Na, Zhang You-Guang. Overview and advances in skyrmionics. Acta Physica Sinica, 2018, 67(13): 131205. doi: 10.7498/aps.67.20180554
[10]	Liang Xue, Zhao Li, Qiu Lei, Li Shuang, Ding Li-Hong, Feng You-Hua, Zhang Xi-Chao, Zhou Yan, Zhao Guo-Ping. Skyrmions-based magnetic racetrack memory. Acta Physica Sinica, 2018, 67(13): 137510. doi: 10.7498/aps.67.20180764
[11]	Hou Zhi-Peng, Ding Bei, Li Hang, Xu Gui-Zhou, Wang Wen-Hong, Wu Guang-Heng. Observation of new-type magnetic skymrions with extremerely high temperature stability and fabrication of skyrmion-based race-track memory device. Acta Physica Sinica, 2018, 67(13): 137509. doi: 10.7498/aps.67.20180419
[12]	Jin Chen-Dong, Song Cheng-Kun, Wang Jin-Shuai, Wang Jian-Bo, Liu Qing-Fang. Research progress of micromagnetic magnetic skyrmions and applications. Acta Physica Sinica, 2018, 67(13): 137504. doi: 10.7498/aps.67.20180165
[13]	Kong Ling-Yao. Research progress on topological properties and micro-magnetic simulation study in dynamics of magnetic skyrmions. Acta Physica Sinica, 2018, 67(13): 137506. doi: 10.7498/aps.67.20180235
[14]	Zhang Lei. Critical behaviors of helimagnetic ordering systems relating to skyrmion. Acta Physica Sinica, 2018, 67(13): 137501. doi: 10.7498/aps.67.20180137
[15]	Li Zi-An, Chai Ke, Zhang Ming, Zhu Chun-Hui, Tian Huan-Fang, Yang Huai-Xin. In situ electron holography of magnetic skyrmions in nanostructures. Acta Physica Sinica, 2018, 67(13): 131203. doi: 10.7498/aps.67.20180426
[16]	Chi Xiao-Dan, Hu Yong. Modulation of skyrmion diameter in centrosymmetric frustrated magnet. Acta Physica Sinica, 2018, 67(13): 137502. doi: 10.7498/aps.67.20172709
[17]	Xia Jing, Han Zong-Yi, Song Yi-Fan, Jiang Wen-Jing, Lin Liu-Rong, Zhang Xi-Chao, Liu Xiao-Xi, Zhou Yan. Overview of magnetic skyrmion-based devices and applications. Acta Physica Sinica, 2018, 67(13): 137505. doi: 10.7498/aps.67.20180894
[18]	Xu Gui-Zhou, Xu Zhan, Ding Bei, Hou Zhi-Peng, Wang Wen-Hong, Xu Feng. Magnetic domain chirality and tuning of skyrmion topology. Acta Physica Sinica, 2018, 67(13): 137508. doi: 10.7498/aps.67.20180513
[19]	Guo Guang-Hua, Zhang Guang-Fu, Wang Xi-Guang. Irreversible exchange-spring processes of antiferromagnetically exchange coupled hard-soft-hard trilayer structures. Acta Physica Sinica, 2011, 60(10): 107503. doi: 10.7498/aps.60.107503
[20]	Cui Yu-Ting, Chen Jing-Lan, Liu Guo-Dong, Wu Guang-Heng, Liao Ke-Jun, Wang Wan-Lu. Characteristics of the premartensitic transition in the Ni50.5Mn24.5G25 single crystals. Acta Physica Sinica, 2005, 54(1): 263-268. doi: 10.7498/aps.54.263

Catalog

Vol. 67, Issue 13 - 2018-07-05

Metrics

Abstract views: 7731
PDF Downloads: 409
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板