磁子霍尔效应

金哲珺雨; 曾钊卓; 曹云姗; 严鹏

doi:10.7498/aps.73.20231589

摘要

霍尔效应是凝聚态领域中古老却又极具潜力的研究领域, 其起源可以追溯到数百年前. 1879 年, 霍尔发现将载流导体置于磁场中时, 磁场带来的洛伦兹力将使得电子在导体的一侧积累, 这一新奇的物理现象被命名为霍尔效应. 之后, 一系列新的霍尔效应被发现, 包括反常霍尔效应、量子霍尔效应、自旋霍尔效应、拓扑霍尔效应和平面霍尔效应等. 值得注意的是, 霍尔效应能够实现不同方向的粒子流之间的相互转化, 因此在信息传输过程中扮演着重要的角色. 在玻色子体系(如磁子)中, 相应的一系列磁子霍尔效应也被发现, 他们共同推动了以磁子为基础的自旋电子学的发展. 本文回顾了近年来在磁子体系中的霍尔效应, 简述其现代半经典的处理方法, 包括虚拟电磁场理论和散射理论等. 并进一步介绍了磁子霍尔效应的物理起源, 概述了不同类型磁子的霍尔效应. 最后, 对磁子霍尔效应的发展趋势进行了展望.

关键词:

Abstract

Hall effect is an ancient but highly potential subfield in condensed matter physics, and its origin can be traced back hundreds of years. In 1879, Hall made a momentous discovery that when a current-carrying conductor is placed in a magnetic field, the Lorentz force pushes its electrons to one side of the conductor. This intriguing phenomenon was dubbed Hall effect. Since then, a series of novel Hall effects have been discovered, including anomalous Hall effect, quantum Hall effect, spin Hall effect, topological Hall effect, and planar Hall effec. Notably, Hall effects play an important role in realizing the information transport, since it can realize the mutual conversion of current in different directions. In bosonic systems such as magnons, a series of magnon Hall effects have been found, jointly driving the development of the magnon-based spintronics. In this perspective, we review the researches of the Hall effect in magnonic system in recent years, and briefly introduce its modern semi-classical theories, including virtual electromagnetic field theory and scattering theory. Furthermore, we introduce the different magnon Hall effects and clarify the physics behind them. Finally, the prospect of magnon Hall effect is discussed.

Keywords:

作者及机构信息

电子科技大学物理学院, 电子薄膜与集成器件国家重点实验室, 成都　611731

通信作者: 严鹏, yan@uestc.edu.cn

基金项目: 国家重点研发计划(批准号: 2022YFA1402802)和国家自然科学基金(批准号: 12074057, 12374103)资助的课题.

Authors and contacts

State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding author: Yan Peng, yan@uestc.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402802) and the National Natural Science Foundation of China (Grant Nos. 12074057, 12374103).

文章全文 : translate this paragraph

参考文献

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[9]	Tian Y, Ye L, Jin X 2009 Phys. Rev. Lett. 103 087206 Google Scholar
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[14]	Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Böni P 2009 Phys. Rev. Lett. 102 186602 Google Scholar
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[21]	Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 465 901 Google Scholar
[22]	Heinze S, Bergmann K V, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blügel S 2011 Nat. Phys. 7 713 Google Scholar
[23]	Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915 Google Scholar
[24]	Matsumoto R, Murakami S 2011 Phys. Rev. Lett. 106 197202 Google Scholar
[25]	Zhang L, Ren J, Wang J, Li B 2013 Phys. Rev. B 87 144101 Google Scholar
[26]	Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241 Google Scholar
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[29]	Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, Tokura Y 2010 Science 329 297 Google Scholar
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[43]	Kim S K, Nakata K, Loss D, Tserkovnyak Y 2019 Phys. Rev. Lett. 122 057204 Google Scholar
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[46]	Iwasaki J, Beekman A J, Nagaosa N 2014 Phys. Rev. B 89 064412 Google Scholar
[47]	Schütte C, Garst M 2014 Phys. Rev. B 90 094423 Google Scholar
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[53]	Wang Z, Yuan H Y, Cao Y, Li Z, Duine R A, Yan P 2021 Phys. Rev. Lett. 127 037202 Google Scholar
[54]	Wang Z, Yuan H Y, Cao Y, Yan P 2022 Phys. Rev. Lett. 129 107203 Google Scholar
[55]	Schultheiss H, Vogt K, Hillebrands B 2012 Phys. Rev. B 86 054414 Google Scholar
[56]	Tymchenko M, Gomez-Diaz J S, Lee J, Nookala N, Belkin M A, Alù A 2015 Phys. Rev. Lett. 115 207403 Google Scholar
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施引文献

图 1 (a)磁子波包的自转和绕着系统边界的磁子流; (b)沿着边界传输且与边界形状无关的磁子流; (c)平衡态时的边界磁子流; (d)温度梯度导致的有限热霍尔磁子流^[24]

Fig. 1. (a) Self-rotation of a magnon wave packet and a magnon edge current; (b) the magnon near the boundary proceeds along the boundary, irrespective of the edge shape; (c) magnon edge current in equilibrium; (d) under the temperature gradient, a finite thermal Hall current will appear^[24]

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图 2 DM相互作用在烧绿石(111)平面中诱导的幅角$ \phi_i $分布(a)和在扭曲的钙钛矿的z-x平面中诱导的幅角分布(b)^[30]; (c) 磁子的霍尔效应示意图^[29]

Fig. 2. Spital distribution of $ \phi_i $ induced by DM interaction in the (111) plane of the pyrochlore lattice (a) and the z-x plane of the distorted perovskite structure (b)^[30]; (c) schematic of magnon Hall effect^[29]

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图 3 (a)磁子的极化, 即自旋的进动轨迹和波矢的关系; (b) 偶极-偶极相互作用力在反铁磁体系中诱导的磁子自旋霍尔效应的示意图^[31]

Fig. 3. (a) The polarization, i.e., the trajectory of the spin precession as a function of wave vectors; (b) schematic of magnon spin Hall effect induced by the dipolar interaction^[31].

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图 4 (a) 磁椭球中磁子的色散关系; (b) 钇铁石榴石 (YIG) 中不同类型的静磁模自旋波^[35]

Fig. 4. (a) Dispersion relation of SW for a magnetic ellipsoid; (b) different types of magnetostatic SWs in yttrium iron garnet (YIG)^[35]

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图 5 在$ H_0=M_0 $情况下, 静磁前向体模式的色散关系(a)和贝里曲率分布(b)^[34]

Fig. 5. Dispersion (a) and Berry curvature (b) for the magnetostatic forwardvolume-wave mode for $ H_0/M_0=1 $^[34].

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图 6 (a)磁子经过磁织构之后的斜散射和边跳跃行为^[38]; 磁子经过(b)亚铁磁和(c)反铁磁斯格明子之后的偏转轨迹^[42,43]; (d)散射理论计算得到的不同入射磁子能量下的微分散射截面, $ \varepsilon_{\rm gap} $为k = 0时的磁子能量^[47]; (e)磁子的彩虹散射过程^[47]

Fig. 6. (a) Skew scattering and side jump of spin wave across magnetic texture^[38]; the trajectories of spin wave across (b) antiferromagnetic and (c) ferrimagnetic skyrmion^[42,43]; (d) differential cross section evaluated from scattering theory for various energies, $ \varepsilon_{\rm gap} $ is the magnon gap^[47] at k = 0; (e) the rainbow scattering process of magnons^[47]

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图 7 (a)由贝里曲率诱导的反常霍尔效应和贝里曲率偶极子诱导的非线性霍尔效应示意图^[50]. (b)非线性磁子流和交换系数$ J_1 $的关系^[51]. 磁子的(c)能带、(d)贝里曲率和(e)贝里曲率偶极子在动量空间的分布^[51]

Fig. 7. (a) Schematics of the anomalous Hall effect induced by the finite Berry curvature and the nonlinear Hall effect induced by the finite Berry curvature dipoles in the entire space, respectively^[50]. (b) Nonlinear magnon current as a function of exchange constant $ J_1 $^[51]. Distribution of (c) the band structure, (d) berry curvature, and (e) berry curvature dipole of magnons in the momentum space^[51]

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图 8 (a)非线性三磁子过程示意图; (b) 三磁子散射诱导的磁子频率梳示意图^[53]; (c) 非线性四磁子过程示意图

Fig. 8. (a) Schematic diagram of the nonlinear three-magnon process; (b) schematic diagram of three-magnon scattering induced magnon frequency comb^[53]; (c) schematic diagram of the nonlinear four-magnon process

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图 9 (a)磁子非线性拓扑自旋霍尔效应示意图; (b)虚拟磁场B 和B'的空间分布以及对应磁子的运动轨迹(分别在B和B+B'作用下); (c)不同磁子模式的波函数的等值线分布; (d)线性非线性霍尔角和入射磁子频率$ \omega_{\mathrm{s}} $以及非线性阶数m的关系^[59]

Fig. 9. (a) Schematic illustration of the nonlinear topological magnon spin Hall effect in magnon-AFM skyrmion scattering; (b) spatial distribution of dimensionless field B and B' as well as the corresponding spin wave trajectories in real space; (c) isoline maps for different magnon modes; (d) the Hall angle as a function of the incident magnon frequencie $ \omega_{\mathrm{s}} $ and mode index m^[59]

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map

[1]	Žutić L, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323 Google Scholar
[2]	Lenk B, Ulrichs H, Garbs F, Münzenberg M 2011 Phys. Rep. 507 107 Google Scholar
[3]	Chumak A V, Vasyuchka V I, Serga A A, Hillebrands B 2015 Nat. Phys. 11 453 Google Scholar
[4]	Yuan H Y, Cao Y, Kamra A, Duine R A, Yan P 2022 Phys. Rep. 965 1 Google Scholar
[5]	Hall E H 1879 Am. J. Math. 2 287 Google Scholar
[6]	Nagaosa N, Sinova J, Onoda S, MacDonald A H, Ong N P 2010 Rev. Mod. Phys. 82 1539 Google Scholar
[7]	Jungwirth T, Niu Q, MacDonald A H 2002 Phys. Rev. Lett. 88 207208 Google Scholar
[8]	Liang T, Lin J, Gibson Q, Kushwaha S, Liu M, Wang W, Xiong H, Sobota J A, Hashimoto M, Kirchmann P S, Shen Z, Cava R J, Ong N P 2018 Nat. Phys. 14 451 Google Scholar
[9]	Tian Y, Ye L, Jin X 2009 Phys. Rev. Lett. 103 087206 Google Scholar
[10]	Hirsch J E 1999 Phys. Rev. Lett. 83 1834 Google Scholar
[11]	Sinova J, Culcer D, Niu Q, Sinitsyn N A, Jungwirth T, MacDonald A H 2004 Phys. Rev. Lett. 92 126603 Google Scholar
[12]	Kato Y K, Myers R C, Niu Q, Gossard A C, Jawschalom D D 2004 Science 306 1910 Google Scholar
[13]	Sinova J, Valenzuela S O, Wunderlich J, Back C H, Jungwirth T 2015 Rev. Mod. Phys. 87 1213 Google Scholar
[14]	Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Böni P 2009 Phys. Rev. Lett. 102 186602 Google Scholar
[15]	Yin G, Liu Y, Barlas Y, Zang J, Lake R K 2015 Phys. Rev. B 92 024411 Google Scholar
[16]	Göbel B, Mook A, Henk J, Mertig I 2017 Phys. Rev. B 96 060406 Google Scholar
[17]	Akosa C A, Tretiakov O A, Tatara G, Manchon A 2018 Phys. Rev. Lett. 121 097204 Google Scholar
[18]	Berry M V 1984 Proc. R. Soc. A 392 45
[19]	Skyrme T H R 1962 Nucl. Phys. 31 556 Google Scholar
[20]	Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Böni P 2009 Science 323 915 Google Scholar
[21]	Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 465 901 Google Scholar
[22]	Heinze S, Bergmann K V, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blügel S 2011 Nat. Phys. 7 713 Google Scholar
[23]	Sundaram G, Niu Q 1999 Phys. Rev. B 59 14915 Google Scholar
[24]	Matsumoto R, Murakami S 2011 Phys. Rev. Lett. 106 197202 Google Scholar
[25]	Zhang L, Ren J, Wang J, Li B 2013 Phys. Rev. B 87 144101 Google Scholar
[26]	Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241 Google Scholar
[27]	Moriya T 1960 Phys. Rev. 120 91 Google Scholar
[28]	Katsura H, Nagaosa N, Lee P A 2010 Phys. Rev. Lett. 104 066403 Google Scholar
[29]	Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, Tokura Y 2010 Science 329 297 Google Scholar
[30]	Ideue T, Onose Y, Katsura H, Shiomi Y, Ishiwata S, Nagaosa N, Tokura Y 2012 Phys. Rev. B 85 134411 Google Scholar
[31]	Shen K 2020 Phys. Rev. Lett. 124 077201 Google Scholar
[32]	Yu H, Xiao J, Schultheiss H 2021 Phys. Rep. 905 1 Google Scholar
[33]	Li Z X, Cao Y, Yan P 2021 Phys. Rep. 915 1 Google Scholar
[34]	Murakami S, Okamoto A 2017 J. Phys. Soc. Jpn. 86 011010 Google Scholar
[35]	Serga A A, Chumak A V, Hillebrands B 2010 J. Phys. D: Appl. Phys. 43 264002 Google Scholar
[36]	van Hoogdalem K A, Tserkovnyak Y, Loss D 2013 Phys. Rev. B 87 024402 Google Scholar
[37]	Holstein T, Primakoff H 1940 Phys. Rev. 58 1098 Google Scholar
[38]	Lan J, Xiao J 2021 Phys. Rev. B 103 054428 Google Scholar
[39]	Lan J, Yu W, Xiao J 2021 Phys. Rev. B 103 214407 Google Scholar
[40]	Thiele A A 1973 Phys. Rev. Lett. 30 230 Google Scholar
[41]	Iwasaki J, Mochizuki M, Nagaosa N 2013 Nat. Commun. 4 1463 Google Scholar
[42]	Daniels M W, Yu W, Cheng R, Xiao J, Xiao D 2019 Phys. Rev. B 99 224433 Google Scholar
[43]	Kim S K, Nakata K, Loss D, Tserkovnyak Y 2019 Phys. Rev. Lett. 122 057204 Google Scholar
[44]	Jin Z, Meng C Y, Liu T T, Chen D Y, Fan Z, Zeng M, Lu X B, Gao X S, Qin M H, Liu J M 2021 Phys. Rev. B 104 054419 Google Scholar
[45]	Liu Y, Liu T T, Jin Z, Hou Z P, Chen D Y, Fan Z, Zeng M, Lu X B, Gao X S, Qin M H, Liu J M 2022 Phys. Rev. B 106 064424 Google Scholar
[46]	Iwasaki J, Beekman A J, Nagaosa N 2014 Phys. Rev. B 89 064412 Google Scholar
[47]	Schütte C, Garst M 2014 Phys. Rev. B 90 094423 Google Scholar
[48]	Berry M V, Mount K E 1972 Rep. Progr. Phys. 35 315 Google Scholar
[49]	Sodemann I, Fu L 2015 Phys. Rev. Lett. 115 216806 Google Scholar
[50]	Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M M, Wu S, Du Z, Hsu C H, Fang S, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Kaxiras E, Lu H Z, Lin H, Fu L, Gedik N, Herrero P J 2019 Nature 565 337 Google Scholar
[51]	Kondo H, Akagi Y 2022 Phys. Rev. Res. 4 013186 Google Scholar
[52]	Schultheiss H, Janssens X, Kampen M V, Ciubotaru F, Hermsdoerfer S J, Obry B, Laraoui A, Serga A A, Lagae L, Slavin A N, Leven B, Hillebrands B 2009 Phys. Rev. Lett. 103 157202 Google Scholar
[53]	Wang Z, Yuan H Y, Cao Y, Li Z, Duine R A, Yan P 2021 Phys. Rev. Lett. 127 037202 Google Scholar
[54]	Wang Z, Yuan H Y, Cao Y, Yan P 2022 Phys. Rev. Lett. 129 107203 Google Scholar
[55]	Schultheiss H, Vogt K, Hillebrands B 2012 Phys. Rev. B 86 054414 Google Scholar
[56]	Tymchenko M, Gomez-Diaz J S, Lee J, Nookala N, Belkin M A, Alù A 2015 Phys. Rev. Lett. 115 207403 Google Scholar
[57]	Li G, Chen S, Pholchai N, Reineke B, Wong P W H, Pun E Y B, Cheah K W, Zentgraf T, Zhang S 2015 Nat. Mater. 14 607 Google Scholar
[58]	Li Y, Yesharim O, Hurvitz I, Karnieli A, Fu S, Porat G, Arie A 2020 Phys. Rev. A 101 033807 Google Scholar
[59]	Jin Z, Yao X, Wang Z, Yuan H Y, Zeng Z, Wang W, Cao Y S, Yan P 2023 Phys. Rev. Lett. 131 166704 Google Scholar
[60]	Zyuzin V A, Kovalev A A 2016 Phys. Rev. Lett. 117 217203 Google Scholar
[61]	Xiao J, Bauer G E W, Uchida K, Saitoh E, Maekawa S 2000 Phys. Rev. B 81 214418
[62]	Mook A, Plekhanov K, Klinovaja J, Loss D 2021 Phys. Rev. X 11 021061
[63]	Zhang X, Zhang Y, Okamoto S, Xiao D 2019 Phys. Rev. Lett. 123 167202 Google Scholar
[64]	Cao Y, Fatemi V, Demir A, Fang S, Tomarken S, Luo J, Sanchez-Yamagishi J, Watanabe K, Taniguchi T, Kaxiras E, Ashoori R, Jarillo-Herrero P 2018 Nature 556 80
[65]	Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P 2018 Nature 556 43
[66]	Duan J, Jian Y, Gao Y, Peng H, Zhong J, Feng Q, Mao J, Yao Y 2022 Phys. Rev. Lett. 129 186801 Google Scholar
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