块状和超薄磁性材料中巨大且可调控的面内自旋角位移

李乾阳; 袁帅杰; 杨锦; 王勇; 马祖海; 陈宇; 周新星

doi:10.7498/aps.72.20221643

摘要

磁光克尔效应是指处于磁场中的光束在磁体表面发生反射时, 反射光的偏振面相对入射光发生旋转的物理现象, 它反映了磁化强度对磁性材料光学性质的影响. 磁性介质的磁光克尔效应则由含磁光常数的介电张量表征, 因此对磁光常数进行精确测量具有重要的科学意义. 光子自旋霍尔效应表现为光束在折射率不同的介质界面上传输时由于自旋-轨道相互作用而产生的光子自旋分裂现象. 过去大多数研究利用光子自旋霍尔效应的横向空间位移来表征磁光常数. 然而, 现有工作只考虑了单个磁场方向的磁光克尔效应, 并且由于微小的自旋空间位移而需要引入复杂的弱测量技术. 本文从理论上全面探究了3种磁光克尔效应条件下的面内自旋角位移, 发现通过改变磁场方向和磁性材料的厚度(考虑块状和超薄)可以实现对光子自旋霍尔效应的有效操纵. 同时, 该研究提出了一种直接测量磁光常数的新方法, 即通过直接观测巨大的面内自旋角位移来表征磁光常数的振幅与相位. 该方法不需要引入弱测量系统, 不仅为磁光常数的测量提供了直接有效的探针, 并且扩展了自旋光子学的相关研究.

关键词:

Abstract

The magneto-optical Kerr effect (MOKE) refers to the rotation of the polarization plane when a linearly polarized light is reflected at the surface of magnetic material. The MOKE reveals the magnetization of the optical properties of magnetic material and can be characterized by the dielectric tensor containing the magneto-optical constant. Thus, exploring the MOKE requires very precise determination of the magneto-optical constant. The photonic spin Hall effect (PSHE), which corresponds to the lateral and in-plane spin-dependent splitting of the beam, can be used as an effective method to characterize the magneto-optical constant due to its advantage of being extremely sensitive to changes in the physical parameters of the material. Most of the previous studies only considered the case of a single thickness of magnetic material and a single MOKE and need to introduce complex weak measurement techniques to observe the photonic spin Hall effect. In this work, we theoretically investigate the in-plane spin angular shifts in three MOKE cases in bulk and ultrathin magnetic materials. We can effectively tune the in-plane angular displacements of different magnetic material thickness by changing the magnetic field direction corresponding to different MOKEs and changing the magneto-optical constants (including amplitude and phase). The research results show that in the case of bulk and ultrathin magnetic materials, the internal spin angular displacements under different MOKEs will show different trends when the magneto-optical constants change the amplitude and phase, especially in ultra-thin magnetic material. In the lateral Kerr effect in thin material, the photon in-plane angular displacement does not affect the change of the magneto-optical constant, but in other cases, the amplitude relative to the phase has a much larger effect on the photon in-plane angular displacement. In this regard, we propose a new method which can directly determine the amplitude and phase of the magneto-optical constant by using the huge in-plane spin angular displacement without considering the weak measurements and can also judge different MOKEs according to the variation of the in-plane angular displacement in the bulk and ultrathin magnetic materials. This method not only provides a new probe for measuring magneto-optical constants but also expands the study of spin photonics.

Keywords:

作者及机构信息

1.
湖南师范大学物理与电子科学学院, 量子效应及其应用协同创新中心, 低维量子结构与调控教育部重点实验室, 长沙　410081

2.
深圳大学微纳光电子学研究院, 二维材料光电科技国际合作联合实验室, 深圳　510086

通信作者: 陈宇, yuchen@szu.edu.cn ; 周新星, xinxingzhou@hunnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11604095)、湖南省自然科学基金(批准号: 2017JJ3209)和长沙市杰出创新青年培养计划(批准号: KQ2107013)资助的课题.

Authors and contacts

1.
Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, School of Physics and Electronics, Hunan Normal University, Changsha 410081, China

2.
International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology, Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen 510086, China

Corresponding author: Chen Yu, yuchen@szu.edu.cn ; Zhou Xin-Xing, xinxingzhou@hunnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No.11604095), the Natural Science Foundation of Hunan Province, China(Grant No. 2017JJ3209), and the Training Program for Excellent Young Innovators of Changsha, China (Grant No. KQ2107013).

文章全文 : translate this paragraph

参考文献

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[7]	Soldatov I V, Schäfer R 2017 J. Appl. Phys. 122 153906 Google Scholar
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[21]	王莉岑, 邱晓东, 张志友, 石瑞英 2015 物理学报 64 174202 Google Scholar Wang L C, Qiu X D, Zhang Z Y, Shi R Y 2015 Acta Phys. Sin. 64 174202 Google Scholar
[22]	Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93 083901 Google Scholar
[23]	Bliokh K Y, Rodriguez-Fortuno F J, Nori F, Zayats A V 2015 Nat. Photon. 9 796 Google Scholar
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施引文献

图 1 磁性材料表面的光子自旋霍尔效应　(a), (b)高斯光束在块状铁(空气-铁)和超薄铁(空气-铁-玻璃)上的反射示意图; (c), (d)右旋圆偏振分量(RCP)所产生的角位移$\varDelta _ - ^X = Z\emptyset _ - ^X$示意图. 块状铁的厚度大于450 nm, 超薄铁厚度$d$满足$2{\text{π }}d|{n_1}|\lambda \ll 1$

Fig. 1. The photonic spin Hall effect on the surface of magnetic materials: (a), (b) Schematic diagram of Gaussian beam on bulk Fe (air-Fe) and ultrathin Fe (air-Fe-glass); (c), (d) schematic diagram of angular shifts $\varDelta _ - ^X = Z\emptyset _ - ^X$ induced by right-handed circularly-polarized component (RCP). The thickness of bulk Fe is greater than 450 nm, which is considered an infinite thickness, and the thickness of ultrathin Fe satisfies$2{\text{π }}d|{n_1}|\lambda \ll 1$.

下载: 全尺寸图片幻灯片

图 2 特殊入射条件下的磁性材料铁表面(块状和超薄)的面内巨大角位移　(a)(b)显示了极向克尔效应和横向克尔效应下块状铁的角位移; (c)(d)显示了极向克尔效应和横向克尔效应下超薄铁的角位移. 其中, Δ^bulk, Δ^ultrathin分别表示为块状铁和超薄铁的光子面内角位移

Fig. 2. Giant spin angular shifts under special incident conditions (bulk and ultrathin): (a)(b) The angular shifts of bulk Fe under the condition of Polar Kerr effect and Transverse Kerr effect; (c)(d) for ultrathin Fe. Δ^bulk, Δ^ultrathinare denoted as the angular shifts for bulk and ultrathin Fe, respectively.

下载: 全尺寸图片幻灯片

图 3 面内角位移对磁光振幅${Q_0}$ (从$ 0 $增大到对应的饱和值)的敏感程度　(a)—(d)显示了在极向克尔效应和横向克尔效应下块状铁和超薄铁的角位移变化; (e)—(h)描述了在不同偏振幅${Q_0}$对应的角位移曲线, 其中插图为右圆偏振分量的电场分布

Fig. 3. Sensitivity of in-plane angular displacement on the magneto-optical constant amplitude ${Q_0}$ (increasing from $ 0 $ to the corresponding saturation value): (a)–(d) The variation of angular shifts of bulk Fe and ultrathin Fe under the Polar and Transverse Kerr effect; (e)–(h) the angular shifts curves corresponding to their left panels at different amplitudes${Q_0}$. Here, the insets denote electric field distribution of the right-handed circularly polarized component.

下载: 全尺寸图片幻灯片

图 4 面内角位移对磁光常数相位q (从0增大到相应的饱和值)的敏感程度　(a)—(d)显示了在极向和横向克尔效应下块状铁和超薄铁的面内角位移变化; (e)—(h)描述了在对应于左图的不同相位q的角位移曲线

Fig. 4. Sensitivity of in-plane angular displacement on the magneto-optical constant phases q (increasing from 0 to the corresponding saturation value): (a)–(d) The variation of angular shifts of bulk Fe and ultrathin Fe under the Polar and Transverse Kerr effects; (e)–(h) the angular shift curves corresponding to their left panels at different phases q.

下载: 全尺寸图片幻灯片

[1]	Stanciu C D, Hansteen F, Kimel A V, Kirilyuk A, Tsukamoto A, Itoh A, Rasing T 2007 Phys. Rev. Lett. 99 047601 Google Scholar
[2]	Lee O J, You L, Jang J, Subramanian V, Salahuddin S 2015 Appl. Phys. Lett. 107 252401 Google Scholar
[3]	Zhao X, Zhang X, Yang H, Cai W, Zhao Y, Wang Z, Zhao W 2019 Nanotechnology 30 335707 Google Scholar
[4]	Hansteen F, Kimel A, Kirilyuk A, Rasing T 2005 Phys. Rev. Lett. 95 047402 Google Scholar
[5]	Kerr LL D J 1877 Philos. Mag. J. Sci. 3 321
[6]	Moog E R, Bader S D 1985 Superlattices Microstruct. 1 543 Google Scholar
[7]	Soldatov I V, Schäfer R 2017 J. Appl. Phys. 122 153906 Google Scholar
[8]	Akahane K, Kimura T, Otani Y 2004 J. Magn. Soci. Jpn 28 122 Google Scholar
[9]	Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004 Science 306 1910 Google Scholar
[10]	Grunin A A, Zhdanov A G, Ezhov A A, Ganshina E A, Fedyanin A A 2010 Appl. Phys. Lett. 97 261908 Google Scholar
[11]	Florczak J M, Dahlberg E D 1990 J. Appl. Phys. 67 7520 Google Scholar
[12]	Zak J, Moog E R, Liu C, Bader S D 1990 J. Appl. Phys. 68 4203 Google Scholar
[13]	Qiu Z Q, Bader S D 2000 Rev. Sci. Instrum. 71 1243 Google Scholar
[14]	Ren J, Li Y, Lin Y, Qin Y, Wu R, Yang J, Xiao Y, Yang H Y, Gong Q 2012 Appl. Phys. Lett. 101 171103 Google Scholar
[15]	He Y, Xie L, Qiu J, Luo L, Liu X, Li Z, Zhang Z, Du J 2019 J. Appl. Phys. 125 023101 Google Scholar
[16]	Li G, Xiang J, Zhang Y, Deng F, Panmai M, Zhuang W, Lan S, Lei D Y 2021 Nano Lett. 21 2453 Google Scholar
[17]	Tian J, Zuo Y, Hou M, Jiang Y 2021 Opt. Express 29 8763 Google Scholar
[18]	陈聿, 刘垄, 黄忠, 屠林林, 詹鹏 2016 物理学报 65 147302 Google Scholar Chen Y, Liu L, Huang Z, Tu L L, Zhan P 2016 Acta Phys. Sin. 65 147302 Google Scholar
[19]	Qiu X, Zhou X, Hu D, Du J, Gao F, Zhang Z, Luo H 2014 Appl. Phys. Lett. 105 131111 Google Scholar
[20]	Li T, Wang Q, Taallah A, Zhang S, Yu T, Zhang Z 2020 Opt. Express. 28 29086 Google Scholar
[21]	王莉岑, 邱晓东, 张志友, 石瑞英 2015 物理学报 64 174202 Google Scholar Wang L C, Qiu X D, Zhang Z Y, Shi R Y 2015 Acta Phys. Sin. 64 174202 Google Scholar
[22]	Onoda M, Murakami S, Nagaosa N 2004 Phys. Rev. Lett. 93 083901 Google Scholar
[23]	Bliokh K Y, Rodriguez-Fortuno F J, Nori F, Zayats A V 2015 Nat. Photon. 9 796 Google Scholar
[24]	Bliokh K Y, Nori F 2015 Phys. Rep. 592 1 Google Scholar
[25]	Kalhor F, Thundat T, Jacob Z 2016 Appl. Phys. Lett. 108 061102 Google Scholar
[26]	Ling X, Zhou X, Huang K, Liu Y, Qiu C, Luo H, Wen S 2017 Rep. Prog. Phys. 80 066401 Google Scholar
[27]	李星, 周新星, 罗海陆 2014 光学学报 34 0731002 Google Scholar Li X, Zhou X X, Luo H L 2014 Acta Opt. Sin. 34 0731002 Google Scholar
[28]	Ling X H, Yi X N, Zhou X X, Liu Y C, Shu W X, Luo H L, Wen S C 2014 Appl. Phys. Lett. 105 151101 Google Scholar
[29]	Li Y Q, Wu Z S, Zhang Y Y, Wang M J 2014 Chin. Phys. B 23 074202
[30]	易煦农, 李瑛, 刘亚超, 凌晓辉, 张志友, 罗海陆 2014 物理学报 63 094203 Google Scholar Yi X N, Li Y, Liu Y C, Ling X H, Zhang Z Y, Luo H L 2014 Acta Phys. Sin. 63 094203 Google Scholar
[31]	Shitrit N, Ulevich I. Y, Maguid E, Ozeri D, Eksler D V, Kleiner V, Hasman E 2013 Science 340 724 Google Scholar
[32]	Zhou X, Sheng L, Ling X 2018 Sci. Rep. 8 1221 Google Scholar
[33]	Xie L, Qiu X, Luo L, Liu X, Li Z, Zhang Z, Du J, Wang D 2017 Appl. Phys. Lett. 111 191106 Google Scholar
[34]	Zhou X, Xiao Z, Luo H, Wen S 2012 Phys. Rev. A85 043809
[35]	Zhou X, Ling X, Luo H, Wen S 2012 Appl. Phys. Lett. 101 251602 Google Scholar
[36]	Bliokh K Y, Smirnova D, Nori F 2015 Sci. 348 1448 Google Scholar
[37]	Qin Y, Li Y, Feng X, Liu Z, He H, Xiao Y, Gong Q 2010 Opt. Express. 18 16832 Google Scholar
[38]	Zhang W, Wu W, Chen S, Zhang J, Ling X, Shu W, Lou H, Wen S 2018 Photon. Res. 6 511 Google Scholar
[39]	Zhou X, Zhang J, Ling X, Chen S, Luo H, Wen S 2013 Phys. Rev. A 88 053840
[40]	Kort-Kamp W J. M 2017 Phys. Rev. Lett. 119 147401 Google Scholar
[41]	Nalitov A V, Malpuech G, Terças H, Solnyshkov D D 2015 Phys. Rev. Lett. 114 026803 Google Scholar
[42]	Cai L, Liu M, Chen S, Liu Y, Shu W, Luo H, Wen S 2017 Phys. Rev. A 95 013809 Google Scholar
[43]	Kort-Kamp W J M, Culchac F J, Capaz R B, Pinheiro F A 2018 Phys. Rev. B 98 195431
[44]	Zhou X, Xiao Z, Luo H, Wen S 2012 Phys. Rev. A 85 043809 Google Scholar
[45]	Zhou X X, Ling X, Luo H L, Wen S C 2014 Appl. Phys. Lett. 104 051130
[46]	Wu Y, Sheng L, Xie L, Li S, Nie P, Chen Y, Zhou X, Ling X 2020 Carbon 166 396 Google Scholar
[47]	Chen S, Ling X, Shu W, Luo H, Wen S 2020 Phys. Rev. Appl. 13 014057 Google Scholar
[48]	Yang Z J, Scheinfein M R 1993 J. Appl. Phys. 74 6810 Google Scholar
[49]	Bliokh K Y, Kivshar Y S, Nori F 2014 Phys. Rev. Lett. 113 033601 Google Scholar
[50]	You C Y, Shin S C 1998 J. Appl. Phys. 84 541 Google Scholar

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块状和超薄磁性材料中巨大且可调控的面内自旋角位移