Giant and controllable in-plane spin angular shifts in bulk and ultrathin magnetic materials

Li Qian-Yang; Yuan Shuai-Jie; Yang Jin; Wang Yong; Ma Zu-Hai; Chen Yu; Zhou Xin-Xing

doi:10.7498/aps.72.20221643

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:

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).

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References

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Cited By

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$2{\text{π }}d|{n_1}|\lambda \ll 1$

Figure 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$2{\text{π }}d|{n_1}|\lambda \ll 1$.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

[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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