Magnetization dynamics and related phenomena in semiconductors with ferromagnetism

Lin Chen; Jianhua Zhao; Dieter Weiss; Christian H. Back; Fumihiro Matsukura; Hideo Ohno

doi:10.1088/1674-4926/40/8/081502

Journals >Journal of Semiconductors >Volume 40 >Issue 8 >Page 081502 > Article

Journal of Semiconductors
Vol. 40, Issue 8, 081502 (2019)

Magnetization dynamics and related phenomena in semiconductors with ferromagnetism

Lin Chen¹, Jianhua Zhao², Dieter Weiss¹, Christian H. Back^1、3, Fumihiro Matsukura⁴, and Hideo Ohno^4、5

Author Affiliations

¹Institute of Experimental and Applied Physics, University of Regensburg, 93049 Regensburg, Germany

²State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

³Department of Physics, Technical University of Munich, Garching b. Munich, Germany

⁴Center for Innovative Integrated Electronic Systems, Tohoku University, Sendai 980-0845, Japan

⁵Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan

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DOI: 10.1088/1674-4926/40/8/081502 Cite this Article

Lin Chen, Jianhua Zhao, Dieter Weiss, Christian H. Back, Fumihiro Matsukura, Hideo Ohno. Magnetization dynamics and related phenomena in semiconductors with ferromagnetism[J]. Journal of Semiconductors, 2019, 40(8): 081502 Copy Citation Text

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Abstract

We review ferromagnetic resonance (FMR) and related phenomena in the ferromagnetic semiconductor (Ga,Mn)As and single crystalline Fe/GaAs (001) hybrid structures. In both systems, spin-orbit interaction is the key ingredient for various intriguing phenomena.

$ \frac{{{\rm{d}}{{M}}(t)}}{{{\rm{d}}t}} = - \gamma {{M}}(t) \times {\mu _0}{{{H}}_{{\rm{eff}}}} + \frac{\alpha }{{|{{M}}|}}{{M}}(t) \times \frac{{{\rm d}{{M}}(t)}}{{{\rm{d}}t}}, $

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$ \begin{aligned} F = & \frac{M}{2}\bigg\{ { - 2H\left[ {\cos {\theta _{ M}}\cos {\theta _{ H}} + \sin {\theta _{ M}}\sin {\theta _{ H}}\cos \left( {{\varphi _{ M}} - {\varphi _{ H}}} \right)} \right]} \bigg.\\ & + {H_{ K}}{{\cos }^2}{\theta _{ M}} - \displaystyle\frac{{{H_{\rm{B}}}}}{2}\frac{{3 + \cos 4{\varphi _{ M}}}}{4}{{\sin }^4}{\theta _{{{ M}}}}\\ & - {H_{\rm{U}}}{{\sin }^2}{\theta _{ M}}{{\sin }^2}\left( {{\varphi _{ M}} - \displaystyle\frac{\pi }{4}} \right) - {H_{{\rm{U}}2}}{{\sin }^2}{\theta _{ M}}{{\sin }^2}\left. {\left( {{\varphi _{ M}} - \displaystyle\frac{\pi }{2}} \right)} \right\}. \end{aligned} $

(2)

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$ {\left( {\frac{\omega }{\gamma }} \right)^2} = \frac{1}{{{\mu _0}{{ M}^2{{\sin^2}}}{\theta _{ M}}}}\left[ {\frac{{{\partial ^2}F}}{{\partial \theta _{ M}^2}} - \left( {\frac{{{\partial ^2}F}}{{\partial {\theta _{ M}}\partial {\varphi _{ M}}}}} \right)} \right], $

(3)

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$ \Delta {H_{\rm{G}}} = \frac{\alpha }{ M}\left( {\frac{{{\partial ^2}F}}{{\partial \theta _{ M}^2}} - \frac{1}{{{{\sin }^2}{\theta _{ M}}}}\frac{{{\partial ^2}F}}{{\partial \varphi _{ M}^2}}} \right){\left| {\frac{{{\rm d}(\omega /\gamma )}}{{{\rm d}{H_{\rm{R}}}}}} \right|^{ - 1}}. $

(4)

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