Journal
PHYSICAL REVIEW B
Volume 83, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.83.085203
Keywords
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Funding
- Natural Science Foundation of China [10725417]
- Chinese Academy of Sciences
- Kurata Memorial Hitachi Science and Technology Foundation
- Sumitomo Foundation
- [1948027]
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We calculate the magnetization torque due to the spin polarization of the itinerant electrons by deriving the kinetic spin Bloch equations based on the s-d model. We find that the first-order gradient of the magnetization inhomogeneity gives rise to the current-induced torques, which are consistent to the previous works. At the second-order gradient, we find an effective magnetic field perpendicular to the spin stiffness field. This field is proportional to the nonadiabatic parameter beta. We show that this vertical spin stiffness term can significantly modify the domain-wall structure in ferromagnetic semiconductors and hence should be included in the Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.
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