Magnetization direction dependent spin Hall effect in 3d ferromagnets

Abstract

We have studied the intrinsic spin Hall conductivity of 3d transition metal ferromagnets using first-principles calculations. We find the spin Hall conductivity of bcc Fe and fcc Ni, prototypes of ferromagnetic systems, depends on the direction of magnetization. The spin Hall conductivity of electrons with their spin orientation orthogonal to the magnetization are found to be larger than that when the two are parallel. For example, the former can be more than four times larger than the latter in bcc Fe. Such a difference arises due to the anisotropy of the spin current operator in the spinor space: Its expectation value with the Bloch states depends on the relative angle between the conduction electron spin and the magnetization. A simple analytical form is developed to describe the relation between the spinor states, with respect to the magnetization direction, and the Berry and spin Berry curvatures. The model can account for the characteristics found in the calculations. These results show that ferromagnets can be used to generate spin current and its magnitude can be controlled by the magnetization direction.

arXiv comment5 pages, 3 figures

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• Spin Hall Conductivity and Anomalous Hall Conductivity in Full Heusler compounds
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• Controllable Spin Current in van der Waals Ferromagnet Fe3GeTe2
• Theoretical Study of Extrinsic Spin-current Generation in Ferromagnets Induced by Anisotropic Spin-flip Scattering
• Theory of magnetic spin and orbital Hall and Nernst effects in bulk ferromagnets
• Perpendicularly Polarized Spin Hall Effects Induced by Spin-Dependent Scattering in Ferromagnetic Metals
• Measuring the magnetic anisotropy of the spin Hall effect and spin relaxation length in nickel and permalloy via electrical spin injection
• Anisotropy of the spin Hall effect in a Dirac ferromagnet