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Spin-charge conversion in a nonmagnetic material generally follows the spin Hall symmetry, i.e. the charge current, spin current and spin polarization are all orthogonal to each other. Similar spin-charge conversion has been studied in a ferromagnetic material, but only in the anomalous Hall configuration such that the spin polarization is parallel with the magnetization. There are very few studies on the configuration where the spin polarization is transverse to the magnetization, possibly due to the consideration of transverse spin dephasing. Here I will show that despite dephasing, transverse spin-orbit effects in ferromagnetic metals are significant and exhibit unique symmetries.
From a purely symmetry-based argument, a charge current through a ferromagnet can generate a spin current with conventional spin Hall symmetry. If the spin polarization is transverse to magnetization, spin can precess, leading to a spin current with a different spin polarization. We refer to these two effects as the transverse spin Hall effects with conventional symmetry (TSHE-C) and spin rotation symmetry (TSHE-SR), respectively. Both TSHE-C and TSHE-SR can generate transversely polarized spin current flowing within and out of the ferromagnet. The transversely polarized spin current flowing within the ferromagnet leads to anomalous spin-orbit torques at the surface of the ferromagnet. The transversely polarized spin current flowing out of the ferromagnet may possess a unconventional symmetry, allowing magnetization control of a second ferromagnet. The fact that ferromagnet itself can generate transversely polarized spin current may challenge the current understanding of spin-orbit effects including spin-orbit torque and spin pumping-spin galvanic effect.
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