Spin dynamics in orbital-textured magnetic solids

Understanding the spin dynamics in magnetic materials is one of the important aims in the field of spintronics. It is known that important properties governing the spin dynamics, such as magnetic anisotropy, Gilbert damping, and current-induced spin-orbit torque [1,2] are rooted in the electron orbitals through spin-orbit interaction. Recent studies revealed that the dynamics of orbital angular momentum [3,4] and position [5] are distinct from the spin dynamics. Given that the spin and orbital dynamics are coupled through spin-orbit interaction, it is important to investigate their coupled dynamics. In this work, starting from the p-orbital system with spin-orbit interaction, we show that the Landau-Lifshitz-Gilbert (LLG) equation for spin dynamics contains the magnetic anisotropy, Gilbert damping, and inertial term due to spin-orbit interaction. We describe these terms rooted in the electron orbitals with the electronic band parameters. Our study emphasizes the important role of orbital texture and orbital dynamics on spin dynamics and provides fruitful insights on the phenomenological parameters appearing on LLG equation.

References

[1] S. Ding, et al., Physical Review Letters 125, 177201 (2020)

[2] S. Lee, et al., Communicatoins Physics 4, 234 (2021)

[3] D. Go, et al., Physical Review Letters 121, 086602 (2018)

[4] Y. G. Choi, et al., Nature 619, 52 (2023)

[5] S. Han, et al., Physical Review Letters 128, 176601 (2022)