We present a theoretical study of two-dimensional spatially and temporally varying magnetic textures in the presence of spin-orbit coupling (SOC) of both the Rashba and Dresselhaus types. We show that the effective gauge field due to these SOCs, contributes to the dissipative and reactive spin torques in exactly the same way as in electromagnetism. Our calculations reveal that Rashba (Dresselhaus) SOC induces a chiral dissipation in interfacial (bulk) inversion asymmetric magnetic materials. Furthermore, we show that in addition to chiral dissipation ${\alpha }_c$, these SOCs also produce a chiral renormalization of the gyromagnetic ratio ${\tilde{\gamma }}_c$, and show that the latter is intrinsically linked to the former via a simple relation ${\alpha }_c=(\tau /{\tau }_{\mathrm{ex}}){\tilde{\gamma }}_c$, where ${\tau }_{\mathrm{ex}}$ and $\tau$ are the exchange time and the electron relaxation time, respectively. Finally, we propose a theoretical scheme based on the Scattering theory to calculate and investigate the properties of damping in chiral magnets. Our findings should in principle provide a guide for material engineering of effects related to chiral dynamics in magnetic textures with SOC.

• Received 19 September 2018
• Revised 29 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.184424