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Both applied electric currents and magnetization dynamics modify theDzyaloshinskii-Moriya interaction (DMI), which we call current-induced DMI(CIDMI) and dynamical DMI (DDMI), respectively. We report a theory of CIDMI andDDMI. The inverse of CIDMI consists in charge pumping by a time-dependentgradient of magnetization $\partial^2 M(r,t)/\partial r\partial t$, while theinverse of DDMI describes the torque generated by $\partial^2 M(r,t)/\partialr\partial t$. In noncollinear magnets CIDMI and DDMI depend on the localmagnetization direction. The resulting spatial gradients correspond to torquesthat need to be included into the theories of Gilbert damping, gyromagnetism,and current-induced torques (CITs) in order to satisfy the Onsager reciprocityrelations. CIDMI is related to the modification of orbital magnetism induced bymagnetization dynamics, which we call dynamical orbital magnetism (DOM), andspatial gradients of DOM contribute to charge pumping. We present applicationsof this formalism to the CITs and to the torque-torque correlation in texturedRashba ferromagnets.

physical review. b./physical review. b

Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role  for damping, gyromagnetism, and current-induced torques in noncollinear  magnets