Effect of spin transfer via eddy current on propagating domain wall in ferromagnetic microwire

We discuss the interaction of the magnetization in the domain-wall (DW) area with the eddy current that is induced by the DW propagation in a bi-stable microwire of a ferromagnetic metal. The ordering structure of the microwire consists of an axially magnetized inner core and an outer shell of radially or circumferentially magnetized domains. The electrical current in the ferromagnetic medium is spin-polarized; thus, it exerts the spin-transfer torque on the magnetization inside DWs. The effect is inherent in a soluble (Ishimori-like) model of the nonlinear magnetization dynamics that is adapted to describing the inner core of the microwire. Previously established static DWs in microwires are known as transverse, vortex, planar, and conical DWs, of whom planar DWs are specific due to lack of rotational symmetry. We analyze dynamical single-DW solutions, thus noticing our model to be capable of describing an observed unidirectional effect in the field-driven propagation of planar DWs. Thus, we claim a significant eddy-current effect on moving DW to realize in DWs of that kind.