Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films

We analyze the electric current and magnetic field driven domain wall motion in perpendicularly magnetized ultrathin ferromagnetic films in the presence of interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and in-plane uniaxial anisotropies. We obtain exact analytical Walker-type solutions in the form of one-dimensional domain walls moving with constant velocity due to both spin-transfer torques and out-of-plane magnetic field. These solutions are embedded into a larger family of propagating solutions found numerically. Within the considered model, we find the dependencies of the domain wall velocity on the material parameters and demonstrate that adding in-plane anisotropy may produce domain walls moving with velocities in excess of 500 m/s in realistic materials under moderate fields and currents.