Dynamics of elliptic domain walls

With the use of the generalized Landau-Lifshitz-Bloch equation of motion for a ferromagnet at finite temperatures we investigate the dynamic properties of domain walls (DWs) taking into account their ellipticity, i.e., the deficit of the magnetization value M in the DW in comparison with that of the domains. The translational motion of elliptic DWs is accompanied by longitudinal relaxation, which governs the DW dynamics even in the case of small ellipticity, if the relaxation constants are small. The linear DW mobility μ calculated in the whole temperature range 0⩽T⩽Tc shows a singular behavior in the point T=T∗ where the elliptic DW restructures into a linear one. At low temperatures the calculated dependence of μ on the transverse field Hx is consistent with the experimental observations. The longitudinal relaxation mechanism of the DW damping switches off for the DW velocities υ≳υ0≈lΓ1 (l is the DW width, Γ1 is the longitudinal relaxation rate), and the dependence υ(H) may show a hysteresis. We also derive Slonczewski-like reduced equations of motion for the DW parameters with an additional equation for the magnetization deficit. With the use of these equations the stability of the stationary DW motion is investigated. It is shown that in some cases there are three separate stable sections of the curve υ(H). Finally, the dynamic susceptibility of a ferromagnetic sample due to the displacement of elliptic domain walls is calculated.