Dynamics of domain wall containing a Bloch line

A general formalism for the determination of the effective mass of the nanoscale structural inhomogeneities of the domain wall in uniaxial ferromagnets

“…The result (provide a reference to the final equation) coincides with the corresponding formula given in article [6] …”

“…An analysis of this expression shows that m BP does not depend on the bias field gradient, in contrast to the dependence of the effective mass on the vertical BL (see expression (6)). This results from the local character of the DW area distortion by the Bloch point (~Λ 2 ), the nature of which is determined by the surface tension of the domain wall (the terms~Λ 2 ∂/∂x 2 and~Λ 2 ∂/∂z 2 in the first equation of the system (8)).…”

“…Note that the viscosity of the system is taken into account by introducing into the balance of forces a dissipative linear vector function [16], which, to simplify the consideration of the problem, we do not consider in our article. Its effect on the stationary motion of the BL and BP results in finite values of the mobility of the DW structural inhomogeneities, causing negligibly small additions to their effective masses [1,6,7]. However, in yttrium-iron garnets, where the viscosity is due to an exchange relaxation of the magnetization vector [17], the viscosity can considerably affect the BP dynamics [18].…”

“…In this case, from article [6], it follows that the DW gyrotropic bend in the BL center has the form…”

“…Accordingly, m L,BP are determined from the 'kinetic potentials' constructed on the basis of systems of integrodifferential equation solutions of the BL and BP dynamics. This approach presents significant difficulties [4][5][6][7], and it would be laudable to build a simpler theoretical formalism for finding m L,BP in the DW of different domain configurations. Another difficulty with the previous formalism is related to the dependence of the BL and BP parameters of the quantum effects, which take place for these magnetic structures in the subhelium temperature range, on their effective mass expressions [8,9].…”