Two-dimensional domain walls in ferromagnetic films. IV. Wall motion

Abstract

The Ritz model for the wall separating two antiparallel domains in ferromagnetic films is modified, by the addition of a third Ritz parameter, to contain the extra asymmetry appropriate to a wall in motion. The modification is such that the magnetostatic self-energy is still calculated analytically and the numerical integration involved in the calculation of the exchange-energy term is not more complicated than in the case of the stationary wall. Numerical results are given for 1000-Å-thick uniaxial Permalloy film at zero applied field, for a wall velocity in the range 104 to 105 cm/sec. This is the range in which Schlomann’s approximations led to some ’’critical’’ velocity, only no such critical velocity is encountered here. The difference between the energy of the moving wall and that of the stationary wall changes quite considerably with wall velocity. This means that if one uses the conventional definition for the difference as a kinetic energy, the mass of the wall changes with velocity. Its value ranges between 7×10−11 g/cm2 for a velocity of 104 cm/sec and 4×10−11 g/cm2 for a velocity of 105 cm/sec. But most of this change is in a rather small be taken as an abrupt change that experimentalists would call a critical velocity.