The thermal activation of magnetic domain walls from continuous and discontinuous planar pinning sites

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Abstract
It is shown that thermally activated escape of a 180° domain wall, from a continuous planar pin, is possible in a magnetic field that is less than the absolute-zero coercive field. The model treated assumes a pinning force that depends on the square of the wall displacement. A thermally activated blister can form in a critical field that is less than the coercive field, and may then peel away allowing the wall to escape. A generalized solution for the blister energy is developed which can be scaled to fit the magnetic constants of different materials. An expression for the coercive field is derived which depends linearly on temperature (if the basic magnetic parameters of the pin and matrix are temperature-independent). An expression for a magnetic viscosity parameter is also derived. At a sufficiently high temperature, a discontinuous planar pin will behave as though it is continuous. The criterion is that the area of the discontinuous fragments must exceed a value proportional to T−½ .