The effect of local magnetic field gradient on coercive field of domain walls

Local magnetic field gradient /spl beta/ keeping a domain wall (DW) close to the equilibrium position has very strong effect on the value of coercive field H/sub cw/ of DW. We present a model calculation of the dependence of H/sub cw/ on /spl beta/ using the pinning field H/sub p/ expressed as a stochastic function of the DW coordinate x. H/sub p/ is described by the Wiener-Levy process with two correlation lengths /spl xi//sub 1/ and /spl xi//sub 2/ such that H/sub p/ is stationary for /spl Delta/x/spl Gt//spl xi//sub 2/ and dHp/dx is well defined for /spl Delta/x/spl Lt//spl xi//sub 1/. In the case of /spl xi//sub 1//spl rarr/0 and /spl xi//sub 2//spl rarr//spl infin/ we obtained hyperbolic decrease H/sub cw//spl prop/1//spl beta/ while finite /spl xi//sub 1/ and /spl xi//sub 2/ yield H/sub cw/(/spl beta/) closer to the experimental dependence, in particular: (i) finite H/sub cw/ for any finite DW velocity and for /spl beta//spl rarr/0, (ii) for higher /spl beta/ H/sub cw/ decreases much steeper than /spl prop/1//spl beta/.