# Domain-wall coercivity in ferromagnetic systems with nonuniform local magnetic field

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## Abstract

Domain-wall (DW) coercive field, H-CW, which characterizes pinning of DW's in soft magnetic materials, decreases strongly with increasing value of gradient, G, of the effective local DW-position-restoring magnetic field. Particular shapes of the dependence, H-CW(G), can be calculated from the mean energy dissipation of the DW moving over the particular profile of the DW pinning field, H-p. In this paper, H-CW(G) is calculated from a wall-pinning field, H-p, which is expressed as a stochastic function of the DW coordinate, x(DW). The wall-pinning field, H-p, is described as a Wiener-Levy stochastic process modified by two correlation lengths in such a way that H-p is stationary for large DW displacements and dH(p) /dx(DW) is well defined for small DW displacements. The computed H-CW(G) is close to a hyperbolic decrease, but it approaches finite values if G-->O and it decreases in a much steeper way than alpha 1/G for high values of G, which agrees with the experimental observations. Experimentally, the dependence H-CW(G) was measured on close-packed arrays of cylindrical bubble domains in two thin films of magnetic garnets, where the local field gradient, G, was controlled within the range 10(9)-10(10) A/m(2) by changing distances between neighboring DW's. The DW coercive field, H-CW, extrapolated from the measured values for G-->O was close to 80 A/m for both samples, while H-CW(G approximate to 10(10) A/m(2)) was several times smaller. Fitting the calculated H-CW(G) dependence to the experimental data, we obtained values of the Wiener-Levy correlation lengths well comparable to the DW width parameters.

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