On the magnetic inhomogeneity based on Landau-Ginzburg theory

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Abstract
Magnetic inhomogeneity in a magnetic medium can be demonstrated with the use of Landau-Ginzburg theory. One-dimensional solutions for the spatial variation of the magnetisation M(X) have been found in terms of the Landau-Ginzberg coefficients under various conditions. The solutions show two types of variations: (i) oscillatory between positive and negative values, and between two positive values of M; (ii) discontinuous in M(X). The discontinuities in the latter lead to M(X)=constant as the only solution. An analytical expression has been obtained that helps to predict values at peaks or troughs in M(X).