Magnetization patterns in ferromagnetic nanoelements as functions of complex variable.

The assumption of a certain hierarchy of soft ferromagnet energy terms, realized in small enough flat nanoelements, allows us to obtain explicit expressions for their magnetization distributions. By minimizing the energy terms sequentially, from the most to the least important, magnetization distributions are expressed as solutions of the Riemann-Hilbert boundary value problem for a function of complex variable. A number of free parameters, corresponding to positions of vortices and antivortices, still remain in the expression. Thus, the presented approach is a factory of realistic Ritz functions for analytical (or numerical) micromagnetic calculations. Examples are given for multivortex magnetization distributions in a circular cylinder, and for two-dimensional domain walls in thin magnetic strips.