Landau domain structure. I. Theory

A new treatment is presented for the Landau domain structure that is realized when a magnetic field less than $H_c$ is applied at a small angle to the large faces of a flat plate of a type-I superconductor. We work within the established framework of the Landau-Sharvin theory but attempt to take into account the nonlinear aspect of the magnetic interaction energy. The result is a new expression for the domain periodicity as a function of the fraction of the sample surface in the normal state, both of which quantities are direct experimental observables. Recent experimental work lends support to our result.