Domain-wall energy in magnetic garnet bubble materials

Analytical and numerical integrations are used to calculate the magnetic domain-wall energy in bubble materials which possess a mixture of cubic and induced uniaxial anisotropies. Limiting cases are considered which take into account the possibility that the magnetization vector may deviate out of the wall plane. It is found that when the magnitudes of the cubic and uniaxial anisotropy constants are equal, the wall energy calculated by ignoring the cubic contribution is too low by more than 5.5% but less than 13%. For epitaxial garnet bubble materials, the magnitude of the uniaxial anisotropy constant is typically several times larger than the cubic. For such materials the value of the wall energy is predicted to vary from that calculated for the purely uniaxial case by at most a few percent.