Minimum-energy configurations of isotropic ferromagnetic shells

We calculate the exchange and magnetic ('dipolar') energies in various configurations of magnetization of spherical shells of ferromagnetic material with no intrinsic anisotropy. In general, the state of lowest energy is magnetized along lines of constant latitude. We compare this to states in which the magnetization follows lines of constant longitude or is radial, which have higher total energies. A continuum of intermediate states exists, so that in the absence of anisotropy, external fields, or pinning of magnetization, all states may spontaneously decay to latitudinally magnetized states. Although the latitudinal state has no magnetic moment, it may have significant permeability.