Heating of materials by microwaves is selective and dependent on their properties. Dielectric materials are efficiently heated by the electric field of microwaves while magnetic materials by the magnetic field. We emphasize that electron system first responds to microwaves to absorb energy, and that a path of steady and irreversible energy flow from electrons to lattice atoms must be present. We showed using a classical Heisenberg model that dissipation is essential for energy relaxation [Phys.Rev.B, 2009]. However, the origin of dissipation has yet to be identified where mediation of electromagnetic waves - spin waves and/or hypersound waves is highly expected. We are performing both classical Heisenberg and ab initio simulations to elucidate the origin of dissipation from atomistic level. Our concern is whether such dissipation is materials specific or universal. In this paper, we will present our theoretical study of magnetic material heating in the microwave magnetic field.