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Transport equations of energy for ferromagnetic insulators in contact with electrodes

A phenomenological derivation of the transport equations for ferromagnetic moments and associated energy and heat is proposed. The model describes the transfer of energy through an interface composed of a ferromagnetic insulator in contact with normal electrodes. A reduction method applied to the ferromagnetic degrees of freedom allows a two-channel model to be defined for the transport of magnetic moments. It is shown that a heat current flowing into the insulating ferromagnet—produced e.g. by electromagnetic resonance, thermal gradient, magneto-mechanical or magneto-optical excitations—can generate a magneto-voltaic potential and a pure spin-current in the non-ferromagnetic electrode.