Exchange Energy, Stress, and Momentum in a Rigid Ferrimagnet

Abstract

A self-consistent formulation of the exchange energy density, effective exchange field, and Poynting vector is carried out, for a general ferrimagnet, in terms of the spin and orbital angular momentum densities. When there is more than one magnetic lattice or when the gyromagnetic ratios are tensor quantities, this formulation leads to an exchange energy density and Poynting vector that differ from those commonly employed. The associated boundary conditions at a surface of passive discontinuity are also discussed; power flow considerations lead to the conclusion that one of these is a dynamic boundary condition. With the help of the correspondence principle and a quasi particle interpretation of spin waves, a small-signal energy density, momentum density, and stress tensor are postulated for a ferromagnet. The associated small-signal force density (postulated to equal the divergence of the stress tensor minus the time rate of change of the momentum density) is found to be the negative of the force density that accelerates the envelope of the spin wave packet and is interpreted as a reaction force density acting upon the lattice. A prediction is made that a magnon incident upon a surface of discontinuity such as a material—air interface, will exert an exchange-radiation pressure on it.