Role of magnons and the size effect in heat transport through an insulating ferromagnet taking into account the magnetic field

Abstract

We solve a kinetic, space-dependent problem in an insulator/ferromagnet/insulator heterostructure in the presence of a magnetic field. At the same time, to interpret experiments on thermal transfer across ferromagnet / insulator boundaries, the Little acoustic mismatch theory is usually used, in which the temperature jump at the interface is determined only by the acoustic characteristics of the medium. We show that the theory of acoustic mismatch is convenient only for sufficiently thick insulating ferromagnets. Of the greatest interest to us is the opposite limiting case of thin ferrodielectric films, where the role of magnons in the formation of a temperature jump at the ferromagnet/insulator interface becomes decisive. We show that for T ≪ Θ D a nonlinear heat flux Q crossing the ferrodielectric/insulator interface, both the size effect and its decreasing dependence on the external magnetic field increase. Namely, Q depends on the magnetic properties of thin heated ferromagnetic films, and the role of magnons is essential in the heat transfer regime, which we call magnon overheating. On the contrary, for thick heated layers of a ferromagnet, Q can be described by the Little formula, which does not take into account the magnetic properties of the ferromagnet layer.