Generalized Two-Temperature Model for Coupled Phonon-Magnon Diffusion

Abstract

We generalize the two-temperature model [Sanders and Walton, Phys. Rev. B, 15, 1489 (1977)] for coupled phonon-magnon diffusion to include the effect of the concurrent magnetization flow. Working within the framework of Boltzmann transport equation, we derive the constitutive equations for coupled phonon-magnon transport driven by gradients of both temperature and external magnetic fields, and the corresponding conservation laws. Our equations reduce to the original Sanders-Walton two-temperature model under a uniform external field, but predict a new magnon cooling effect driven by a non-uniform magnetic field in a homogeneous single-domain ferromagnet. We estimate the magnitude of the cooling effect in yttrium iron garnet, and show it is within current experimental reach. With properly optimized materials, the predicted cooling effect can potentially supplement the conventional magnetocaloric effect in cryogenic applications in the future.Spin caloritronics [1,2] is a nascent field of study that looks into the interaction between heat and spin. In addition to providing ways of thermally manipulating magnetization and magnetic domain walls [3][4][5] as supplements to conventional spintronics, it also holds promise of novel energy harvesting and cooling applications owing to the recent

Generalized Two-Temperature Model for Coupled Phonons in Nanosized Graphene

“…In TTM, different energy carriers are considered as two interacting subsystems, such as the electron-phonon 18,19 and phonon-magnon 16,20 . Liao et al have generalized TTM for the coupled phonon-magnon diffusion and predicted a magnon cooling effect 16 .…”

Thermodynamic transport theory of spin waves in ferromagnetic insulators

“…Instead, when the magnetic subsystem is partially decoupled from the lattice, alternative methods, as those used in Ref. [34], can be applied.…”

Spin caloritronics, origin and outlook

“…This thermodynamic derivation of the Landau-Lifshitz damping was also obtained by Saslow.62 In the presence of a magnetization current J M given by (27) and the current given by (9), the continuity equation (26) for the magnetization yields a modified Landau-Lifshitz equation with : 70 An analysis of the magnon mean-free path has also been conducted in a simple kinetic gas theory approach.71…”

“…25 In particular, magnons and phonons may have different temperatures. 26 The accumulation of magnons at an interface, due to presence of a temperature gradient, has been described in terms of a Bose-Einstein condensation.2728 A review on the theory of spin Seebeck effect can be found in 29.…”