Magnons coherent transmission and heat transport at ultrathin insulating ferromagnetic nanojunctions

A model calculation is presented for the magnons coherent transmission and corresponding heat transport at insulating magnetic nanojunctions. The system consists of a ferromagnetically ordered ultrathin insulating junction between two semi-infinite ferromagnetically ordered leads with ideally flat crystal interfaces. The ground state of the system is depicted by an exchange Hamiltonian neglecting smaller dipolar and anisotropy terms. The spin dynamics are analyzed using the equations of motion for the spin precession displacements, valid in the limit of low temperatures compared to an order-disorder transition temperature characteristic of the system. The coherent transmission and reflection spectra at the nanojunction boundary are calculated in the Landauer-Buttiker formalism using the matching theory, for all the magnons in the lead bulk, at arbitrary angles of incidence on the boundary, and for variable temperatures. The model calculations yield the thermal conductivity κm due to the magnons coherent transmission between the two leads maintained at slightly different temperatures. The model is general, and is applied in particular to the Fe/Gd/Fe system to calculate the coherent transmission of magnons and their thermal conductivity at the junction boundary, for different thicknesses of the Gd junction and its corresponding magnetic order. The calculated results elucidate the comparison between the heat transport from magnons with that in parallel channels from electrons and phonons, at the nanojunction boundary