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A model calculation is presented for the magnons coherent transmission and corresponding heat transport at magnetic insulating nanojunctions. The system consists of a ferromagnetically ordered ultrathin insulating junction between two semi-infinite ferromagnetically ordered leads. Spin dynamics are analyzed using the equations of motion for the spin precession displacements, valid for the range of temperatures of interest. Coherent scattering cross-sections at the junction boundary are calculated using the phase field matching theory, for all the incidence angles on the boundary from the lead bands, for arbitrary angles of incidence, at variable temperatures, and for different nano thicknesses of the ultrathin junction. The model is general; it is applied in particular to the Fe/Gd/Fe system with a sandwiched ferromagnetic Gd junction. It yields also the thermal conductivity due to the magnons coherent transmission between the two leads when these are maintained at slightly different temperatures. The calculation is carried out for state of the art values of the exchange constants, and elucidates the relation between the coherent scattering transmission of magnons and their thermal conductivity, for different thicknesses

Magnons coherent transmission and its heat transport at ultrathin insulating ferromagnetic nanojunctions