A model calculation is presented for the coherent magnon transmission and thermal transport at ferromagnetic nanojunction boundaries. The system consists of a Gd ultrathin film sandwiched between two Fe semi-infinite ferromagnetically ordered crystals. The dynamic of the system is analyzed using the equations of motion for the spin precession amplitudes on the lattice sites, valid for the range of temperatures of interest. The coherent transmission and reflection cross sections at the nanojunction boundary are calculated using the matching method. These calculations are presented for arbitrary directions on the boundary, for all accessible frequencies in the propagating bands, at variable temperatures and for a given thicknesses of the ultrathin nanojunction, with no externally applied magnetic field. The model is applied in particular to the Fe/Gd(5)/Fe system with a ferromagnetic Gd nanojunction. Our model yields the total integrated coherent thermal conductivity due to coherent magnons transmission via the sandwiched five Gd spin layers of the nanojunction. It elucidates, in particular, the dependence of the coherent magnons transmission and thermal transport in relation to the spatially inhomogeneous magnetic order of the atomic planes of the nanojunction for a given thickness.
Numerical study of the magnetic field diffusion in the toroidal field coils of the TFTR