Chotorlishvili L., Toklikishvili Z., Etesami S.R., Dugaev V.K., Barnaś J., Berakdar J.

The influence of an asymmetric in-plane magnetic anisotropy Kx≠KyKx≠Ky on the thermally activated spin current is studied theoretically for two different systems: (i) the F|NF|N system consisting of a ferromagnetic insulator (F) in a direct contact with a nonmagnetic metal (N ) and (ii) the sandwich structure N|F|NN|F|N consisting of a ferromagnetic insulating part sandwiched between two nonmagnetic metals. It is shown that when the difference between the temperatures of the two nonmagnetic metals in a N|F|NN|F|N structure is not large, the spin pumping currents from the magnetic part to the nonmagnetic ones are equal in amplitude and have opposite directions, so only the spin torque current contributes to the total spin current. The spin current flows then from the nonmagnetic metal with the higher temperature to the nonmagnetic metal having a lower temperature. Its amplitude varies linearly with the difference in temperatures. In addition, we have found that if the magnetic anisotropy is in the layer plane, then the spin current increases with the magnon temperature, while in the case of an out-of-plane magnetic anisotropy the spin current decreases when the magnon temperature enhances. Enlarging the difference between the temperatures of the nonmagnetic metals, the linear response becomes important, as confirmed by analytical expressions inferred from the Fokker?Planck approach and by the results obtained upon a full numerical integration of the stochastic Landau?Lifshitz?Gilbert equation.

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