Valley-locked thermospin effect in silicene and germanene with asymmetric magnetic field induced by ferromagnetic proximity effect

Silicene and germanene, as graphene like materials with observable spin-orbit couplings and two distinctive valleys, have potential applications in future low-dissipation spintronics and valleytronics. We here propose a magnetic system of silicene or germanene intercalated between two ferromagetic (FM) dielectric layers, and find that the system with a proximity-induced asymmetric magnetic field supports an attractive phenomenon named the valley-locked spin-dependent Seebeck effect (VL-SSE) driven by a thermal gradient. The VL-SSE indicates that the carries from only one valley could be thermally excited, with opposite spin polarization counterpropagating along the thermal gradient direction, while nearly no carrier from the other insulating valley is excited due to the relatively wide band gap. It is also illustrated that the VL-SSE here does not survive in the usual FM or anti-FM systems, and can be destroyed by the overlarge temperature broadening. Moreover, we prove that the signal for VL-SSE can be weakened gradually with the enhancement of the local interlayer electric field, and be strengthened lineally by increasing the source-drain temperature difference in a caloritronic field effect transistor. Further calculations indicate that the VL-SSE is robust against many perturbations, including the global and local Fermi levels as well as the magnetic strength. These findings about the valley-locked thermospin effect provide a nontrivial and convenient dimension to control the quantum numbers of spin and valley and are expected to be applied in future spin-valley logic circuits and energy-saving devices.