Threshold behaviors of direct and Hall currents in topological spin-Hall effect

We study spin-dependent direct and Hall conductivities in the threshold region of Fermi energy, ɛF=2J, where J is the exchange integral between the conduction electron spins and the skyrmion spin texture. For ɛF at the threshold value and above the spin-down electrons are allowed to exist. We find the two in the direct and four narrow peaks in the Hall conductivities for Fermi energies slightly below the threshold value. The found effects are dramatic because the electric current changes by approximately eight times in the narrow range of gate voltages (∼4 meV). The values of the peaks strongly depend on skyrmion size. For small and very large skyrmion sizes the peak amplitudes are small compared to the conductivity absolute values. At the skyrmion radius a=6nm and very light conduction electrons, m∗∼10−2me, the extrema are the most pronounced. The temperature evolution reveals the strong smearing effect where the peak-wise behavior completely disappears at room temperatures. Spin transistor could be considered for possible applications where in the narrow region of gate voltage the sharp conductivity change occurs.