Temperature effects in spin-dependent Hall currents in an ideal skyrmion gas

Abstract

The quest for novel reliable and fast-performing logic and memory elements in classical and quantum computing requires discoveries of new effects in novel quantum materials. Skyrmions are such magnetic textures where electron scattering can essentially change the shape and location of the skyrmion, which can be used as a memory element being more efficient than domain walls as a memory device in classical computing. Because the skyrmion motion is sensitive even to very small currents, we study electron scattering by skyrmions in an ideal skyrmion gas in a ferromagnetic environment. In such systems, the direct and Hall currents become spin-dependent. For applications, it is important to consider a Hall effect in the whole range of temperatures under the assumption of the skyrmion existence. In this study, we find the nonmonotonic temperature dependence of the direct spin-up conductivity, i.e., the conductivity for the current directed along the applied electric field due to the electrons with the spin parallel to the ferromagnetic moment. Such a behavior contradicts the traditional understanding where the temperature only increases the value of the conductivity. The spin-down Hall conductivity is found to be even more dramatic exhibiting a conductivity sign change (i.e., a change in the current direction) with temperature for small skyrmion sizes. The found effects strongly depend on Fermi energy. The most pronounced dependencies take place if the Fermi energy is slightly below and above the bottom of the upper (spin-down) energy band of an ideal two-dimensional electron gas. In addition, we also find that the direct and Hall resistivities, ${\ensuremath{\rho}}_{xx}$ and ${\ensuremath{\rho}}_{xy}$, are independent of the exchange integral $J$ for $2J>{\ensuremath{\varepsilon}}_{F}$.