Relativistic spin-Hall effect in an external magnetic field in Al and Pt

Abstract

The relativistic Rashba contribution to the spin-Hall effect in external electric and magnetic fields in Al and Pt was investigated. Schemes of edge accumulation of spins are proposed that take into account the flip of spins when they do not coincide with the direction of the magnetic field. Based on the obtained experimental data on the spin-Hall effect, an assessment of the spin-orbit interaction in the studied paramagnets was made.

Figures (6)

• Figure 1: (a) Splitting of doubly degenerate energy levels at non-centrosymmetric points of the Brillouin zone due to the SO interaction; (b) spin orientation in eigenstates in the case of the Rashba effect; (c) the same in an external electric field $\textbf{E}$, causing edge accumulation of spins.
• Figure 2: Voltage $U_{y}$ of an asymmetric aluminum sample, measured as a function of external magnetic $B^{\pm z}$ and d.c. electric $E^{\pm x}$ fields at T = 4.2 K. (Sample geometry: $L_{x}=1cm; L_{y}=5mm; (A_{xz}^{1}/A_{xz}^{3})\approx 5; ~$electron mean free path $l_{c}\sim 0.15 mm;~ L_{y} > \lambda_{sf}$.)
• Figure 3: Scheme of proper edge accumulation of spins in asymmetric samples of normal metal with a spin relaxation region (2) of length [$L_{y} - 2\lambda_{sf}$] ($\emph{B}_{i}$ is the intrinsic magnetic field of the metal, $L_{y}$ is the size of the sample along y).
• Figure 4: Schemes of edge accumulation of spins in external magnetic $\mathbf{B}_{ext}$ and electric $\textbf{E}$ fields. (a) Flip of spins "down", polarized against "$B_{z}$"; (b) Flip of spins "up", polarized against "$-B_{z}$".
• Figure 5: Dependence of the relativistic spin-Hall effect in aluminum on the magnitude of the external magnetic field (in a sample with the geometry shown in Fig. 2).