Anisotropic spin relaxation induced by surface spin-orbit effects

Abstract

It is a common perception that the transport of a spin current in polycrystalline metal is isotropic and independent of the polarization direction, even though spin current is a tensor-like quantity and its polarization direction is a key variable. We demonstrate surprising anisotropic spinrelaxation in mesoscopic polycrystalline Cu channels in nonlocal spin valves. For directions in the substrate plane, the spin-relaxation length is longer for spins parallel to the Cu channel than for spins perpendicular to it, by as much as 9% at 10 K. Spin-orbit effects on the surfaces of Cu channels can account for this anisotropic spin-relaxation. The finding suggests novel tunability of spin current, not only by its polarization direction but also by electrostatic gating.PACS numbers: 72.25. Ba, 72.25.Rb, 75.76.+j, . INTRODUCTIONSpin current, which is essential to spintronics technology, is a tensor-like quantity describing a flow of spin angular momenta with a polarization direction.1 Tunability of spin current has been a desired functionality since the inception of spintronics, 2 but it remains a major challenge despite some promising progress. 3 Unlike an electrical current, a spin current decays as itpropagates through a material because of the ubiquitous spin-relaxation. Spin-relaxation length, which characterizes the effective transport distance of a spin current, is a crucial quantity for describing many emergent phenomena, such as spin-Hall magnetoresistance, 4-6 spin Seebeck effect, 7 and spin pumping. 8 If spin-relaxation length depends on polarization direction, as the tensor-like nature of spin current would suggest, then the intriguing technological prospect arises 3 that spin current could be tuned by polarization direction through the seemingly undesirable process of spin-relaxation.According to theories, such anisotropic spin-relaxation could arise from various types of spinorbit (SO) effects in semiconductors, 9, 10 graphene, 11,12 or crystalline metals, 13 and is relevant to the fundamental question of whether the spin relaxation is of the Elliot-Yafet 14, 15 or DyakonovPerel type. 16 The anisotropic spin-relaxation time was observed experimentally in lowdimensional semiconductor systems [17][18][19] and attributed to the interplay of various SO contributions. [20][21][22][23] Using transport measurements in graphene-based non-local spin valves (NLSVs), Tombros et al. 24 claimed anisotropic spin signals in graphene for in-plane and out-ofplane polarization directions, but their claim was disputed and the result attributed instead to magnetoresistance effect in graphene with low carrier density under a strong out-of-plane magnetic field. 25 Therefore, anisotropic spin-relaxation in spin transport processes is still an open question and its unambiguous demonstration is desirable for the application of spin current in spintronic devices. Furthermore, polycrystalline metals such as Cu have not been considered for the study of anisotropic spin-relaxation, because of the lack of SO coupling and crys...

Magnetic damping anisotropy in the two-dimensional van der Waals material Fe$_3$GeTe$_2$ from first principles

“…This difference can be attributed to the strong surface effect of highly confined SL FGT. The lowered symmetry at the surface significantly enhances spin-orbit coupling (SOC), 52 which enables the dissipation of angular momentum from electronic spins to the orbital degree of freedom and then into the lattice reser-voir. In addition, as the thickness of a single layer is considerably smaller than the electronic mean free path, conduction electrons in FGT are strongly scattered by the surface.…”

Calculating the spin memory loss at Cu$|$metal interfaces from first principles

“…To avoid this happening while incurring minimal attenuation of the spin current, a thin Cu spacer layer is frequently inserted between Pt and magnetic materials [61][62][63] making it of interest to study such "compound" interfaces. Because of its long SDL that is estimated to be hundreds of nanometers at room temperature [33], Cu is widely used in nonlocal spin valves as a transport channel for a diffusive spin current [37,[64][65][66][67][68][69]. In such studies, the important interfaces are Cu|NM and Cu|FM interfaces where NM is usually Pt or Pd and FM is Py (permalloy, Ni 80 Fe 20 ) or Co. Because of the difficulty of estimating the SML at interfaces involving Cu it is often simply neglected.…”