Spin accumulation generated by the anomalous Hall effects (AHE) in mesoscopic ferromagnetic Ni81Fe19 (permalloy or Py) films is detected electrically by a nonlocal method. The reciprocal phenomenon, inverse spin Hall effects (ISHE), can also be generated and detected all-electrically in the same structure. For accurate quantitative analysis, a series of nonlocal AHE/ISHE structures and supplementary structures are fabricated on each sample substrate to account for statistical variations and to accurately determine all essential physical parameters in-situ. By exploring Py thicknesses of 4 nm, 8 nm, and 12 nm, the Py spin diffusion length is found to be much shorter than the film thicknesses. The product of and the Py spin Hall angle is determined to be independent of thickness and resistivity: = (0.066 ± 0.009) nm at 5 K and (0.041 ± 0.010) nm at 295 K. These values are comparable to those obtained from mesoscopic Pt films.

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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...

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