Nanomechanical detection of the spin Hall effect

Abstract

The spin Hall effect creates a spin current in response to a charge current in a material that has strong spin-orbit coupling. The size of the spin Hall effect in many materials is disputed, requiring independent measurements of the effect. We develop a novel mechanical method to measure the size of the spin Hall effect, relying on the equivalence between spin and angular momentum. The spin current carries angular momentum, so the flow of angular momentum will result in a mechanical torque on the material. We determine the size and geometry of this torque and demonstrate that it can be measured using a nanomechanical device. Our results show that measurement of the spin Hall effect in this manner is possible and also opens possibilities for actuating nanomechanical systems with spin currents.The spin Hall effect [1,2], which is the generation of a spin current in a material due to an applied charge current in the presence of strong spin-orbit coupling, has been proposed as a novel method of spin manipulation for spintronics applications. Spin currents generated by the spin Hall effect have been used to excite high-and lowfrequency magnetic dynamics in nanostructures [3][4][5][6][7][8][9][10][11], and may become useful for future low-power spintronic logic and storage devices [12]. The spin Hall effect has been observed in a variety of materials with strong spin orbit coupling, including semiconductors such as Si and GaAs [13][14][15][16]; graphene with adsorbed impurities [17]; heavy metals with strong spin-orbit coupling such as Pt, Ta and W [4,11,[18][19][20]; and metals doped with large spin-orbit-coupled impurities [21][22][23]. However, quantification of the SHE through fundamental parameters remains a challenge.The figure-of-merit for SHE materials is the spin Hall angle, Θ SH , which is often stated as the proportionality between the magnitude of generated spin current and the magnitude of input charge current, |J s | = h 2e Θ SH J c [24,25], where J s is the component of the spin current perpendicular to the charge current and J c is the charge current. Measurements and characterization of Θ SH have, as yet, been limited to methods based on optical, electrical, and magnetic effects, which require knowledge of Kerr rotation coupling, metallic interfaces, magnetic properties, and spin diffusion parameters to quantify Θ SH accurately [15,26]. As such, reported values of Θ SH span orders of magnitude for materials such as Pt and Pd [19,[27][28][29][30][31][32][33][34][35]. Open questions such as the dependence of Θ SH on growth conditions, film thickness, impurity level, frequency, and other systematic parameters must be addressed both experimentally and theoretically. Since the inverse SHE is used to measure spin transport due to the spin Seebeck effect and spin pumping, accurate knowledge of the spin Hall angle is important for metrology. One intriguing new result implies that the spin Hall angle is complex-valued, resulting in a phase shift between an applied AC charge current and the resulting AC spin cu...

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