Direct Electrical Detection of Spin Chemical Potential Due to Spin Hall Effect in $\beta$-Tungsten and Platinum Using a Pair of Ferromagnetic and Normal Metal Voltage Probes

Abstract

The phenomenon of Spin Hall Effect (SHE) generates a pure spin current transverse to an applied current in materials with strong spin-orbit coupling, although not detectable through conventional electrical measurement. An intuitive Hall effect like measurement configuration is implemented to directly measure pure spin chemical potential of the accumulated spins at the edges of heavy metal (HM) channels that generates large SHE. A pair of transverse linearly aligned voltage probes in placed in ohmic contact with the top surface of HM , one being a ferromagnetic metal (FM) with non-zero spin polarization and other is the reference metal (RM) with zero polarization of carriers. This combination of FM/RM electrodes is shown to induce an additional voltage proportional to a spin accumulation potential, which is anti symmetric with respect to opposite orientations of FM controlled by a 2D vector magnet. Proof of concept of the measurement scheme is verified by comparing the signs of voltages for HM channels of Tungsten (W) and Platinum (Pt) which are known to generate opposite spin accumulation under similar conditions of applied current. The same devices are also able to detect the reciprocal effect, inverse spin Hall effect (ISHE) by swapping the current and voltage leads and the results are consistent with reciprocity principle. Further, exploiting a characteristic feature of W thin film deposition, a series of devices were fabricated with W resistivity varying over a wide range of 10 - 750 $\mu \Omega$-cm and the calculated spin Hall resistivity exhibits a pronounced power law dependence on resistivity. Our measurement scheme combined with almost two decades of HM resistivity variation provides the ideal platform required to test the underlying microscopic mechanism responsible for SHE/ISHE.