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Abstract

As an established paradigm of spin-charge conversion, the spin Hall effect (SHE) and its inverse effect have been widely utilized to generate, detect, and characterize spin-orbit torques. However, recent experiments suggested that the archetypal SHE geometry could be violated in materials with special crystal symmetry, such as semimetal WTe2 and its variances. We propose a phenomenological description for such generalized spin-charge transport, bringing about a new concept dubbed tensorial SHE (t-SHE). In the presence of the spin diffusion process, the t-SHE gives rise to: 1) unconventional spin-orbit torques with unique features, and 2) a new form of magnetoresistance generalizing the known spin-Hall magnetoresistance. By solving the magnetization dynamics driven by a time-harmonic current, we predict a series of harmonic signals arising from the t-SHE and its ensuing magnetoresistance, which enables practical methods to experimentally characterize the unconventional spin-orbit torques originating from the t-SHE.