Strong spin-Hall and Nernst effects in a p-band semimetal

Since spin currents can be generated, detected, and manipulated via the spin Hall effect (SHE), the design of strong SHE materials has become a focus in the field of spintronics. Because of the recent experimental progress also the spin Nernst effect (SNE), the thermoelectrical counterpart of the SHE, has attracted much interest. Empirically strong SHEs and SNEs are associated with $d$-band compounds, such as transition metals and their alloys – the largest spin Hall conductivity (SHC) in a $p$-band material is $\sim 450$ $\left(\mathrm{\hslash }\mathrm{/}e\right){(\mathrm{\Omega }\cdot cm)}^{-1}$ for a Bi-Sb alloy, which is only about a fifth of platinum. This raises the question whether either the SHE and SNE are naturally suppressed in $p$-bands compounds, or favourable $p$-band systems were just not identified yet. Here we consider the $p$-band semimetal InBi, and predict it has a record SHC $\sigma_{xy}^{z}\approx 1100
\left(\hbar/e\right)\left(\Omega\cdot cm\right)^{-1}$ which is due to the presence of nodal-lines in its band structure. Also the spin-Nernst conductivity ${\alpha }_{zx}^y\approx 1.2(\mathrm{\hslash }\mathrm{/}e)(A\mathrm{/}m\cdot K)$ is very large, but our analysis shows its origin is different as the maximum appears in a different tensor element. This insight gained on InBi provides guiding principles to obtain a strong SHE and SNE in $p$-band materials and establishes a more comprehensive understanding of the relationship between the SHE and SNE.