The ultrathin tungsten (W) layer has been utilized as a spin-generating source for memory application in magnetic heterostructures. We investigate the spin Hall conductivity (SHC, ${\sigma }_{xy}^z$) of W-N compounds, focusing on WN and ${\mathrm{W}}_2\mathrm{N}$, employing first-principles calculations. We evaluate the SHC, formation energy ($\mathrm{\Delta }F$), and phonon frequencies for all cases. Three possible structures, including NaCl, hexagonal, and NbO type, are considered for WN. While the SHC of WN in NaCl and a hexagonal structure are substantial, the thermodynamic average of WN is $-194(\hslash /e)\text{S/cm}$, much smaller than pure W. However, ${\mathrm{W}}_2\mathrm{N}$, whose stability is confirmed by phonon calculations, shows a large SHC of ${\sigma }_{xy}^z=-966(\hslash /e)\text{S/cm}$ with a spin Hall angle (${\theta }_{\text{SH}}$) of $-0.44$, in good agreement with the experiment, enhanced by 18% over $\beta \text{−}\mathrm{W}$. Most of the spin Berry curvature, responsible for such large ${\sigma }_{xy}^z$, stems from the $\left[1\overline{1}0\right]$ ($k_x=k_y$) plane and is analyzed from a symmetry perspective using representations of group theory.

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• Electronic structure
• Spin Hall effect
• Spintronics
• Group theory