First-principles calculations of Berry curvature for Tungsten metals and compound*

With rapid progress in spintronics, utilizing spin Hall effect or interface spin phenomena has become highly demanding for practical applications with high interests. In this sense, calculation of spin Hall angle ($\theta_{SH}$) or Berry curvature ($\Omega_z$) based on first-principles calculations is of great significant in exploration for materials search. Here, we adapt the method proposed by previous work \footnote{G. Y. Guo, S. Murakami, T.-W. Chen, and N. Nagaosa, Phys. Rev. Lett. {\bf 100}, 096401 (2008).}, which has been implemented in FLAPW method. As large spin Hall angle has been reported in tungsten \footnote{Kai-Uwe Demasius and {\em et al.} Nat. Comm. {\bf 7}, 10644 (2016).}, calculations on tungsten metals - for $bcc$ and $A15$ structure are presented. Also results on WTe$_2$ are shown further.