Measurement of spin mixing conductance in Ni$_{81}$Fe$_{19}$/$\alpha$-W and Ni$_{81}$Fe$_{19}$/$\beta$-W heterostrucutures via ferromagnetic resonance

We present measurements of interfacial Gilbert damping due to the spin pumping effect in Ni$_{81}$Fe$_{19}$/W heterostructures. Measurements were compared for heterostructures in which the crystallographic phase of W, either $\alpha$(bcc)-W or $\beta$(A15)-W, was enriched through deposition conditions and characterized using X-ray diffraction (XRD) and high-resolution cross-sectional transmission electron microscopy (HR-XTEM). Single phase Ni$_{81}$Fe$_{19}$/$\alpha$-W heterostructures could be realized, but heterostructures with $\beta$-W were realized as mixed $\alpha$-$\beta$ phase. The spin mixing conductances (SMC) for W at interfaces with Ni$_{81}$Fe$_{19}$ were found to be significantly lower than those for similarly heavy metals such as Pd and Pt, but comparable to those for Ta, and independent of enrichment in the $\beta$ phase.