Modulating Spin Current Induced Effective Damping in $\beta -W/Py$ Heterostructures by a Systematic Variation in Resistivity of the Sputtered Deposited $\beta -W$ films

Abstract

Utilizing the spin-induced pumping from a ferromagnet (FM) into a heavy metal (HM) under the ferromagnetic resonance (FMR) condition, we report an enhancement in effective damping in $\beta$- W/Py bilayers by systematically varying resistivity (${\rho }_W$) of $\beta$-W films. Different resistivity ranging from 100 $\mu \Omega$-cm to 1400 $\mu \Omega$-cm with a thickness of 8 nm can be achieved by varying the argon pressure ($P_{Ar}$) during the growth by the method of sputtering. The coefficient of effective damping ${\alpha }_{eff}$ is observed to increase from 0.010 to 0.025 with ${\rho }_W$, which can be modulated by $P_{Ar}$. We observe a modest dependence of ${\alpha }_{eff}$ on the sputtering power ($p_S$) while keeping the $P_{Ar}$ constant. ${\alpha }_{eff}$ dependence on both $P_{Ar}$ and $p_S$ suggests that there exists a strong correlation between ${\alpha }_{eff}$ and ${\rho }_W$. It is thus possible to utilize ${\rho }_W$ as a tuning parameter to regulate the ${\alpha }_{eff}$, which can be advantageous for faster magnetization dynamics switching. The thickness dependence study of Py in the aforementioned bilayers manifests a higher spin mixing conductance ($g_{eff}^{\uparrow \downarrow }$) which suggests a strong spin pumping from Py into the $\beta$-W layer. The effective spin current ($J_{S(eff)}$) is also evaluated by considering the spin-back flow in this process. Intrinsic spin mixing conductance ($g_W^{\uparrow \downarrow }$) and spin diffusion length (${\lambda }_{SD}$) of $\beta$-W are additionally investigated using thickness variations in $\beta$-W. Furthermore, the low-temperature study in $\beta$-W/Py reveals an intriguing temperature dependence in ${\alpha }_{eff}$ which is quite different from ${\alpha }_b$ of single Py layer and the enhancement in ${\alpha }_{eff}$ at low temperature can be attributed to the spin-induced pumping from Py layer into $\beta$-W.