Spin transport in tantalum studied using magnetic single and double layers

We report on spin transport in sputter-grown Ta films measured by ferromagnetic resonance. Spin diffusion length and spin mixing conductance are determined from magnetic damping measurements for a varying thickness of Ta layer $0\le d_{\mathrm{Ta}}\le 10$ nm. The different boundary conditions of single- and double-magnetic-layer heterostructures $\mathrm{Py}|\mathrm{Ta}$ and $\mathrm{Py}\left|\mathrm{Ta}\right|\left[\mathrm{Py}|\mathrm{Fe}\right]$ allow us to significantly narrow down the parameter space and test various models. We show that a common approach of using bulk resistivity value in the analysis yields inconsistent spin diffusion length and spin mixing conductance values for magnetic single- and double-layer structures. X-ray diffraction shows that bulk Ta is a combination of $\beta \text{−}\mathrm{Ta}$ and $\text{bcc-}\mathrm{Ta}$. However, in the region of significant spin transport, $\lesssim 2$ nm, there is an intermediate region of growth where the Ta lacks long-range structural order, as observed by transmission electron microscopy. Thickness-dependent resistivity measurements confirm that the bulk and intermediate regions have significantly different resistivity values. We find that the data can be well represented if the intermediate region resistivity value is used in the analysis. Additionally, the data can be fit if resistivity has the measured thickness dependence and spin diffusion length is restricted to be inversely proportional to resistivity. Finally, we rule out a model in which spin diffusion length is a constant, while the resistivity has the measured thickness dependence.

Figure 1

Resistivity as a function of Ta film thickness grown on glass substrate. The inset shows the geometry and labeling scheme for the four-point probe measurements.

Figure 2

Out-of-plane $\theta \text{−}2\theta$ XRD scan of (a) $\mathrm{Si}|\text{Ta}\left(3\right)|\text{Py}\left(3.5\right)\left|\text{Ta}\left(20.1\right)\right|\text{Au}\left(3.6\right),\mathrm{glass}|\text{Ta}\left(20.1\right)$ and of (b) $\mathrm{glass}|\mathrm{Ta}\left(d_{\mathrm{Ta}}\right)$. (c) In-plane XRD scan at a $0.5^{\circ }$ grazing incidence angle of $\mathrm{glass}|\mathrm{Ta}\left(d_{\mathrm{Ta}}\right)$. (d) Cross-sectional bright-field TEM and (e) HRTEM micrographs of the $\mathrm{Si}|\mathrm{Ta}$(3)$|\mathrm{Py}$(3.5)$|\mathrm{Ta}$(20)$|\mathrm{Au}$(3.6) structure. The FFTs of three different regions in the Ta(20) layer are displayed in the corresponding square insets. A dashed white line is drawn around the $\beta \text{−}\mathrm{Ta}$ grain to outline its edges.

Figure 3

Example 6.5-GHz FMR spectra for (a) SL $\left({\mathrm{FM}}_1=\mathrm{Py}\right)$ and (b) DL $\left({\mathrm{FM}}_1=\mathrm{Py},{\mathrm{FM}}_2=\mathrm{Py}|\mathrm{Fe}\right)$ samples with $d_{\mathrm{Ta}}=1.0$ nm. Inset of (b) is an expanded view of the ${\mathrm{FM}}_1=\mathrm{Py}$ resonance line. (c) FMR linewidth as a function of frequency. SL samples with $d_{\mathrm{Ta}}= \left(•\right)$ 0 nm $\left(\otimes \right)$ 0.8 nm, and $\left(\odot \right)$ 10 nm with $\alpha =10.2$, 12.4, and $13.3 \times {10}^{-3}$, respectively. DL sample with $d_{\mathrm{Ta}}= \left(\oplus \right)$ 0.8 nm and $\alpha =13.2\times {10}^{-3}$.

Figure 4

Damping due to spin pumping into the Ta overlayer as a function of $d_{\mathrm{Ta}}$ for SL $\left(•\right)$ and DL $\left(♦\right)$ samples. (a) Simultaneous fits using model 1. (b) Main: dashed and solid lines are simultaneous fits using models 2a and 2b, respectively. Inset: individual fits for the SL and DL are shown as solid lines on the left and right panels, respectively. The dashed lines are plots of the complementary data set using the individual fit parameters. (c) Main: simultaneous fit using model 3. Inset: ${\lambda }_{\mathrm{sd}}\left(d_{\mathrm{Ta}}\right)$. (d) The solid lines are simultaneous fit while the dashed line is a fit to only the SL data.