Spin pumping in the Heusler alloy $\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}/\mathrm{Mo}{\mathrm{S}}_2$ heterostructure: Ferromagnetic resonance experiment and theory

Spin pumping from the full Heusler alloy $\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}$ film into the transition-metal dichalcogenide $\mathrm{Mo}{\mathrm{S}}_2$ is reported. Plasma-assisted sulfurization of ion-beam sputtered Mo films of different nominal thicknesses is employed to first fabricate large area high-quality $\mathrm{Mo}{\mathrm{S}}_2$ sheets [thicknesses: 1, 2, 3, and 4 monolayers (MLs)] on $\mathrm{Si}{\mathrm{O}}_2/\mathrm{Si}$ substrates, followed by deposition of $\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}$ films with a fixed thickness of 8 nm. The spin pumping is investigated by measuring the changes in the damping constant in the Al(5 nm) capped $\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}/\mathrm{Mo}{\mathrm{S}}_2$ bilayers using ferromagnetic resonance spectroscopy. The study demonstrates that even 1 ML of $\mathrm{Mo}{\mathrm{S}}_2$ possesses high enough spin-orbit coupling strength to enhance damping from $5.5(\pm 0.2)\times {10}^{-3}$ in $\mathrm{Al}\left(5\mathrm{nm}\right)/\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}\left(8\mathrm{nm}\right)$ to a nearly saturated value of $8.3(\pm 0.2)\times {10}^{-3}$ in $\mathrm{Al}\left(5\mathrm{nm}\right)/\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}\left(8\mathrm{nm}\right)/\mathrm{Mo}{\mathrm{S}}_2\left(1\mathrm{ML}\right)$, which is suppressed by inserting a thin Al layer at the $\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}/\mathrm{Mo}{\mathrm{S}}_2$ interface. The observed enhancement in damping is in agreement with the results from first-principles calculations based on density functional theory. These results open up a paradigm for designing spintronic devices based on heterostructures comprising a full Heusler alloy and the inherently stable $\mathrm{Mo}{\mathrm{S}}_2$.

Figure 1

XRD pattern of $\mathrm{Al}\left(5\mathrm{nm}\right)/\mathrm{CFA}\left(8\mathrm{nm}\right)/\mathrm{Mo}{\mathrm{S}}_2\left(3\mathrm{ML}\right)/\mathrm{Si}{\mathrm{O}}_2/\mathrm{Si}$ sample. Blue and black lines correspond to the experimental and simulated patterns, respectively. Symbol “*” represents a peak corresponding to the substrate.

Figure 2

(a) Optical micrograph showing the top view of the different surface regions (in different colors) of $\mathrm{Al}\left(5\right)/\mathrm{CFA}\left(8\right)/\mathrm{Mo}{\mathrm{S}}_2$, 1 ML $\mathrm{Mo}{\mathrm{S}}_2$, and bare oxidized Si(100) substrate. (b) and (c) are AFM images of regions marked as “1” and “2” in Fig. 1 corresponding to Al(5)/CFA(8)/1 ML $\mathrm{Mo}{\mathrm{S}}_2$ and 1 ML $\mathrm{Mo}{\mathrm{S}}_2$, respectively. (d) The line-scan profile recorded on the step marked as “3” in Fig. 1 supporting the formation of 1-ML-thick $\mathrm{Mo}{\mathrm{S}}_2$.

Figure 3

Raman spectra of $\mathrm{Mo}{\mathrm{S}}_2$ films showing the $A_{1g}$ and $E_{2g}$ modes. The separation between the $A_{1g}$ and $E_{2g}$ peaks (indicated by the dotted lines) is $\sim 20.6\mathrm{c}{\mathrm{m}}^{-1}$, which confirms the 1 ML thickness of this particular $\mathrm{Mo}{\mathrm{S}}_2$ film. Inset: Observed peak separation (Δ) between the $A_{1g}$ and $E_{2g}$ modes in the four $\mathrm{Mo}{\mathrm{S}}_2$ films having a different number of MLs $\left(n_{\mathrm{ML}}\right)$.

Figure 4

(a) FMR resonance spectra recorded on an $\mathrm{Al}\left(5\right)/\mathrm{CFA}\left(8\right)/\mathrm{Mo}{\mathrm{S}}_2\left(1\mathrm{ML}\right)$ sample by scanning the dc field at various indicated frequencies (Inset: Schematic of the generation and flow of spin current density $J_S$ at $\mathrm{CFA}/\mathrm{Mo}{\mathrm{S}}_2$ interface as a consequence of transfer of spin angular momentum). (b) Linewidth vs frequency of $\mathrm{Al}\left(5\right)/\mathrm{CFA}\left(8\right)/\mathrm{Mo}{\mathrm{S}}_2\left(n_{\mathrm{ML}}\right)$ samples, where $n_{\mathrm{ML}}$ indicates the number of MLs. (c) ${\alpha }_{\mathrm{eff}}$ vs $n_{\mathrm{ML}}$ in these heterostructures.

Figure 5

(a) Effective damping constant $\left({\alpha }_{\mathrm{eff}}\right)$ vs CFA layer thicknesses $\left(t_{\mathrm{CFA}}\right)$ for various seed layers. Lines are a guide to the eye. (b) ${\alpha }_{\mathrm{eff}}$ vs $1/t_{\mathrm{CFA}}$. The intercepts of the fits (solid red lines) using Eq. (3) yield the intrinsic damping ${\alpha }_{\mathrm{CFA}}$ of CFA in the three sample series.

Figure 6

(a) The resonance field ${\mu }_0{H}_r$ vs $f$ for all $\mathrm{Al}\left(5\right)/\mathrm{CFA}\left(8\right)/\mathrm{Mo}{\mathrm{S}}_2\left(n_{\mathrm{ML}}\right)$ heterostructures with different $n_{\mathrm{ML}}$ [lines are the Kittel's fit to the data using Eq. (2)]. (b) $n_{\mathrm{ML}}$ dependence of effective magnetization $\left({\mu }_0{M}_{\mathrm{eff}}\right)$ and saturation magnetization $\left({\mu }_0{M}_S\right)$ obtained from FMR and VSM, respectively. (c) Experimental $M\text{−}H$ magnetization loops for all the samples with different $n_{\mathrm{ML}}$.

Figure 7

(a) Energy band structures (top) and DOS plots (bottom) calculated for 1, 2, and 4 MLs of $\mathrm{Mo}{\mathrm{S}}_2$, respectively (numbers along with vertical line indicates the band-gap energy). (b) Total DOS for the $\mathrm{C}{\mathrm{o}}_2\mathrm{FeAl}$ full Heusler alloy. (c) Total DOS resulting from the corresponding interface in the $\mathrm{CFA}/n_{\mathrm{ML}}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ system $(n_{\mathrm{ML}}:0–4)$. The majority and minority states are displayed by up/down arrows. The actual atomic arrangements (geometry and number of atoms) shown to the left of DOS plots in these figures correspond to that used in the DFT calculations in $\mathrm{Mo}{\mathrm{S}}_2$, CFA, and the $\mathrm{CFA}/n_{\mathrm{ML}}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ interface, respectively.

Figure 8

(a) The $n_{\mathrm{ML}}$ dependence of $G$ (left axis) and total $\mathrm{DOS}\left(E_F\right)$ (right axis) at the $\mathrm{CFA}/\mathrm{Mo}{\mathrm{S}}_2$ interface in the heterostructures. (b) Theoretically calculated magnetic moments of all the elements effectively contributing to the $\mathrm{CFA}/\mathrm{Mo}{\mathrm{S}}_2$ interface (Inset: a zoomed view near the origin for highlighting the magnetic moment induced in Mo and S).