Disorder Dependence of Interface Spin Memory Loss

The discontinuity of a spin-current through an interface caused by spin-orbit coupling is characterized by the spin memory loss (SML) parameter $\delta$. We use first-principles scattering theory and a recently developed local current scheme to study the SML for $\mathrm{Au}|\mathrm{Pt}$, $\mathrm{Au}|\mathrm{Pd}$, $\mathrm{Py}|\mathrm{Pt}$, and $\mathrm{Co}|\mathrm{Pt}$ interfaces. We find a minimal temperature dependence for nonmagnetic interfaces and a strong dependence for interfaces involving ferromagnets that we attribute to the spin disorder. The SML is larger for $\mathrm{Co}|\mathrm{Pt}$ than for $\mathrm{Py}|\mathrm{Pt}$ because the interface is more abrupt. Lattice mismatch and interface alloying strongly enhance the SML that is larger for a $\mathrm{Au}|\mathrm{Pt}$ than for a $\mathrm{Au}|\mathrm{Pd}$ interface. The effect of the proximity-induced magnetization of Pt is negligible.

Figure 1

A fully polarized spin-current $j_s$ injected at 300 K from the left Au lead into a $\mathrm{Au}(50)|\mathrm{Pt}(140)$ bilayer sandwiched between Au leads decays exponentially in Au and in Pt; the numbers in brackets denote the number of atomic layers. The solid lines indicate fits for $j_s(z)$ in individual layers using solutions of the VF equations. (Top inset) Schematic of the scattering region. (Middle and bottom insets) Temperature dependence of the interface parameters $\delta$ (yellow) and $R_{\text{I}}$ (purple) for a $\mathrm{Au}|\mathrm{Pt}$ interface (circles). The corresponding parameters for $\mathrm{Au}|\mathrm{Pd}$ at 300 K are included (diamonds).

Figure 2

A fully polarized spin current $j_s(z)$ is injected into a $\mathrm{Au}|\mathrm{Pt}$ bilayer with a sharp interface (vertical black line), two layers of $\mathrm{A}{\mathrm{u}}_{50}\mathrm{P}{\mathrm{t}}_{50}$ interface (yellow shaded region), and four layers of $\mathrm{A}{\mathrm{u}}_{50}\mathrm{P}{\mathrm{t}}_{50}$ interface (green shaded region) between them. The calculated spin currents $j_s(z)$ for the three cases are shown as gray circles, yellow diamonds, and green squares, respectively. The solid blue line indicates a fit to the VF equation in Au. The solid, dashed, and dotted red lines indicate fits to the VF equation in Pt for $\mathrm{Au}|\mathrm{Pt}$, $\mathrm{Au}|{\mathrm{Au}}_{50}\mathrm{P}{\mathrm{t}}_{50}(2)|\mathrm{Pt}$, and $\mathrm{Au}|{\mathrm{Au}}_{50}\mathrm{P}{\mathrm{t}}_{50}(4)|\mathrm{Pt}$, respectively. (Inset) $\delta$ vs $A{R}_{\text{I}}$ for $N=0$, 2, and 4 interface layers of mixed $\mathrm{A}{\mathrm{u}}_{50}\mathrm{P}{\mathrm{t}}_{50}$.

Figure 3

(a) Open circles: spin current $j_s(z)$ through a $\mathrm{Pt}|\mathrm{Py}|\mathrm{Pt}$ trilayer calculated for $T=300\mathrm{K}$. The solid blue (orange) curve is a fit to the VF equations in bulk Pt (Py). These fits are extrapolated to the interface $z_{\text{I}}$ to obtain the values $j_{s,\mathrm{Pt}}(z_{\text{I}})$ and $j_{s,\mathrm{Py}}(z_{\text{I}})$, shown in detail in the right inset. (Left inset) The spin current with (red) and without (blue) proximity-induced moments in Pt. (b) $\delta$ for $\mathrm{Py}|\mathrm{Pt}$ (circles, solid lines) and $\mathrm{Co}|\mathrm{Pt}$ (diamonds, dashed lines) plotted as a function of temperature. (Inset) $\delta$ for $\mathrm{Py}|\mathrm{Pt}$ compared with results with only lattice disorder in $\mathrm{Py}|\mathrm{Pt}$ (open circles, dotted lines). (c),(d) Interface parameters $A{R}_{\text{I}}$ and $\gamma$ for $\mathrm{Py}|\mathrm{Pt}$ (circles, solid and dotted lines) and $\mathrm{Co}|\mathrm{Pt}$ (diamonds, dashed lines) plotted as a function of temperature. The dotted lines show the results for $\mathrm{Py}|\mathrm{Pt}$ with only lattice disorder.