Scaling of spin relaxation and angular momentum dissipation in permalloy nanowires

We study the relationship between the damping $\left(\alpha \right)$ and the nonadiabaticity of the spin transport $\left(\beta \right)$ in permalloy nanowires. $\alpha$ is engineered by Ho doping, and from the characteristics of the current-induced domain-wall velocity, determined by high-resolution x-ray magnetic circular-dichroism photoemission electron microscopy, $\beta$ due to spin relaxation is measured. We find that $\beta$ scales with $\alpha$ and conclude that the spin relaxation that leads to nonadiabatic spin torque originates from the same underlying mechanism as the angular momentum dissipation that causes viscous damping.

Figure 1

(Color online) XMCD-PEEM images taken [(a) and (c)] before and [(b) and (d)] after a current pulse of duration $25\mu \text{s}$ and density $j\sim {10}^{12}\text{A}/{\text{m}}^2$. For $j<1.05\times {10}^{12}\text{A}/{\text{m}}^2$, the DW motion occurs without spin-structure transformations. For $j>1.05\times {10}^{12}\text{A}/{\text{m}}^2$, vortex-core nucleation and annihilation, and propagation of multivortex walls occurs. (e) Average DW velocity $v$ as a function of current density $j$ determined by XMCD-PEEM imaging, for 1500-nm-wide, 20-nm-thick Py wires. Below the Walker threshold current density $j_W$ the data are fitted by Eq. (2). The inset is a simulation of a vortex wall in a Py wire with contrast equivalent to the XMCD-PEEM images (a) and (b).

Figure 2

(Color online) (a) Average DW velocity $v$ as a function of current density $j$ for $j\le j_W$ for a 1500-nm-wide, 20-nm-thick pure Py wire and for Py wires doped with Ho. The damping $\alpha$ increases with the Ho content. The data are fitted with Eq. (2). (b) Damping $\alpha$ and nonadiabaticity $\beta$ as a function of Ho concentration. Scaling of $\beta$ and $\alpha$ occurs up to $4\text{at}\text{.}\%$ Ho. (c) Average field-induced DW velocity as a function of $1/\alpha$ determined by time-resolved MOKE (squares). The solid line is the prediction from the 1D model $v=\left(\gamma \Delta /\alpha \right)H$, with $\gamma =176\text{GHz}/\text{T}$, $\Delta =20\text{nm}$, and $H=11\text{Oe}$.