Adiabatic and nonadiabatic spin torques induced by a spin-triplet supercurrent

We study spin-transfer torques induced by a spin-triplet supercurrent in a magnet with the superconducting proximity effect. By a perturbative approach, we show that spin-triplet correlations realize new types of torques, which are analogous to the adiabatic and nonadiabatic ($\beta$) torques, without extrinsic spin-flip scattering. Remarkable advantages compared to conventional spin-transfer torques are highlighted in domain-wall manipulation. Oscillatory motions of a domain wall do not occur for a small Gilbert damping, and the threshold current density to drive its motion becomes zero in the absence of extrinsic pinning potentials due to the nonadiabatic torque controlled by the triplet correlations.

Figure 1

Proposed setup. A ferromagnet (FM) with a domain wall is attached on a superconductor, which produces a spin-triplet proximity effect. We apply a supercurrent in the $xy$ plane and drive the domain-wall motion.

Figure 2

(a) ${\tilde{P}}_x$ and (b) ${\tilde{\beta }}_x$ in a domain-wall configuration with ${\varphi }_0=\pi /4$ as functions of the position $x$ for different $\delta$, where $d$ vector is $\mathit{d}\left(\mathit{k}\right)=(-sin{k}_{y}a,sin{k}_{x}a,\delta sin{k}_{x}a)$. (c) The profile of the domain wall. (d) $\tau \left({\varphi }_0\right)$ and (e) $F\left({\varphi }_0\right)$ as functions of ${\varphi }_0$ for different $\delta$, where we define $j_0=Se{v}_c{a}^{-3}$.

Figure 3

Velocity of a domain-wall center for $\delta =0$ in (a) and (c), and for $\delta =0.5$ in (b) and (d). (a) shows the velocity averaged over the oscillation period after sufficiently long time, and (b) shows the velocity after sufficiently long time. In (c) and (d), the time evolution of the velocity for different $j_x/j_0$ (indicated by different colors) is presented. We have set $\alpha ={10}^{-4}$, and the initial conditions are ${\varphi }_0(t=0)=\pi$ and $\dot{X}(t=0)$.