Supercurrent-Driven Néel Torque in Superconductor/Altermagnet Hybrids

Abstract

We predict a supercurrent-driven Néel spin-orbit torque in a superconductor/$d$-wave altermagnet heterostructure, associated with the emergence of spin-triplet correlations. The effect can be understood as a consequence of the supercurrent-induced spin polarization, owing to the interplay between spin-orbit coupling and momentum-dependent spin splitting, as found, for example, in altermagnets. Remarkably, the supercurrent can be tuned by the Néel-vector direction, and the supercurrent-induced torque can both propel magnetic domain walls and reverse the Néel-vector orientation within a domain wall. These findings establish superconductor/altermagnet heterostructures as a versatile platform for the dissipationless control of the Néel vector, with potential applications in racetrack memory, dissipationless superconducting electronics, and unconventional computing.

Figures (3)

• Figure 1: (a) S/AM heterostructure with a supercurrent density ${\mathbf J}_s \|\hat{x}$, Néel vector ${\mathbf n}$, and proximity-induced pairing gap $\Delta$, and superconducting phase $\varphi$. (b) ${\mathbf J}_s$-induced staggered NSOT field ($\mathbf{B}_{N1}, \mathbf{B}_{N2}$) and $180^\circ$ domain wall with sublattice magnetizations $\mathbf{M}_1$, $\mathbf{M}_2$ and related $\mathbf{n} = (\mathbf{M}_1-\mathbf{M}_2)/|\mathbf{M}_1-\mathbf{M}_2|$. (c) ${\mathbf J}_s$-induced uniaxial anisotropy, described by the free-energy-density difference $\delta\mathcal{F}_{\mathbf n}=\mathcal{F}_{\mathbf n}-\mathcal{F}_{\hat{x}}$ for ${\mathbf n}=\hat{z}$ as a function of the momentum $\hbar q$ (blue) and the altermagnetic interaction $t_m$ (red), in units of the hopping $t$, $a$ is the lattice spacing. (d) Similarly for the ${\mathbf J}_s$-induced Néel field contribution for ${\bf n}=\hat{y}$. BdG (Ana) label the numerical (analytical) results by lines (crosses). Parameters: $\mu=0.05t$, $t_{\mathrm{so}}=0.2t$, $t_m=0.2t$, $\Delta_0=0.2t$, and $T=0.1T_c$.
• Figure 2: (a) The free-energy density obtained from Eq. (\ref{['eq:F']}) (labeled BdG), together with the analytical results from Eqs. (\ref{['eq:F_expand_main_vec']}) and (\ref{['eq:F0_main_nz']}), for the Néel vector ${\mathbf n}$ rotating in the $\hat{x}$-$\hat{y}$ plane and (b) in the $\hat{z}$-$\hat{x}$ and $\hat{z}$-$\hat{y}$ planes. (c) The BdG and self-consistent free-energy densities for ${\mathbf n}$ rotating in the $\hat{x}$-$\hat{y}$ plane and (d) in the $\hat{z}$-$\hat{x}$ plane. Parameters are $\mu=0.05t$, $t_{\mathrm{so}}=0.2t$, $t_m=0.2t$, and $\Delta=0.2t$. We use $\mathbf{q}a=(qa,0,0)$ throughout, with (a) $qa=0.1$, (b) $0.01$, and (c), (d) $0.2$. The self-consistent calculations in (c) and (d) are performed for a system of size $L_x\times L_y=30a\times25a$ with $V_s=5t$.
• Figure 3: (a) The self-consistent supercurrent, $I$, for a uniform Néel vector ${\mathbf n}$ as a function of the spherical angles $\theta$ and $\phi$ and (b) as a function of $\phi$ for opposite signs of $q$ at $\theta=\pi/2$. The same parameters as in Fig. \ref{['fig:analyticals']} are used. (c) The self-consistent free energy as a function of the domain-wall position $\mathbf{r}_0$ as the wall moves through S along $\hat{x}$ and $\hat{y}$, (d) as function of the internal wall angle $\phi_{dw}$ for opposite directions of current. The insets: The domain walls in the calculations. We use $\delta_{dw}=4a$. In (c), (d) $L_x=50a$ and $L_y=20a$ are used for a domain wall extending along $\hat{x}$, and $L_x=20a$ and $L_y=50a$ for a domain wall extending along $\hat{y}$. The free energy $F$ is referenced to zero for a domain wall at $x=0.2L_x$ in (c) and at $y=0.2L_y$ in (d). We define $I_0=et/(\hbar a)$. The supercurrent is along $\hat{x}$ in all panels and $|qa|=2\pi/50$.