Crossover from diffusive to superfluid transport in frustrated magnets

We investigate the spin transport across the magnetic phase diagram of a frustrated antiferromagnetic insulator and uncover a drastic modification of the transport regime from spin diffusion to spin superfluidity. Adopting a triangular lattice accounting for both nearest-neighbor and next-nearest-neighbor exchange interactions with easy-plane anisotropy, we perform atomistic spin simulations on a two-terminal configuration across the full magnetic phase diagram. We found that as long as the ground state magnetic moments remain in-plane, irrespective of whether the magnetic configuration is ferromagnetic, collinear, or noncollinear antiferromagnetic, the system exhibits spin superfluid behavior with a device output that is independent of the value of the exchange interactions. When the magnetic frustration is large enough to compete with the easy-plane anisotropy and cant the magnetic moments out of the plane, the spin transport progressively evolves towards the diffusive regime. The robustness of spin superfluidity close to magnetic phase boundaries is investigated and we uncover the possibility for proximate spin superfluidity close to the ferromagnetic transition.

Figure 1

The device setup: a noncollinear antiferromagnet of length $L$ is embedded between two heavy metal electrodes (grey). On the left electrode, a charge current is injected, which induces a spin accumulation ${\mu }_L^z$ at the interface with the antiferromagnet via spin Hall effect. This nonequilibrium spin accumulation induces a spin current in the antiferromagnet that is collected on the right electrode via inverse spin Hall effect. The ratio ${\mu }_R^z/{\mu }_L^z$ determines the efficiency of the device.

Figure 2

(a) Schematics of the triangular lattice with nearest and next-nearest-neighbor Heisenberg exchange. (b) Magnetic phase diagram obtained by atomistic spin simulations and (c) snapshots of the magnetic ground state of four representative configurations in the phase diagram. NAF-1 and NAF-2 correspond to $J_2>0$ and $J_2<0$, respectively.

Figure 3

Structure factor $S\left(\mathbf{k}\right)$ in momentum space for four selected magnetic phases of the $J_1-J_2$ phase diagram. The peaks characterize long-range magnetic order. (a) ${120}^{\circ }$ NAF phase with $\mathbf{Q}=\pm \frac{2\pi }{a}(\frac{1}{3},\frac{1}{\sqrt{3}}), \pm \frac{4\pi }{a}(\frac{1}{3},0)$. (b) Ferromagnetic phase with $\mathbf{Q}=(0,0)$. (c) Stripe phase with $\mathbf{Q}=\pm \frac{2\pi }{a}(0,\frac{1}{\sqrt{3}})$. (d) Example of a spin spiral phase showing complex but well-defined $\mathbf{Q}$ pattern.

Figure 4

The spin accumulation ratio (${\mu }_R^z/{\mu }_L^z$) of all four phases of $90\times 30$ sites in $J_1-J_2$ phase diagram. The black and red dots indicate different ($J_1,J_2$) configurations for which length-dependent spin transport properties have been calculated. $J_1$ and $J_2$ are in units of $J=1$ meV. All phase boundaries are indicated by blue dotted lines.

Figure 5

The spin accumulation ratio (${\mu }_R^z/{\mu }_L^z$) as a function of triangular system length L. The exchange interaction strengths are given in the inset. The interpolation curve is based on the ${120}^{\circ }$ NAF and stripe phase curves. $J_1$ and $J_2$ are in units of $J=1$ meV.

Figure 6

The spin accumulation ratio (${\mu }_R^z/{\mu }_L^z$) as a function of triangular system length L. The exchange interaction strengths are given in the inset. The interpolation curve is based on the ${120}^{\circ }$ NAF and stripe phase curves. $J_1$ and $J_2$ are in units of $J=1$ meV.

Figure 7

Example of a complex, inhomogeneous spin spiral ground state, located at $J_1=J$ and $J_2=-0.34J$, close to the boundary with the ferromagnetic state. The high frustration arising from the competition between nearest-neighbor and next-nearest-neighbor exchange interactions results in a highly degenerate ground state. In spite of its high inhomogeneity, this complex magnetic texture is able to transmit spin information almost perfectly due to its proximity with the planar ferromagnetic state.