Nonlocal Magnetoresistance Mediated by Spin Superfluidity

The electrical response of two diffusive metals is studied when they are linked by a magnetic insulator hosting a topologically stable (superfluid) spin current. We discuss how charge currents in the metals induce a spin supercurrent state, which in turn generates a magnetoresistance that depends on the topology of the electrical circuit. This magnetoresistance relies on phase coherence over the entire magnet and gives direct evidence for spin superfluidity. We show that driving the magnet with an ac current allows coherent spin transport even in the presence of U(1)-breaking magnetic anisotropy that can preclude dc superfluid transport. Spin transmission in the ac regime shows a series of resonance peaks as a function of frequency. The peak locations, heights, and widths can be used to extract static interfacial properties, e.g., the spin-mixing conductance and effective spin Hall angle, and to probe dynamic properties such as the spin-wave dispersion. Thus, ac transport may provide a simpler route to realizing nonequilbrium coherent spin transport and a useful way to characterize the magnetic system, serving as a precursor to the realization of dc superfluid spin transport.

Figure 1

Schematics of the series (a) and parallel (b) configurations, as detailed in the text.

Figure 2

Dynamic transresistance for $L=100\ell$ as a function of ac frequency $\omega$. Here, we set $\alpha ={10}^{-3}$ and ${\gamma }^{\uparrow \downarrow }/s\ell ={10}^{-3}$. The solid line corresponds to the case without in-plane anisotropy, while for the dashed line we use $\kappa /K=4\times {10}^{-4}$.

Figure 3

Nonlocal magnetoresistance as a function of system size $L$. Here, we set $\alpha ={10}^{-3}$, ${\gamma }^{\uparrow \downarrow }/s\ell ={10}^{-3}$, and $\kappa /K=4\times {10}^{-4}$ (corresponding to ${\omega }_0\tau =0.02$). The solid line is for $\omega \tau =0.05>{\omega }_0\tau$, while the dashed line is for $\omega \tau =0.019<{\omega }_0\tau$. The inset shows the semilog version of the same plot.