Spin Superfluidity: Engendering a Geometrically-Tunable Nonlocal Spin Hall Magnetoresistance in Lateral Devices

Spin superfluidity (SSF) is mediated by coherent magnetization precession and characterized by sub-exponential decay of spin current with distance. Although conventional easy-plane magnets can exhibit this phenomenon, the required device geometries are incompatible with current fabrication methods. In this work, we analyze the nonlocal spin and charge transfer efficiencies of SSF devices with a lateral geometry, which has been underexplored due to a lack of compatible materials. Using the Landau-Lifshitz-Gilbert formalism and magneto-circuit theory, we show that both efficiencies depend on the ratio of the area of the injector to the uncovered area of the magnetic film, as well as the ratio of the area of the injector to that of the detector. Thus, by keeping the injector much wider than both the transport channel and the detector, the transfer efficiencies of devices with arbitrary channel lengths remain at the theoretical maximum as dictated by the short channel limit. This unique geometric scaling provides an unmistakable signature of SSF. Furthermore, we demonstrate that the SSF-induced resistances at the detector and injector are proportional to the spin Hall magnetoresistance (SMR)—despite their absence from standard SMR theory. Our analysis identifies them as manifestations of the unrecognized Onsager reciprocal of conventional SMR: negative resistance by induced spin pumping. As a result, conventional magnetoresistivity measurements can be leveraged to evaluate candidate SSF materials.