| Summary: | We propose to use the Hall response of topological defects, such as merons and antimerons, to spin currents in two-dimensional magnetic insulator with in-plane anisotropy for identification of the Berezinskii-Kosterlitz-Thouless (BKT) transition in a transistorlike geometry. Our numerical results relying on a combination of Monte Carlo and spin dynamics simulations show transition from spin superfluidity to conventional spin transport, accompanied by the universal jump of the spin stiffness and exponential growth of the transverse vorticity current. We propose a superfluid spin transistor in which the spin and vorticity currents are modulated by changes in density of free topological defects, e.g., by injection of vorticity or by tuning the in-plane magnet across the BKT transition by changing the exchange interaction, magnetic anisotropy, or temperature.
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