  We propose to use the Hall response of topological defects, such as merons
and antimerons, to spin currents in 2D magnetic insulator with in-plane
anisotropy for identification of the Berezinskii-Kosterlitz-Thouless (BKT)
transition in a transistor-like 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 tuning the in-plane magnet across BKT
transition, e.g., by changing the exchange interaction, magnetic anisotropy, or
temperature.
