Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition

Motivated by recent experimental progress in 2D magnetism, we theoretically study spin transport easy-plane magnets at finite temperatures across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, developing a duality mapping to 2+1D electromagnetism with full account of spin's lifetime. In particular, find that non-conservation gives rise distinct signature BKT current decaying distance power-law (exponentially) below (above) transition; this is detectable proposed experiment NiPS$_3$ and CrCl$_3$.