  Motivated by recent progress on synthesizing two-dimensional magnetic van der
Waals systems, we propose a setup for detecting the topological
Berezinskii-Kosterlitz-Thouless (BKT) phase transition in spin-transport
experiments on such structures. We demonstrate that the spatial correlations of
injected spin-currents into a pair of metallic leads can be used to measure the
predicted universal jump of $2/\pi$ in the ferromagnet spin-stiffness as well
as its predicted universal square root dependence on temperature as the
transition is approached from below. Our setup provides a simple route to
measuring this topological phase transition in two-dimensional magnetic
systems, something which up to now has proven elusive. It is hoped that this
will encourage experimental efforts to investigate critical phenomena beyond
the standard Ginzburg-Landau paradigm in low-dimensional magnetic systems with
no local order parameter.
