  We show experimentally that the spin current generated by the spin Hall
effect drives the magnon gas in a ferromagnet into a quasi-equilibrium state
that can be described by the Bose-Einstein statistics. The magnon population
function is characterized either by an increased effective chemical potential
or by a reduced effective temperature, depending on the spin current
polarization. In the former case, the chemical potential can closely approach,
at large driving currents, the lowest-energy magnon state, indicating the
possibility of spin current-driven Bose-Einstein condensation.
