  We describe spin transfer in a ferromagnet/normal metal/ferromagnet
spin-valve point contact. Spin is transferred from the spin-polarized device
current to the magnetization of the free layer by the mechanism of incoherent
magnon emission by electrons. Our approach is based on the rate equation for
the magnon occupation, using Fermi's golden rule for magnon emission and
absorption and the non-equilibrium electron distribution for a biased spin
valve. The magnon emission reduces the magnetization of the free layer. For
anti-parallel alignment of the magnetizations of the layers and at a critical
bias a magnon avalanche occurs, characterized by a diverging effective magnon
temperature. This critical behavior can result in magnetization reversal and
consequently to suppression of magnon emission. However, magnon-magnon
scattering can lead to saturation of the magnon concentration at a large but
finite value. The further behavior depends on the parameters of the system. In
particular, gradual evolution of the magnon concentration followed by a
magnetization reversal is possible. Another scenario corresponds to a step-like
increase of the magnon concentration followed by a slow decrease. In the latter
case a spike in the differential resistance is expected due to a contribution
of electron-magnon scattering. A comparison of the obtained results to existing
experimental data and theoretical approches is given.
