  When current flows through a magnetic tunnel junction (MTJ), there is spin
accumulation at the electrode-barrier interfaces if the magnetic moments of the
two ferromagnetic electrodes are not aligned. Here we report that such
nonequilibrium spin accumulation generates its own characteristic low frequency
noise (LFN). Past work viewed the LFN in MTJs as an equilibrium effect arising
from resistance fluctuations ($S_R$) which a passively applied current ($I$)
converts to measurable voltage fluctuations ($S_{V}=I^{2}S_{R}$). We treat the
LFN associated with spin accumulation as a nonequilibrium effect, and find that
the noise power can be fitted in terms of the spin-polarized current by
$S_{I}f=aI\coth(\frac{I}{b})-ab$, resembling the form of the shot noise for a
tunnel junction, but with current now taking the role of the bias voltage, and
spin-flip probability taking the role of tunneling probability.
