  We consider a magnet with uniaxial anisotropy in an external magnetic field
along the anisotropy direction, but with a field magnitude smaller than the
coercive field. There are three representative magnetization configurations
corresponding to three extrema of the free energy. The equilibrium and
metastable configurations, which are magnetized approximately parallel and
antiparallel to the applied field, respectively, both correspond to local
free-energy minima. The third extremum configuration is the saddle point
separating these minima. It is also called the transition state for
magnetization reversal. The free-energy difference between the metastable and
transition-state configurations determines the thermal stability of the magnet.
However, it is difficult to determine the location of the transition state in
both experiments and numerical simulations. Here it is shown that the
computational Projective Dynamics method, applied to the time dependence of the
total magnetization, can be used to determine the transition state. From
large-scale micromagnetic simulations of a simple model of magnetic nanowires
with no crystalline anisotropy, the magnetization associated with the
transition state is found to be linearly dependent on temperature, and the
free-energy barrier is found to be dominated by the entropic contribution at
reasonable temperatures and external fields. The effect of including
crystalline anisotropy is also discussed. Finally, the influence of the spin
precession on the transition state is determined by comparison of the
micromagnetic simulations to kinetic Monte Carlo simulations of precession-free
(overdamped) dynamics.
