  A solution to energy-efficient magnetization switching in a nanoparticle with
biaxial anisotropy is presented. Optimal control paths minimizing the energy
cost of magnetization reversal are calculated numerically as functions of the
switching time and materials properties, and used to derive energy-efficient
switching pulses of external magnetic field. Hard-axis anisotropy reduces the
minimum energy cost of magnetization switching due to the internal torque in
the desired switching direction. Analytical estimates quantifying this effect
are obtained based on the perturbation theory. The optimal switching time
providing a tradeoff between fast switching and energy efficiency is obtained.
The energy cost of switching and the energy barrier between the stable states
can be controlled independently in a biaxial nanomagnet. This provides a
solution to the dilemma between energy-efficient writability and good thermal
stability of magnetic memory elements.
