  Using Suzuki-Trotter decompositions of exponential operators we describe new
algorithms for the numerical integration of the equations of motion for
classical spin systems. These techniques conserve spin length exactly and, in
special cases, also conserve the energy and maintain time reversibility. We
investigate integration schemes of up to eighth order and show that these new
algorithms can be used with much larger time steps than a well established
predictor-corrector method. These methods may lead to a substantial speedup of
spin dynamics simulations, however, the choice of which order method to use is
not always straightforward.
