  We investigate the dynamical behavior of finite rings of classical spin
vectors interacting via nearest-neighbor isotropic exchange in an external
magnetic field. Our approach is to utilize the solutions of a continuum version
of the discrete spin equations of motion (EOM) which we derive by assuming
continuous modulations of spin wave solutions of the EOM for discrete spins.
This continuous EOM reduces to the Landau-Lifshitz equation in a particular
limiting regime. The usefulness of the continuum EOM is demonstrated by the
fact that the time-evolved numerical solutions of the discrete spin EOM closely
track the corresponding time-evolved solutions of the continuum equation. Of
special interest, our continuum EOM possesses soliton solutions, and we find
that these characteristics are also exhibited by the corresponding solutions of
the discrete EOM. The robustness of solitons is demonstrated by considering
cases where initial states are truncated versions of soliton states and by
numerical simulations of the discrete EOM equations when the spins are coupled
to a heat bath at finite temperatures.

Other Condensed Matter