G. M. Wysin, W. A. Moura-Melo, L. A. S. Mól, A. R. Pereira
Dynamical effects are considered in a model for a spin ice on a square lattice in two dimensions. The spin ice is an array of thin elongated magnetic islands interacting with each other via long-range dipolar forces, which leads to geometrical frustration. Each island is assumed to possess a three-component dipole moment free to point in any direction, but with strong uniaxial anisotropy energies that select preferred directions. The model has real dynamics, including rotation of the magnetic degrees of freedom, going beyond the Ising-type models of spin ice. The dynamics is studied based on a Langevin equation that includes the temperature and a phenomenological damping, which is solved using a second order Heun algorithm. As an important application, the hysteresis in an applied magnetic field is calculated for typical island sizes used in recent experiments. At the same time, thermodynamic properties such as the specific heat can be studied -- a peak in specific heat is related to a type of melting-like phase transition present in the model.
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http://arxiv.org/abs/1208.6557
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