Igor Omelyan, Ihor Mryglod

Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine

Reinhard Folk

Institute for Theoretical Physics, University of Linz, Austria
The computer experiment remains an important tool for the prediction and theoretical understanding of various phenomena in magnetic materials. The methods of Monte-Carlo (MC) and molecular dynamics (MD) were intensively exploited over the years for the investigation of phase diagrams, critical phenomena, scaling, and the dynamic behavior of lattice systems such as the Ising, the XY, and the Heisenberg model [1-3].
The necessity to extend these studies to disordered models of magnetic liquids was motivated by a great amount of additional physical properties arising when both spin (orientational) and liquid (translational) degrees of freedom are taken into account [4-9]. Computer experiments for such systems have been restricted to MC simulations [5,7] in which only static quantities could be calculated. Dynamic phenomena, in particular, spin and density relaxations, and the effects connected with the mutual influence of magnetic and liquid subsystems an be investigated in MD simulations.
Until now, there have been no attempts to simulate spin liquids within the MD approach. This an be explained by the absence of an MD algorithm for handling the corresponding equations of motion. The traditional numerical methods [10] for solving differential equations are unsuitable be cause they become highly unstable on time s ales used in MD simulations. As has been well established for pure liquid systems [11,12], even standard predictor-corrector schemes are not efficient because of poor total energy conservation.
The properties of an acceptable algorithm for long-time observations of a many-body system should be: stability, accuracy, speed and ease of implementation. There exists only a small group of integrators satisfying these criteria. An important one is the velocity Verlet (VV) algorithm [13,14] which allows a high accuracy with minimal costs in terms of time-consuming for e evaluations. However, the VV and other similar schemes [11,15] were designed to simulate pure liquid dynamics. In the case of magnetic liquids the situation is more complicated since the translational positions and momenta are coupled with spin orientations in a characteristic way and, hence, all these dynamical variables must be considered simultaneously. This requires substantial revision of the liquid dynamic algorithms.
Recently, new algorithms have been devised for spin dynamics simulations of lattice systems [16]. They are based (like the VV integrator) on the Suzuki-Trotter (ST) decomposition method and appear to be much more efficient than predictor-corrector schemes. These algorithms are applicable to spin systems if the de composition on two (or several) noninteracting sublattices is possible. However, they cannot be used for models with arbitrary spatial spin distributions and, therefore, not for spin liquids.
In the present study we develop the idea of using ST-like decompositions for spin liquid dynamics and derive the desired MD algorithm. This allows quantitative measurement of dynamical structure fa tors of a Heisenberg ferrofluid. The main result obtained (reflecting the influence of the liquid sybsystem on spin dynamics) is the identification of a new propagative sound-like mode in the spectrum of collective longitudinal spin excitations.
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