GPU-accelerated atomistic parallel Monte Carlo algorithms for computation of magnetization, exchange stiffness, anisotropy, and susceptibilities in large-scale systems.

Monte Carlo algorithms are frequently used in atomistic simulations, including for computation of magnetic parameter temperature dependences in multiscale simulations. Here we show how both the standard and constrained atomistic Monte Carlo algorithms can be parallelized. Compared to the serial algorithms, the parallel Monte Carlo algorithms are typically over 200 times faster, allowing computations in systems with over 10 million atomistic spins on a single GPU with relative ease. Implementation and testing of the algorithms was carried out in large-scale systems, where finite-size effects are reduced, by accurately computing temperature dependences of magnetization, uniaxial and cubic anisotropies, exchange stiffness, and susceptibilities. In particular for the exchange stiffness the Bloch domain wall method was used with a large cross-sectional area, which allows accurate computation of the domain wall width up to the Curie temperature. The exchange stiffness for a simple cubic lattice closely follows an m^k scaling at low temperatures, with k < 2 dependent on the anisotropy strength. However, close to the Curie temperature the scaling exponent tends to k = 2. Furthermore, the implemented algorithms are applied to the computation of magnetization temperature dependence in granular thin films with over 15 million spins, as a function of average grain size and film thickness. We show the average Curie temperature in such systems may be obtained from a weighted Bloch series fit, which is useful for analysis of experimental results in granular thin films.