From Atomic Level to Large-Scale Monte Carlo Magnetic Simulations

Abstract

This paper refers to Monte Carlo magnetic simulations for large-scale systems. We propose scaling rules to facilitate analysis of mesoscopic objects using a relatively small amount of system nodes. In our model, each node represents a volume defined by an enlargement factor. As a consequence of this approach, the parameters describing magnetic interactions on the atomic level should also be re-scaled, taking into account the detailed thermodynamic balance as well as energetic equivalence between the real and re-scaled systems. Accuracy and efficiency of the model have been depicted through analysis of the size effects of magnetic moment configuration for various characteristic objects. As shown, the proposed scaling rules, applied to the disorder-based cluster Monte Carlo algorithm, can be considered suitable tools for designing new magnetic materials and a way to include low-level or first principle calculations in finite element Monte Carlo magnetic simulations.

High and Ultra-High Coercive Materials in Spring-Exchange Systems—Review, Simulations and Perspective

“…Additionally, simulations for other interesting systems, according to the presented review, were also carried out. The disorder-based MC algorithm (developed by our team) was used as a computation method [ 45 , 46 ]. It is important that the algorithm allows for simulating the magnetization processes of systems containing magnetically different phases, and it has successfully been used in the study of similar objects [ 47 ].…”

Enhancement of Hard Magnetic Properties in Fraktal-Like Nano and Mesoscopic Grains

“…Generally, we used the Monte Carlo Metropolis method as the simulation procedure [ 20 ]. Recently, we developed a computational approach which allows the analysis of magnetization processes of hard magnetic systems containing nano and mesoscopic 3D objects [ 21 , 22 ]. We introduced the following two elements: (i) modification of the cluster Wolff algorithm [ 23 ] by an additional factor taking into account information (or configuration) entropy originating from a difference in magnetic properties of system nodes [ 21 ] and (ii) formulation of scaling rules for micromagnetic simulation of mesoscopic objects [ 22 ].…”

“…It is worth noting that the basic energy equation presented in Equation (2) is extended by the scaling rules (described in details in [ 22 ]), in order to model a large-scale mesoscopic systems, with an acceptable level of computing resource consumption. The main idea lies in the assumption that one node in the rescaled system can represent a finite volume consisting of n × n × n original (unscaled) nodes.…”

“…The main idea lies in the assumption that one node in the rescaled system can represent a finite volume consisting of n × n × n original (unscaled) nodes. In this situation, the parameters appearing in Equation (2) should be recalculated using the formulation of scaling rules in [ 22 ]. Table 1 summarizes the main simulation parameters and the scaling rules depending on the scaling factor n .…”

Micromagnetic Monte Carlo method with variable magnetization length based on the Landau–Lifshitz–Bloch equation for computation of large-scale thermodynamic equilibrium states

“…Other works along this line also include a micromagnetic one-dimensional model [11], as well as a two-dimensional model [12]. Alternatively, a thermodynamic rescaling for the atomistic cluster Monte Carlo approach was also discussed [13]. A micromagnetic hybrid Monte Carlo method was introduced previously [14], based on the hybrid (molecular dynamics/Langevin) Monte Carlo approach [15], which reproduces a Boltzmann distribution for the free energy.…”