Two-dimensional array of magnetic particles: The role of an interaction cutoff

TL;DR

This study investigates how the choice of interaction cutoff affects the magnetic ordering in two-dimensional dipolar particle systems, revealing that a cutoff around 5 particle diameters balances computational efficiency and accurate local ordering.

Contribution

The paper provides a systematic analysis of the impact of interaction cutoff on magnetic states in 2D dipolar systems, guiding optimal cutoff selection for simulations.

Findings

Ferromagnetic state is more sensitive to cutoff than anti-ferromagnetic state.

Cutoff around 8 preserves the energetic balance between states.

Cutoff around 4 significantly alters the magnetic ordering.

Abstract

Based on theoretical results and simulations, in two-dimensional arrangements of a dense dipolar particle system, there are two relevant local dipole arrangements: (1) a ferromagnetic state with dipoles organized in a triangular lattice, and (2) an anti-ferromagnetic state with dipoles organized in a square lattice. In order to accelerate simulation algorithms we search for the possibility of cutting off the interaction potential. Simulations on a dipolar two-line system lead to the observation that the ferromagnetic state is much more sensitive to the interaction cutoff $R$ than the corresponding anti-ferromagnetic state. For $R \gtrsim 8$ (measured in particle diameters) there is no substantial change in the energetical balance of the ferromagnetic and anti-ferromagnetic state and the ferromagnetic state slightly dominates over the anti-ferromagnetic state, while the situation is changed rapidly for lower interaction cutoff values, leading to the disappearance of the ferromagnetic ground state. We studied the effect of bending ferromagnetic and anti-ferromagnetic two-line systems and we observed that the cutoff has a major impact on the energetical balance of the ferromagnetic and anti-ferromagnetic state for $R \lesssim 4$. Based on our results we argue that $R \approx 5$ is a reasonable choice for dipole-dipole interaction cutoff in two-dimensional dipolar hard sphere systems, if one is interested in local ordering.