Interparticle Correlations in the Simple Cubic Lattice of Ferroparticles: Theory and Computer Simulations

Abstract

Anisotropic interparticle correlations in the simple cubic lattice of single-domain ferroparticles (SCLF) are studied using both theory and computer simulation. The theory is based on the Helmholtz free energy expansion like classical virial series up to the second virial coefficient. The analytical formula for the Helmholtz free energy is incorporated in a logarithmic form to minimize the effects of series truncation. The new theoretical approach, including discrete summation over lattice nodes coordinates, is compared critically against the classical virial expansion of the Helmholtz free energy for the dipolar hard sphere fluid; the main differences between the Helmholtz free energy of SCLF and dipolar hard sphere fluid are discussed. The theoretical results for the Helmholtz free energy, the magnetization, and the initial magnetic susceptibility of the SCLF are compared against Molecular Dynamic simulation data. In all cases, theoretical predictions using logarithmic form of the Helmholtz free energy are seen to be superior, but they only have an applicability range of the effective dipolar coupling constant $λ_e < 1.5$. For highest values of $λ_e$, the structural transition of the magnetic dipoles in SCLF is observed in Molecular Dynamic simulation. It has been shown that for $λ_e \gtrsim 2$, an antiferromagnetic order appears in the system.