Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory

Abstract

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in two-dimensional XY arrays is addressed. The system is modelled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole–dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking T b temperature is lower than that ( T af ) of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean-field approximation. With the technique of a generalized Ott–Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the AF order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented. This article is part of the theme issue ‘Patterns in soft and biological matters’.

Patterns in soft and biological matters

“…These methods enable the manufacture of elastomers with tailored magneto-mechanical properties. The dynamic reaction of systems of anisotropic (oblate) ferromagnetic particles, which form in-plane patterns in an elastic media, on an alternating magnetic field is studied theoretically by Tyulkina et al [43]. New theoretical approaches that take into account the dipole-dipole interaction between structured particles are suggested in these works.…”

A reduction methodology for fluctuation driven population dynamics

“…More recently, the Ott–Antonsen (OA) Ansatz [10, 11] yielded closed mean-field (MF) equations for the dynamics of the synchronization order parameter for globally coupled phase oscillators on the basis of a wrapped LD of their phases. The nature of these phase elements can vary from the phase reduction of biological and chemical oscillators [12, 13] through superconducting Josephson junctions [14, 15] to directional elements like active rotators [16, 17] or magnetic moments [18].…”

A reduction methodology for fluctuation driven population dynamics

“…More recently, the Ott-Antonsen (OA) Ansatz [10,11] yielded closed mean-field (MF) equations for the dynamics of the synchronization order parameter for globally coupled phase oscillators on the basis of a wrapped LD of their phases. The nature of these phase elements can vary from the phase reduction of biological and chemical oscillators [12,13] through superconducting Josephson junctions [14,15] to directional elements like active rotators [16,17] or magnetic moments [18].…”