The ground states of nanomagnetic dipoles placed on an infinite square lattice

Nanomagnetic materials are excellent experimental tools for the study of electromagnetic phenomena and are suitable for the manufacture of artificial new materials with unusual physical properties. These properties depend on the magnetic structure of the dipole system in a great degree. In the present study, the emphasis is on the exact magnetic structure of a system with an infinite number of nanomagnetic dipoles arranged on a simple square lattice at zero temperature. Using numerical methods, such as the Static Relaxation and Monte Carlo simulation, we have obtained various magnetic configurations and by analyzing them, we found some exact, degenerated ground states for a system with an infinite number of dipoles, with long-range dipole-dipole interactions between themselves that form a simple two-dimensional square lattice. The degenerated ground states turned out to constitute systems of anti-parallel lines which form a ‘magnetic crystalline’ structure with a zero-magnetization vector. Any equilibrium state of dipole system is degenerated by nature of the dipole-dipole interaction: simultaneous inversion of the direction of each dipole of the system to exact opposite one leaves the system in equilibrium and does not change its energy. The degeneracy of the ground state, in combination with fluctuations, boundary and finite-size effects results in several metastable disordered configurations for a system of finite but large number of dipoles, thus macroscopically a nanomagnetic dipole system has zero-magnetization and behaves in a fashion similar to paramagnetic material.