Magnetic properties of a Lie symmetry double square nanostructure: Monte Carlo study

Inspired by Lie symmetries and motivated by the existence of the double hexagonal geometry in the two-dimensional material physics, we study a nanosystem based on the double square structure, which we refer as the B-2 nanostructure, known as SO(5) Lie algebra. This structure involves two squares of unequal side lengths rotated by angle 45 degrees. The model contains eight atoms instead of four ones appearing in the single square structure. The number of atoms is identified with the non- null roots of the B-2 Lie algebra. In particular, we propose a nanolattice model consisting of particles with and S = 1 spins, consisting of two and three states, respectively. Theses spins are placed at the double square sites producing a new geometry formed by structures. More precisely, we study the effect of sigma-sigma and sigma-S coupling exchange interactions. This investigation is made in terms of both external and crystal magnetic fields. First, we elaborate analytically the corresponding ground-state phase diagrams. Second, we investigate the magnetic properties using Monte Carlo method.