Ground states of anisotropic antiferromagnets with single ion and cubic anisotropy

TL;DR

This paper investigates the ground states of anisotropic antiferromagnets under magnetic fields, analyzing how exchange, single ion, and cubic anisotropies influence phase transitions and multicritical points, with implications for related lattice gas models.

Contribution

It provides a comprehensive analysis of ground states and transition lines in anisotropic antiferromagnets, including the effects of cubic anisotropy and the characterization of multicritical points.

Findings

Identified four ground states: PM, AF, SF, BC.

Transition lines can be calculated analytically or numerically.

Cubic anisotropy alters the order of phase transitions and creates reentrant behavior.

Abstract

Anisotropic antiferromagnets in an external magnetic field show a rich variety of different ground states meeting in transition lines and multicritical points. We study the dependence of the ground states of these systems in the three dimensional space on physical parameters as exchange, single ion and cubic anisotropy. One identifies four different ground states: the paramagnetic (PM), the antiferromagnetic (AF), the spin flop (SF) and the biconical (BC) ground state. In the case of absence of a cubic anisotropy the transition lines separating the different ground states can be calculated analytically, otherwise they have to be calculated numerically. We also considered the behavior of the staggered magnetization which characterizes the different ground states. From its behavior the order of the transition from one state to the other is determined. But also the order of the transition changes along the transition lines when including the cubic anisotropy, especially at the reeentrant region where a transition from SF to BC and back to SF by increasing the external field $H$ occurs. Multicritical points are founded which are assumed to be tricritical or critical endpoints. The results obtained may be relevant for other systems since the antiferromagnetic model can be mapped to a lattice gas model where the biconical ground state is interpreted as supersolid phase. Recent renormalization group calculations show that such a phase would indicate the existence of a tetracritical point.