Spin-$1$ $J_1-J_2-J_3$ ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice: A bosonic approach

TL;DR

This paper investigates the phase diagram of a spin-1 ferromagnetic Heisenberg model with frustration and an easy-plane crystal field on a cubic lattice, revealing quantum phase transitions and a potential quantum spin liquid phase.

Contribution

It introduces a bosonic approach to analyze the phase transitions in a frustrated spin-1 model with an easy-plane crystal field, identifying novel quantum phases and transition types.

Findings

Discovery of a disordered nonmagnetic phase as a quantum spin liquid candidate.

Identification of first- and second-order quantum phase transitions depending on frustration.

Phase diagrams showing temperature and frustration effects on magnetic ordering.

Abstract

We examine the phase diagram of the spin-$1$ $J_1-J_2-J_3$ ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice, in which $J_1$ is the ferromagnetic exchange interaction between nearest neighbors, $J_2$ is the antiferromagnetic exchange interaction between next-nearest neighbors and $J_3$ is the antiferromagnetic exchange interaction between next-next-nearest neighbors. Using the bond-operator formalism, we investigate the phase transitions between the disordered paramagnetic phase and the ordered ones. We show that the nature of the quantum phase transitions change as the frustration parameters ($\frac{J_2}{J_1}$, $\frac{J_3}{J_1}$) are varied. The zero-temperature phase diagram exhibits second- and first-order transitions, depending on the energy gap behavior. Remarkably, we find a disordered nonmagnetic phase, even in the absence of a crystal field, which is suggested to be a quantum spin liquid candidate. We also depict the phase diagram at finite temperature for some values of crystal field and frustration parameters.