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

摘要

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