Spin-1/2 Quantum Isotropic Heisenberg Model With a Magnetoelastic Interaction

This study investigates the spin-1/2 quantum isotropic Heisenberg model incorporating magnetoelastic coupling. Using the standard pair Oguchi approximation, we derive the Helmholtz free energy for the system with an exponentially decaying nearest-neighbor interaction on a simple cubic lattice. The magnetic contribution to the free energy is complemented by the static lattice energy, described through a volume-dependent Morse potential, and by the quasi-harmonic Einstein phonon energy. From the total Helmholtz free energy, we obtain the equations of state and relevant thermodynamic quantities within the framework of standard statistical mechanics. Numerical results for the simple cubic lattice reveal that the stability regions of the magnetic phases are strongly affected by the strength of the magnetoelastic coupling. The dependence of the critical boundaries on tunable model parameters shows that, besides the conventional second-order phase transitions, the isotropic Heisenberg model with sufficiently strong magnetoelastic coupling can also exhibit first-order phase transitions and tricritical points. Furthermore, the temperature dependencies of the magnetization, relative volume change, and Helmholtz free energy are presented and discussed in detail.