Ground-State Properties of a Lattice-Coupled Strongly Correlated Model for Solid Oxygen under Pressure

Solid oxygen is an $S=1$ molecular magnet with strong coupling between spin and lattice degrees of freedom. Recent studies suggest that magnetic moments coexist with tetramer distortions under pressure. We derive an effective spin Hamiltonian from a two-orbital Peierls--Hubbard model with spin-orbit coupling. The resulting model contains competing easy-plane single-ion and easy-axis exchange anisotropies. We analyze this model on a square lattice using quantum Monte Carlo simulations and evaluate the magnetic contribution to the lattice stiffness for several lattice distortion patterns including the tetramer pattern. We find that the tetramer pattern is the most favorable among the considered distortion patterns throughout the parameter range studied. Moreover, competition between the two anisotropies enhances the tendency toward lattice distortion and strengthens the preference for tetramerization over the other patterns.