High-temperature noncollinear magnetism in a classical bilinear-biquadratic Heisenberg model

Motivated by the magnetically driven high-temperature ferroelectric behavior of CuO and the subsequent theoretical efforts to understand this intriguing phenomenon, we study a bilinear-biquadratic Heisenberg model on a two-dimensional square lattice, which possesses some of the key features of the models proposed for CuO. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that the biquadratic coupling plays a crucial role in selecting the magnetic ground state. More importantly, a noncollinear magnetic state is found to be stable at finite temperatures. Our study demonstrates that higher-order interaction terms are of crucial importance if the stronger interactions together with the lattice geometry combine to generate a near degeneracy of magnetic states.