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High temperature non-collinear 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 spin model on a two-dimensional square lattice which possesses some of the key features of the models proposed for CuO. The model consists of Heisenberg couplings between nearest and next-nearest neighbor spins, and biquadratic couplings between nearest neighbors. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that even an arbitrarily weak biquadratic coupling plays a crucial role in selecting the magnetic ground state. More importantly, a non-collinear magnetic state, characterized by a finite spin current, is stable at finite temperatures. The interesting aspect is that the present model neither includes an inversion-symmetry-breaking term nor the effects of lattice distortions in the Hamiltonian. We conclude that non-collinear magnetism at high temperatures, as observed in CuO, can be explained via pure spin Hamiltonians. We find that the spiral phase is inhomogeneous, and is stabilized by entropic effects. Our study demonstrates that higher order interaction terms are of crucial importance if the stronger interactions together with the lattice geometry contemplate to generate a near degeneracy of magnetic states. The conclusions presented in this work are of particular relevance to the non-collinear magnetism and ferroelectricity observed at high temperatures in cupric oxide.