  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.
