Abstract:
We develop a general framework, which combines exact diagonalization in small clusters with a density matrix variational principle, to study frustrated magnets at finite temperature. This thermodynamic hierarchical mean-field technique is used to determine the phase diagram and magnetization process of the three-dimensional spin-$1/2$ ${J}_{1}$-${J}_{2}$ antiferromagnet on a stacked square lattice. Its nonmagnetic phase exhibits a thermal crossover from a quantum to a classical paramagnet at a temperature ${T}={T}_{0}$ which can be extracted from thermodynamic measurements. At low temperature an applied magnetic field stabilizes, through order by disorder, a variety of phases with nontrivial spin textures, and a magnetization plateau at half-saturation which continuously disappears at ${T}\sim{T}_{0}$. Our results are relevant for frustrated vanadium oxides.
