Bose-Einstein condensation in antiferromagnets close to the saturation field

Abstract

At zero temperature and strong applied magnetic fields the ground state of an anisotropic antiferromagnet is a saturated paramagnet with fully aligned spins. We study the quantum phase transition as the field is reduced below an upper critical ${H}_{c2}$ and the system enters a $XY$-antiferromagnetic phase. Using a bond operator representation we consider a model spin-1 Heisenberg antiferromagnetic with single-ion anisotropy in hypercubic lattices under strong magnetic fields. We show that the transition at ${H}_{c2}$ can be interpreted as a Bose-Einstein condensation (BEC) of magnons. The theoretical results are used to analyze our magnetization versus field data in the organic compound $\mathrm{Ni}{\mathrm{Cl}}_{2}\text{\ensuremath{-}}4\mathrm{S}\mathrm{C}{(\mathrm{N}{\mathrm{H}}_{2})}_{2}$ (DTN) at very low temperatures. This is the ideal BEC system to study this transition since ${H}_{c2}$ is sufficiently low to be reached with static magnetic fields (as opposed to pulsed fields). The scaling of the magnetization as a function of field and temperature close to ${H}_{c2}$ shows excellent agreement with the theoretical predictions. It allows us to obtain the quantum critical exponents and confirm the BEC nature of the transition at ${H}_{c2}$.