High Field Properties of Geometrically Frustrated Magnets

Above the saturation field, geometrically frustrated quantum antiferromagnetshave dispersionless low-energy branches of excitations corresponding tolocalized spin-flip modes. Transition into a partially magnetized state occursvia condensation of an infinite number of degrees of freedom. The ground statebelow the phase transition is a magnon crystal, which breaks only translationalsymmetry and preserves spin-rotations about the field direction. We give adetailed review of recent works on physics of such phase transitions andpresent further theoretical developments. Specifically, the low-energy degreesof freedom of a spin-1/2 kagom\'e antiferromagnet are mapped to a hard hexagongas on a triangular lattice. Such a mapping allows to obtain a quantitativedescription of the magnetothermodynamics of a quantum kagom\'e antiferromagnetfrom the exact solution for a hard hexagon gas. In particular, we find theexact critical behavior at the transition into a magnon crystal state, theuniversal value of the entropy at the saturation field, and the position ofpeaks in temperature- and field-dependence of the specific heat. Analogousmapping is presented for the sawtooth chain, which is mapped onto a model ofclassical hard dimers on a chain. The finite macroscopic entropies ofgeometrically frustrated magnets at the saturation field lead to a largemagnetocaloric effect.Comment: 22 pages, proceedings of YKIS2004 worksho