Low-energy degrees of freedom of a spin-1/2 kagomé antiferromagnet in the vicinity of the saturation field are mapped to a hard-hexagon model on a triangular lattice. The latter model is exactly solvable. The presented mapping allows to obtain quantitative description of the magnetothermodynamics of a quantum kagomé antiferromagnet up to exponentially small corrections as well as predict the critical behavior for the transition into a magnon crystal state. Analogous mapping is presented for the sawtooth chain, which is mapped onto a model of classical hard dimers on a chain.PACS numbers: 75.50. Ee, 75.45.+j, 75.10.Jm, 75.30.Sg In the past few years there have been increased attention to the behavior of frustrated magnetic materials at high fields. The interest is stimulated by a search for new fundamental effects such as the magnetization plateaus, 1,2,3,4,5,6,7,8,9 the magnetization jumps, 10,11,12,13 new complicated magnetic phase diagrams, 8,14 and new types of the critical behavior 15 as well as by a possible technological application of frustrated magnets in the adiabatic demagnetization refrigerators due to their unique magnetocaloric properties. 16,17 A zerotemperature behavior of geometrically frustrated antiferromagnets in the vicinity of the saturation field H c has been recently discussed by Schulenburg and coworkers. 10,11,12,13 Above H c in the fully polarized phase, these models have a flat branch of magnons with energy (H − H c ). Such dispersionless excitations correspond in real space to localized spin flips, which do not interact with each other unless touched. Upon decreasing magnetic field through H c , the energy of a single excitation becomes negative and magnons condense into a closepacked crystal structure. The present work is devoted to theoretical investigation of the low-temperature thermodynamics of magnon crystals. Specifically, we consider spin-1/2 Heisenberg models on a kagomé lattice and a sawtooth (or ∆) chain, see Fig. 1. While the former lattice is one of the best known examples of geometric frustration, which is realized, e.g., in SrCr 9p Ga 12−9p O 19 , 18 the latter spin model is applicable to magnetic delafossite YCuO 2.5 . 19 We show that the thermodynamic potential in the vicinity of H c for the two quantum models can be calculated exactly up to corrections, which are exponentially small at low temperatures.We consider nearest-neighbor spin-1/2 Heisenberg models in an external fieldFor a kagomé lattice all nearest-neighbor bonds have the same strength J ij ≡ 1. The spectrum of single-magnon excitations in the fully polarized phase iswhere γ k = 1 6 δ e ik·δ is a sum over nearest-neighbor sites on a triangular Bravais lattice. At the saturation field H c = 3 the energy of excitations from the lowest dispersionless branch vanishes. The sawtooth chain exhibits a similar behavior for the special ratio of the two coupling constants J 2 = 1 2 J 1 . In the following we always assume the above choice of the parameters with J 1 ≡ 1. Above H c = 2 the sawtooth chain antiferromag...

A theoretical overview of the phenomenon of spontaneous magnon decays in quantum antiferromagnets is presented. The intrinsic zero-temperature damping of magnons in quantum spin systems is a fascinating many-body effect, which has recently attracted significant attention in view of its possible observation in neutron-scattering experiments. An introduction to the theory of magnon interactions and a discussion of necessary symmetry and kinematic conditions for spontaneous decays are provided. Various parallels with the decays of anharmonic phonons and excitations in superfluid 4 He are extensively used. Three principal cases of spontaneous magnon decays are considered: field-induced decays in Heisenberg antiferromagnets, zero-field decays in spiral antiferromagnets, and triplon decays in quantum-disordered magnets. Analytical results are compared with available numerical data and prospective materials for experimental observation of the decay-related effects are briefly discussed.