We study the ground state of frustrated spin-S chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta $pm Q$, and just below th
e saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around $pm Q$. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the help of this method, we are able to establish the magnetic phase diagram of frustrated chains close to saturation and study phase transitions between several nontrivial states, including a two-component Luttinger liquid, a vector chiral phase, and phases with bound magnons. We study those phase transitions numerically and find a good agreement with our analytical predictions.
$Ni Cl_2$-$4SC(NH_2)_2$ (known as DTN) is a spin-1 material with a strong single-ion anisotropy that is regarded as a new candidate for Bose-Einstein condensation (BEC) of spin degrees of freedom. We present a systematic study of the low-energy excit
ation spectrum of DTN in the field-induced magnetically ordered phase by means of high-field electron spin resonance measurements at temperatures down to 0.45 K. We argue that two gapped modes observed in the experiment can be consistently interpreted within a four-sublattice antiferromagnet model with a finite interaction between two tetragonal subsystems and unbroken axial symmetry. The latter is crucial for the interpretation of the field-induced ordering in DTN in terms of BEC.
