Nuclear Magnetic Resonance study of the magnetic- field- induced ordered phase in the NiCl2-4SC(NH2)2 compound

Nuclear magnetic resonance (NMR) study of the high magnetic field (H) part of the Bose-Einstein condensed (BEC) phase of the quasi one-dimensional (quasi-1D) antiferromagnetic quantum spin-chain compound NiCl2- 4SC(NH2)2 (DTN) was performed. We precisely determined the phase boundary, Tc(H), down to 40 mK, the critical boson density, nc(Tc), and the absolute value of the BEC order parameter Sp at very low temperature (T = 0.12 K). All results are accurately reproduced by numerical quantum Monte Carlo simulations of a realistic 3D model Hamiltonian. Approximate analytical predictions based on 1D Tomonaga- Luttinger liquid description are found to be precise for Tc(H), but less so for Sp(H), which is more sensitive to the strength of 3D couplings, in particular close to the critical field. A mean-field treatment, based on the Hartree-Fock- Popov description, is found to be valid only up to nc = 4% (T < 0.3 K), while for higher nc boson interactions appear to modify the density of states