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Magnetic field-induced phases in a model S=1 Haldane chain system

An $S=1$ Haldane chain is a one-dimensional (1D) quantum magnet where strong fluctuations result in quantum disordered singlet ground state with a gapped excitation spectrum. The gap magnitude is primarily set by the dominant intrachain interaction ($J_\text{1D}$). An applied magnetic field closes the gap at $B_\text{c1}$ and drives the system into a gapless Tomonaga-Luttinger liquid (TLL) regime, followed by, at lower temperatures, a Bose-Einstein condensate (BEC) ground state, persisting up to $B_\text{c2} \propto 4 J_\text{1D}/gμ_B$. Almost all previously studied experimental realizations of such systems were based on transition-metal complexes which typically suffer from intrinsic anisotropies or large $J_\text{1D}$ values, limiting the access to the full theoretical phase diagram. We report a comprehensive study of TLL and BEC phases in the organic Haldane chain system 3,5-bis(N-tert-butylaminoxyl)-3'-nitrobiphenyl (BoNO). The absence of anisotropy and a moderate $J_\text{1D}$ enable exploration of the complete $B-T$ phase diagram. Through $^1$H nuclear magnetic resonance, combined with theoretical analysis, we characterize the TLL properties, map the BEC phase boundary $T_c (B)$, determine the associated critical exponent $ν\approx 0.66$ at $B_\text{c2}$, and demonstrate universal quasiparticle scaling in the quantum-critical regime. These results provide full experimental validation of theoretical predictions for field-induced phases in an $S=1$ Haldane chain, made over two decades ago.