How does a quantum magnet behave under a strong magnetic field? For decades, theory has predicted that a Haldane spin-1 chain, a paradigmatic one-dimensional (1D) quantum magnet, should pass through exotic states: a 1D Tomonaga-Luttinger liquid (TLL) and, a Bose-Einstein condensate (BEC) of magnetic excitations at low temperature (once 3D couplings become relevant). Until now, almost none of these predictions had been tested experimentally on a genuine Haldane chain. An international collaboration including Nicolas Laflorencie and Sylvain Capponi of the Laboratoire de Physique Théorique (LPT) has now filled this gap with an organic crystal, whose behavior is remarkably well captured by state-of-the-art simulations performed at LPT. The work, published in Physical Review Letters as an Editors’ Suggestion, was selected for the journal cover and is highlighted in the APS magazine Physics.
In a Haldane chain, strong quantum fluctuations produce a non-magnetic ground state separated from excited states by a finite energy gap. An external magnetic field can close this gap, and the chain then enters a TLL phase or, at lower temperature, a BEC phase when 3D couplings become relevant. Testing this scenario has been hard, because known Haldane compounds are either too anisotropic or have critical fields out of reach.
The team studied BoNO, a nearly isotropic crystal built from magnetic organic molecules, whose critical fields are accessible. Using proton NMR in fields up to 34 Tesla and temperatures down to 460 mK, together with magnetostriction measurements, they mapped the full field-temperature phase diagram. The theoretical side, led in Toulouse, combined quantum Monte Carlo and density-matrix renormalization group calculations. The main results are:
- The BEC-TLL phase boundary is fully determined, and quantum Monte Carlo reproduces its shape.
- Near the upper critical field, the critical behavior follows the predicted law with exponent ν = 2/3, with universal quasiparticle scaling.
- The TLL phase shows attractive interactions between excitations, long sought in a Haldane chain.
These results validate theoretical predictions made more than twenty years ago and establish BoNO as a model system for field-induced quantum phases.
Reference and links: I. Jakovac, M. S. Grbić, M. Dupont, N. Laflorencie, S. Capponi, Y. Hosokoshi, S. Krämer, Y. Skourski, S. Luther, M. Takigawa, M. Horvatić, Magnetic-Field-Induced Tomonaga-Luttinger Liquid and Bose-Einstein Condensate Phases in an Organic S=1 Haldane Chain, Phys. Rev. Lett. 137, 136702 (2026).
- PRL article: https://journals.aps.org/prl/abstract/10.1103/89k5-p261
- PRL cover: https://journals.aps.org/prl/covers/137/13
- Physics Synopsis (“Realizing a Spin Chain”): https://physics.aps.org/articles/v19/s121
- arXiv link: https://arxiv.org/abs/2601.10489