Quasiparticle condensation and breakdown in a quantum spin liquid*

Piperazinium hexachlorodicuprate (PHCC) is a frustrated bilayer antiferromagnet with a disordered quantum spin-liquid (QSL) ground state at zero field [1] and a diverse magnetic field versus temperature phase diagram which includes two field- induced quantum critical points [2]. The spin excitations in PHCC have a spectral gap of $\Delta \approx 1$~meV above which they follow a nearly 2D-isotropic dispersion with a bandwidth slightly larger than $\Delta$. Field dependent neutron scattering and thermodynamic measurements reveal a lower critical field, $H_{c1}=7.5$~T, separating the QSL phase from a three dimensional spin-ordered state and an upper critical field, $H_{c2}=37$~T, marking the onset of a saturated ferromagnetic phase. The two-dimensional antiferromagnet supports a field induced long range ordered phase well described as a Bose-Einstein condensate (BEC) embedded within a gapless quasi-two-dimensional paramagnetic regime. Inelastic neutron scattering experiments also reveal a peculiar type of hybridization of magnetic excitations in PHCC with their two- particle continuum [3], similar to the post-roton regime in superfluid helium. The excitations at this point become broadened and diffuse, no longer describable as quasiparticles. Although such effects are expected to be strongest in one- dimensional systems with gapped spectra [4], such as Haldane chains, direct observation therein is difficult due to a weak scattering structure factor in the vicinity of the quasiparticle breakdown point [5,6]. The dimer-dominated magnetism in PHCC, on the other hand, is favorable for investigating changes in quasiparticle spectra in the vicinity of their breakdown point. Our results have implications for a variety of condensed matter systems, in particular for other QSLs, where spin excitations have a bandwidth greater than the gap energy. \newline [1] M. B. Stone, {\it et al}. Phys. Rev. B {\bf 64}, 144405 (2001).\newline [2] M. B. Stone, {\it et al}. Phys. Rev. Lett. {\bf 96}, 257203 (2006).\newline [3] M. B. Stone, {\it et al}. Nature, {\bf 440}, 187 (2006).\newline [4] T. Giamarchi, Quantum Physics in One Dimension, Oxford University Press (2005).\newline [5] S. Ma, {\it et al}. Phys. Rev. Lett. {\bf 69}, 3571 (1992).\newline [6] I. A. Zaliznyak, {\it et al}. Phys. Rev. Lett. {\bf 87}, 017202 (2001).