Interplay Between Magnetic Frustration and Quantum Criticality in the Unconventional Ladder Antiferromagnet C9H18N2CuBr4
Quantum fluctuation in frustrated magnets and quantum criticality at the transition between different quantum phases of matter are two thrilling subjects in condensed matter physics. Here we demonstrate the nontrivial interplay between them in the spin-1/2 coupled two-leg ladder antiferromagnet C9H18N2CuBr4 (DLCB for short). Employing high-resolution neutron spectroscopy, we unambiguously identify a weakly first-order hydrostatic pressure-driven quantum phase transition, which arises from fluctuations enhanced by the frustrating interlayer coupling. An exotic pressure-induced quantum disordered state is evidenced by the broad spectral linewidth observed near the phase transition. We also find that the temperature dependence of the gapped transverse excitations in the Neel-ordered phase at ambient pressure cannot be described by the conventional S=1 magnons, i.e., the spin wave quanta, associated with explicit symmetry breaking. Instead, the thermal renormalization of the gap energies at ambient pressure shows a remarkable agreement with the theoretical calculation for the three-dimensional (3D) O(3) nonlinear-sigma model, which indicates that the ground state at ambient pressure is best described as a disordered singlet with a spin gap. Accordingly, the origin of the spin gap in DLCB is not owing to the spin anisotropy and the 3D magnetic order ought to emerge in an unconventional way. Haldane's conjecture on spin-1 chains is proposed to explain the opening of the spin gap in DLCB and the analysis of the free energy supports that the magnetic order of DLCB can arise exclusively from thermal fluctuations by order-by-disorder. Our results indicate the presence of a symmetry-protected topological phase at ambient pressure in this material.