Quantum critical scaling at a Bose-glass/superfluid transition: Theory and experiment for a model quantum magnet

Abstract

In this paper we investigate the quantum phase transition from magnetic Bose Glass to magnetic Bose-Einstein condensation induced by a magnetic field in NiCl${}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}$4SC(NH${}_{2}$)${}_{2}$ (dichloro-tetrakis-thiourea-nickel, or DTN), doped with Br (Br-DTN) or site diluted. Quantum Monte Carlo simulations for the quantum phase transition of the model Hamiltonian for Br-DTN, as well as for site-diluted DTN, are consistent with conventional scaling at the quantum critical point and with a critical exponent $z$ verifying the prediction $z=d$; moreover the correlation length exponent is found to be $\ensuremath{\nu}=0.75(10)$, and the order parameter exponent to be $\ensuremath{\beta}=0.95(10)$. We investigate the low-temperature thermodynamics at the quantum critical field of Br-DTN both numerically and experimentally, and extract the power-law behavior of the magnetization and of the specific heat. Our results for the exponents of the power laws, as well as previous results for the scaling of the critical temperature to magnetic ordering with the applied field, are incompatible with the conventional crossover-scaling Ansatz proposed by Fisher et al. [Phys. Rev. B 40, 546 (1989)]. However they can all be reconciled within a phenomenological Ansatz in the presence of a dangerously irrelevant operator.