Quantum and Classical Criticality in a Dimerized Quantum Antiferromagnet

We perform high-resolution neutron spectroscopy experiments to probe the spin excitations of the quantum antiferromagnet TlCuCl$_3$ throughout the phase diagram by controlling the pressure and temperature. Because this material has a pressure-induced quantum critical point (QCP) at $p_c = 1.07$ kb and a thermal ordering transition at $T_N(p)$ for $p > p_c$ [1], we demonstrate a number of remarkable properties arising at the interface between quantum and classical physics. Quantum and thermal fluctuations have very similar effects in melting the magnetically ordered phase and in opening excitation gaps, but they operate quite independently close to the QCP. In the QC regime there is robust $\omega/T$ scaling of the energies and $\Gamma/T$ scaling of the widths of the critically damped excitations. This scaling crosses over to a classical critical form in a narrow region around $T_N(p)$. The critically damped longitudinal, or Higgs, mode of the ordered phase [2] is exquisitely sensitive to thermal fluctuations and becomes overdamped in the classical regime. \\[4pt] [1] Ch. R\"uegg {\it et al.}, PRL {\bf 93}, 257201 (2004). \\[0pt] [2] Ch. R\"uegg {\it et al.}, PRL {\bf 100}, 205701 (2008).