Quantum Critical Behavior for a Model Magnet

Abstract

The classical, thermally driven transition in the dipolar-coupled Ising ferromagnet LiHo${\mathrm{F}}_{4}$ $({T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.53\phantom{\rule{0ex}{0ex}}\mathrm{K})$ can be converted into a quantum transition driven by a transverse magnetic field ${H}_{t}$ at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. The transverse field, applied perpendicular to the Ising axis, introduces channels for quantum relaxation, thereby depressing ${T}_{c}$. We have determined the phase diagram in the ${H}_{t}\ensuremath{-}T$ plane via magnetic susceptibility measurements. The critical exponent, $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, has a mean-field value in both the classical and quantum limits. A solution of the full mean-field Hamiltonian using the known LiHo${\mathrm{F}}_{4}$ crystal-field wave functions, including nuclear hyperfine terms, accurately matches experiment.