Quantum Critical Behavior for a Model Magnet

The classical, thermally driven transition in the dipolar-coupled Ising ferromagnet LiHo${\mathrm{F}}_4$ $(T_c=1.53\mathrm{K})$ can be converted into a quantum transition driven by a transverse magnetic field $H_t$ at $T=0\mathrm{}$. 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 $H_t-T$ plane via magnetic susceptibility measurements. The critical exponent, $\gamma =1\mathrm{}$, 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.