Dimensional Reduction in Quantum Dipolar Antiferromagnets

We report ac susceptibility, specific heat, and neutron scattering measurements on a dipolar-coupled antiferromagnet LiYbF$_4$. For the thermal transition, the order-parameter critical exponent is found to be 0.20(1) and the specific-heat critical exponent -0.25(1). The exponents agree with the 2D XY/h$_4$ universality class despite the lack of apparent two-dimensionality in the structure. The order-parameter exponent for the quantum phase transitions is found to be 0.35(1) corresponding to (2+1)D. These results are in line with those found for LiErF$_4$ which has the same crystal structure, but largely different T$_N$, crystal field environment and hyperfine interactions. Our results therefore experimentally establish that the dimensional reduction is universal to quantum dipolar antiferromagnets on a distorted diamond lattice.