Classical and Quantum Critical Phenomena in the Dipolar Antiferromagnet LiErF4

The collective behavior of systems consisting of interacting dipoles is a subject of considerable studies. The anisotropic nature of such interactions opens an arena to explore fundamental questions in correlated electron physics, ranging from quantum entanglement, phase transitions, spin glass states to disorder and fluctuations. LiHoF4 is a textbook example of a ferromagnetic Ising-dipolar model, offering a simple and well-understood Hamiltonian. The system undergoes a quantum phase transition (QPT) in a field transverse to the easy axis, which induces quantum fluctuations between the ground state doublet. Dilution of Ho sites with non-magnetic Yttrium ions lowers only the transition temperature (Tc), and eventually lead to spin-glass state. While Tc decreases in a linear fashion, as expected from simple mean-field (MF) calculation, critical field decreases much faster. The behavior upon dilution has been pointed out to be related to randomness and off-diagonal dipolar interactions. In chapter 5 of this thesis I quantify the deviation of experimental results from neutron scattering studies from MF prediction, with the aim that this analysis can be used in future theoretical efforts towards a quantitative description. The aim of this thesis, however, deals with LiErF4 which is an unexplored planar dipolar antiferromagnetic member of LiReF4 family, with TN ≃ 370 mK. The system undergoes a QPT in an applied field H∥c = 4.0±0.1 kOe, confirmed by a softening of the characteristic excitations at Hc. A combined neutron scattering, specific heat, and magnetic susceptibility study reveals a novel non-MF critical scaling of the classical phase transition, belonging to the 2DXY /h4 universality class. In accord with this, the quantum phase transition at Hc exhibits a three-dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic anisotropic nature of the dipolar interaction. Four-fold anisotropy and degeneracy breaking could be due to the "order-by-disorder" phenomena, which could open a gap in dispersion of the magnetic excitations.