Effective-medium theory and inelastic neutron scattering are used to study the magnetic excitations in the Ising ferromagnet LiHoF4 near its magnetic-field-induced quantum phase transition (QPT). As expected, the dominant mode softens at the QPT, but reaches a finite, rather than vanishing, limit due to the hyperfine interaction. The experimental phase diagram and excitation spectra are well described by an effective-medium theory to first order in the 1/z expansion. There are some differences between theory and experiments, which may be due to domain walls, their dynamics and shape effects, and to magnetoelastic couplings.
Frédéric Mila, Bruce Normand, Philippe Heller, Nicolas Laflorencie