Magnetostatic modes and criticality in quantum Ising magnets

We analyze modes in a dipole-dipole coupled quantum Ising material, taking into consideration shape effects present in any real magnet. We find that the soft mode governing quantum criticality in a nonellipsoidal sample is a magnetostatic mode that nulls out the effects of dynamic-demagnetization-field fluctuations. The demagnetization field is analyzed from a microscopic perspective. Two additional modes are calculated relying solely on knowledge of the demagnetization factor of the sample, one of which has lower energy than the soft mode governing quantum criticality in the bulk of the magnet. Experimental evidence for these theoretical results is provided by analysis of electronuclear modes in LiHoF4, an archetypal quantum Ising material.