Ryan McKenzie, Iowa State University and Ame National Laboratory

The quantum Ising model is, perhaps, the simplest possible model exhibiting quantum critical behaviour. In a transverse field it exhibits a quantum phase transition between an ordered magnetic state and a paramagnetic state. Associated with the phase transition is a soft mode, which has recently been measured in the archetypal quantum Ising magnet LiHoF4, in which the dominant coupling between the spins is dipolar. In any real material, one must address additional features such as hyperfine interactions, and demagnetization field effects. Here we address the domain structure and demagnetization fields present in non-ellipsoidal samples of LiHoF4. We show that the soft mode governing criticality in the system is not a uniform (Kittel) mode, but rather an inhomogeneous (magnetostatic/Walker) mode, the effect of which is to cancel the demagnetization fields stemming from the sample boundary. We provide experimental evidence supporting this claim.