Single-ion anisotropy and magnetic field response in the spin-ice materials Ho2Ti2O7 and Dy2Ti2O7

Abstract

Motivated by its role as a central pillar of current theories of the dynamics of spin ice in and out of equilibrium, we study the single-ion dynamics of the magnetic rare-earth ions in their local environments, subject to the effective fields set up by the magnetic moments with which they interact. This effective field has a transverse component with respect to the local easy axis of the crystal electric field, which can induce quantum tunneling. We go beyond the projective spin-1/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers versus non-Kramers nature, as well as the symmetries of the crystal-field Hamiltonian, result in different perturbative behavior at small fields (≲1T), with transverse field effects being more pronounced in Ho2Ti2O7 than in Dy2Ti2O7. Remarkably, the energy splitting range we find is consistent with time scales extracted from experiments. We also present a study of the static magnetic response, which highlights the anisotropy of the system in the form of an off-diagonal g tensor, and we investigate the effects of thermal fluctuations in the temperature regime of relevance to experiments. We show that there is a narrow but accessible window of experimental parameters where the anisotropic response can be observed.