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

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