Single-ion anisotropy and magnetic field response in spin ice materials Ho$_{2}$Ti$_{2}$O$_{7}$ and Dy$_{2}$Ti$_{2}$O$_{7}$

TL;DR

This paper investigates the single-ion dynamics and magnetic responses of Ho$_{2}$Ti$_{2}$O$_{7}$ and Dy$_{2}$Ti$_{2}$O$_{7}$ spin ice materials, emphasizing quantum tunnelling effects, anisotropy, and the influence of transverse magnetic fields.

Contribution

It provides a detailed analysis beyond the simplified spin-1/2 model by incorporating the full crystal-field Hamiltonian, revealing differences in quantum tunnelling behavior between Kramers and non-Kramers ions.

Findings

Transverse field effects are more pronounced in Ho$_{2}$Ti$_{2}$O$_{7}$ than in Dy$_{2}$Ti$_{2}$O$_{7}$.

Energy splittings are consistent with experimental time scales.

Anisotropic magnetic response can be observed within specific experimental conditions.

Abstract

Motivated by its role as a central pillar of current theories of 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 they interact with. This effective field has a transverse component with respect to the local easy-axis of the crystal electric field, which can induce quantum tunnelling. We go beyond the projective spin-1/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers vs non-Kramers nature, as well as the symmetries of the crystal-field Hamiltonian, result in different perturbative behaviour at small fields ($\lesssim 1$ T), with transverse field effects being more pronounced in Ho$_{2}$Ti$_{2}$O$_{7}$ than in Dy$_{2}$Ti$_{2}$O$_{7}$. 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 yet accessible window of experimental parameters where the anisotropic response can be observed.