Intermediate magnetisation state and competing orders in Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$

TL;DR

This study investigates the magnetic behavior of Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ spin-ice materials, proposing an effective Hamiltonian that explains an intermediate polarisation phase and highlights the role of lattice distortions in frustration.

Contribution

The paper develops a new effective Hamiltonian based on experimental susceptibility data and theoretical analysis, revealing an intermediate polarisation phase in spin-ice compounds.

Findings

Effective Hamiltonian reproduces experimental susceptibility results.

Identification of an intermediate polarisation phase.

Lattice distortions may preserve frustration effects.

Abstract

Among the frustrated magnetic materials, spin-ice stands out as a particularly interesting system. Residual entropy, freezing and glassiness, Kasteleyn transitions and fractionalisation of excitations in three dimensions all stem from a simple classical Hamiltonian. But is the usual spin-ice Hamiltonian a correct description of the experimental systems? Here we address this issue by measuring magnetic susceptibility in the two most studied spin-ice compounds, Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, using a vector magnet. Using these results, and guided by a theoretical analysis of possible distortions to the pyrochlore lattice, we construct an effective Hamiltonian and explore it using Monte Carlo simulations. We show how this Hamiltonian reproduces the experimental results, including the formation of a phase of intermediate polarisation, and gives important information about the possible ground-state of real spin-ice systems. Our work suggests an unusual situation in which distortions might contribute to the preservation rather than relief of the effects of frustration.