Magnetisation process in Er2Ti2O7 and Tb2Ti2O7 at very low temperature

TL;DR

This paper develops a mean field model to explain high field magnetisation in Er2Ti2O7 and Tb2Ti2O7, capturing their distinct ground states and including complex interactions, with implications for understanding pyrochlore spin liquids and antiferromagnets.

Contribution

It introduces a comprehensive mean field model incorporating full crystal field, dipolar, and anisotropic exchange interactions for pyrochlore systems, accounting for their different ground states and symmetry breaking.

Findings

Model accurately predicts high field magnetisation in Er2Ti2O7 and Tb2Ti2O7.

Inclusion of symmetry breaking is essential for Tb2Ti2O7.

Comparison with quantum spin ice model highlights differences in low-temperature behaviour.

Abstract

We present a model which accounts for the high field magnetisation at very low temperature in two pyrochlore frustrated systems, Er2Ti2O7 and Tb2Ti2O7. The two compounds present very different ground states: Er2Ti2O7, which has a planar crystal field anisotropy, is an antiferromagnet with T_N=1.2K, whereas Tb2Ti2O7 is expected to have Ising character and shows no magnetic ordering down to 0.05K, being thus labelled a ``spin liquid''. Our model is a mean field self-consistent calculation involving the 4 rare earth sites of a tetrahedron, the building unit of the pyrochlore lattice. It includes the full crystal field hamiltonian, the infinite range dipolar interaction and anisotropic nearest neighbour exchange described by a 3-component tensor. For Er2Ti2O7, we discuss the equivalence of our treatment of the exchange tensor, taken to be diagonal in a frame linked to a rare earth - rare earth bond, with the pseudo-spin hamiltonian recently developped for Kramers doublets in a pyrochlore lattice. In Tb2Ti2O7, an essential ingredient of our model is a symmetry breaking developping at very low temperature. We compare its prediction for the isothermal magnetisation with that of ``the quantum spin ice'' model.