Field evolution of the magnetic structures in Er$_2$Ti$_2$O$_7$ through the critical point

TL;DR

This study investigates the evolution of magnetic structures in Er$_2$Ti$_2$O$_7$ under an external magnetic field, revealing how moments align at the critical point and demonstrating the importance of anisotropic exchange interactions.

Contribution

The paper provides a detailed neutron diffraction analysis of Er$_2$Ti$_2$O$_7$ across the quantum critical point and shows that anisotropic exchange models accurately describe the magnetic behavior.

Findings

All Er moments align along the field at the critical point.

Anisotropic exchange tensor reproduces experimental data well.

Isotropic exchange does not match the observed moment variations.

Abstract

We have measured neutron diffraction patterns in a single crystal sample of the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase (T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the [110] direction. We determine all the characteristics of the magnetic structure throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er moments align along the field at $H_c$ and their values reach a minimum. Using a four-sublattice self-consistent calculation, we show that the evolution of the magnetic structure and the value of the critical field are rather well reproduced using the same anisotropic exchange tensor as that accounting for the local paramagnetic susceptibility. In contrast, an isotropic exchange tensor does not match the moment variations through the critical point. The model also accounts semi-quantitatively for other experimental data previously measured, such as the field dependence of the heat capacity, energy of the dispersionless inelastic modes and transition temperature.