Magnetic dilution and domain selection in the XY pyrochlore antiferromagnet Er$_{2}$Ti$_2$O$_7$

TL;DR

This study investigates how magnetic dilution affects the magnetic domain structure of Er$_2$Ti$_2$O$_7$, revealing that dilution destabilizes the pure $2$ state and leads to a mosaic of $2$ and $3$ domains, challenging previous robustness assumptions.

Contribution

It provides experimental evidence that magnetic vacancies destabilize the $
e2$ state and induce a mixed domain state, contrasting with prior theories of robustness to disorder.

Findings

$
e2$ domain selection vanishes with 10-20% Y substitution.

The ground state becomes a mosaic of $
e2$ and $
e3$ domains.

Destabilization occurs well below the percolation threshold.

Abstract

Below $T_N = 1.1$K, the XY pyrochlore Er$_2$Ti$_2$O$_7$ orders into a $k=0$ non-collinear, antiferromagnetic structure referred to as the $\psi_2$ state. The magnetic order in Er$_2$Ti$_2$O$_7$ is known to obey conventional three dimensional (3D) percolation in the presence of magnetic dilution, and in that sense is robust to disorder. Recently, however, two theoretical studies have predicted that the $\psi_2$ structure should be unstable to the formation of a related $\psi_3$ magnetic structure in the presence of magnetic vacancies. To investigate these theories, we have carried out systematic elastic and inelastic neutron scattering studies of three single crystals of Er$_{2-x}$Y$_x$Ti$_2$O$_7$ with $x=0$ (pure), 0.2 (10$\%$-Y) and 0.4 (20$\%$-Y), where magnetic Er$^{3+}$ is substituted by non-magnetic Y$^{3+}$. We find that the $\psi_2$ ground state of pure Er$_2$Ti$_2$O$_7$ is significantly affected by magnetic dilution. The characteristic domain selection associated with the $\psi_2$ state, and the corresponding energy gap separating $\psi_2$ from $\psi_3$, vanish for Y$^{3+}$ substitutions between 10$\%$-Y and 20$\%$-Y, far removed from the 3D percolation threshold of $\sim$60$\%$-Y. The resulting ground state for Er$_2$Ti$_2$O$_7$ with magnetic dilutions from 20$\%$-Y up to the percolation threshold is naturally interpreted as a frozen mosaic of $\psi_2$ and $\psi_3$ domains.