Phase diagram of diluted Ising ferromagnet LiHo$_x$Y$_{1-x}$F$_4$

TL;DR

This study investigates how dilution affects the phase diagram of LiHo$_x$Y$_{1-x}$F$_4$, revealing that thermal transition decreases linearly while the quantum critical point is suppressed faster due to competing interactions.

Contribution

The paper combines neutron scattering and mean-field calculations to quantify deviations in the phase diagram of diluted LiHo$_x$Y$_{1-x}$F$_4$ from theoretical predictions.

Findings

Thermal phase transition decreases linearly with dilution.

Critical transverse field at quantum critical point is suppressed faster than mean-field predicts.

Analysis of deviations aids future theoretical modeling.

Abstract

We present a systematic study of the phase diagram of LiHo$_x$Y$_{1-x}$F$_4$ ($0.25<x<1$) Ising ferromagnets obtained from neutron scattering measurements and mean-field calculations. We show that while the thermal phase transition decreases linearly with dilution, as predicted by mean-field theory, the critical transverse field at the quantum critical point is suppressed much faster. This behavior is related to competition between off-diagonal dipolar coupling and quantum fluctuations that are tuned by doping and applied field, respectively. In this paper, we quantify the deviation of the experimental results from mean-field predictions, with the aim that this analysis can be used in future theoretical efforts towards a quantitative description.