Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems

TL;DR

This study uses large-scale Monte Carlo simulations to demonstrate that dilute dipolar Ising systems, like LiHo_xY_{1-x}F_4, exhibit a spin-glass phase even at extremely low concentrations, with the critical temperature decreasing linearly with concentration.

Contribution

It provides numerical evidence that a spin-glass phase persists in dilute dipolar systems down to zero concentration, supporting mean field predictions.

Findings

Spin-glass phase exists down to 0.1% concentration.

Critical temperature decreases linearly with concentration.

Results align with mean field theory predictions.

Abstract

The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin-glasses are subject of controversy and ongoing scrutiny, e.g., in ${{\rm LiHo_xY_{1-x}F_4}}$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration or not. We study an effective model of ${{\rm LiHo_xY_{1-x}F_4}}$ using large-scale Monte Carlo simulations that combine parallel tempering with a special cluster algorithm tailored to overcome the numerical difficulties that occur at extreme dilutions. We find a paramagnetic to spin-glass phase transition for all Ho ion concentrations down to the smallest concentration numerically accessible of 0.1%, and including Ho ion concentrations which coincide with those studied experimentally up to 16.7%. Our results suggest that randomly-diluted dipolar Ising systems have a spin-glass phase in the limit of vanishing dipole concentration, with a critical temperature vanishing linearly with concentration, in agreement with mean field theory.