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

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 the subject of controversy and ongoing scrutiny, e.g., in LiHoxY1−xF4 , 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 LiHoxY1−xF4 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, 0.1%, and including Ho+ ion concentrations that 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. The agreement of our results with mean-field theory testifies to the irrelevance of fluctuations in interactions strengths, albeit being strong at small concentrations, to the nature of the low-temperature phase and the functional form of the critical temperature of dilute anisotropic dipolar systems. Deviations from linearity in experimental results at the lowest concentrations are discussed.

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Plain Language Summary

LiHoxY1−xF4 is an archetypal dipolar quantum magnet and, at the same time, one of the most versatile materials to study fascinating phenomena in condensed-matter physics, such as many-body quantum systems and large-spin tunneling. Despite intense scrutinization of the properties of this rare-earth magnet—experimentally, numerically, and theoretically—the nature of its low-temperature phase at small Ho concentrations remains an open question. We investigate the ordering mechanism of anisotropic dipolar systems at small magnetic ion concentrations. We numerically employ a special cluster algorithm tailored to overcome the central obstacle that has hindered progress to date, namely, the enhancement of fluctuations as concentration is reduced, and are able to show that the low-concentration limit is governed by a spin-glass state, hence adding to the versatility of this jack-of-all-trades material.

We use large-scale Monte Carlo simulations that combine parallel tempering Monte Carlo with a special cluster algorithm and show that a spin-glass phase extends to the lowest concentrations accessible numerically: a record-breaking 0.1%. We note that this concentration is 2 orders of magnitude lower than the values investigated by other studies. The critical temperature is linear with Ho concentration for 2 orders of magnitude, demonstrating that the low-temperature phase is stable against fluctuations and shows geometric similarity down to the smallest concentrations, and highlighting the adequacy of mean-field description for the determination of the phase of dilute anisotropic dipolar systems.

These results will serve as a basis for any experiment in anisotropic dipolar systems at low concentrations. By establishing a spin-glass phase down to zero concentration, we also establish the existence of the paramagnetic phase at higher temperatures. Therefore, relatively large experimental estimates for the critical temperature at rather low concentrations may be reinterpreted as a dynamic crossover to a frozen regime, rather than a thermodynamic transition.