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 subject of controversy and ongoing scrutiny, e.g., in $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$, 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 $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ 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.

arXiv comment6 pages, 3 figures, 2 tables

References in corpus (34)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Entangled Quantum States of Magnetic Dipoles
• Critical Behavior of the Three-Dimensional Ising Spin Glass
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Nuclear spin driven quantum relaxation in LiY_0.998Ho_0.002F_4
• Tunable Quantum Tunneling of Magnetic Domain Walls
• Quantum Phase Transition of a Magnet in a Spin Bath
• Estimate of the Cutoff Errors in the Ewald Summation for Dipolar Systems
• Coherent Spin Oscillations in a Disordered Magnet
• Induced Random Fields in the LiHo${}_x$Y${}_{1-x}$F${}_4$ Quantum Ising Magnet in a Transverse Magnetic Field
• Quantum and Classical Glass Transitions in $LiH{o}_x{Y}_{1-x}{F}_4$
• Ferromagnet in a continuously tuneable random field
• $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ as a random field Ising ferromagnet
• Observation of Spin Glass Dynamics in Dilute LiHo${}_x$Y${}_{1-x}$F${}_4$
• Significance of the Hyperfine Interactions in the Phase Diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses
• The low-$T$ phase diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Quantum spin glass and the dipolar interaction
• The quantum dynamics of atomic magnets, co-tunneling and dipolar-biased tunneling
• Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo_xY_{1-x}F_4
• Spin Glass Transition at Nonzero Temperature in a Disordered Dipolar Ising System: The Case of LiHoxY{1-x}F4
• Ferroelectric and Dipolar Glass Phases of Non-Crystalline Systems
• Phase diagram of the dilute magnet LiHo_xY_{1-x}F_4
• Absence of Dipole Glass Transition for Randomly Dilute Classical Ising Dipoles
• Low-temperature properties of the dilute dipolar magnet LiHo_xY_(1-x)F_4
• Using thermal boundary conditions to engineer the quantum state of a bulk magnet
• Experimental Phase Diagram and Dynamics of a Dilute Dipolar-Coupled Ising System
• The ferromagnetic transition and domain structure in LiHoF4
• Replica theory for Levy spin glasses
• Novel disordering mechanism in ferromagnetic systems with competing interactions
• Quantum Projection in an Ising Spin Liquid
• Correlated random fields in dielectric and spin glasses
• Critical behavior and universality in Levy spin glasses
• Direct Measurement of Random Fields in the $LiH{o}_x{Y}_{1-x}{F}_4$ Crystal

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