Theory of the Magnetic phase diagram of LiHoF${}_4$

Abstract

The properties of LiHoF${}_4$ are believed to be well described by a long-range dipolar Ising model. We go beyond mean-field theory and calculate the phase diagram of the Ising model in a transverse field using a quantum Monte Carlo method. The relevant Ising degrees of freedom are obtained using a non-perturbative projection onto the low-lying crystal field eigenstates. We explicitly take the domain structure into account, and the strength of the near-neighbor exchange interaction is obtained as a fitting parameter. The on-site hyperfine interaction is approximately taken into account through a renormalization of the transverse applied magnetic field. Finally, we propose a spectroscopy experiment to precisely measure the most important parameter controlling the location of the phase boundary.

15 pages, 8 figures : Minor typos corrected. Refs. 8 and 28 added

References in corpus (3)

• Nuclear spin driven quantum relaxation in LiY_0.998Ho_0.002F_4
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Coherent Spin Oscillations in a Disordered Magnet

Cited by in corpus (58)

• Quantum Phase Transition of a Magnet in a Spin Bath
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit
• 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
• Significance of the Hyperfine Interactions in the Phase Diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Quantum criticality of two-dimensional quantum magnets with long-range interactions
• The low-$T$ phase diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
• Spin Glass Transition at Nonzero Temperature in a Disordered Dipolar Ising System: The Case of LiHoxY{1-x}F4
• Phase diagram of the dilute magnet LiHo_xY_{1-x}F_4
• Quantum Monte Carlo Study of Long-Range Transverse-Field Ising Models on the Triangular Lattice
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• Collective Phenomena in the LiHo_xY_{1-x}F4 Quantum Ising Magnet: Recent Progress and Open Questions
• Neutron spectroscopic study of crystal-field excitations and the effect of the crystal field on dipolar magnetism in Li$R$F${}_4$ ($R$ = Gd, Ho, Er, Tm, and Yb)
• Monte Carlo study of the spin-glass phase of the site-diluted dipolar Ising model
• Specific Heat of the Dilute Ising Magnet LiHo${}_x$Y${}_{1-x}$F${}_4$
• Low-temperature properties of the dilute dipolar magnet LiHo_xY_(1-x)F_4
• Perturbative Quantum Monte Carlo Study of LiHoF4 in a Transverse Magnetic Field
• Probing many-body localization in a disordered quantum magnet
• Emergence of mesoscale quantum phase transitions in a ferromagnet
• Pure and Random-Field Quantum Criticality in the Dipolar Ising Model: Theory of $M{n}_{12}$ acetates
• Field Driven Quantum Criticality in the Spinel Magnet ZnCr${}_2$Se${}_4$
• Faraday rotation echo spectroscopy and detection of quantum fluctuations
• The ferromagnetic transition and domain structure in LiHoF4
• Experimental Phase Diagram and Dynamics of a Dilute Dipolar-Coupled Ising System
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Direct Observation of Collective Electronuclear Modes About a Quantum Critical Point
• LiHoF${}_4$: Cuboidal Demagnetizing Factor in an Ising Ferromagnet
• Novel disordering mechanism in ferromagnetic systems with competing interactions
• Effective Spin-1/2 Description of Transverse-Field-Induced Random Fields in Dipolar Spin Glasses with Strong Single-Ion Anisotropy
• Quantum spin glass in anisotropic dipolar systems
• Theory of magnon-polaritons in quantum Ising materials
• Phase diagram of diluted Ising ferromagnet LiHo${}_x$Y${}_{1-x}$F${}_4$
• Limits to magnetic quantum criticality from nuclear spins
• Phases of anisotropic dipolar antiferromagnets
• Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes
• Edge modes in a frustrated quantum Ising chain
• Precise determination of low energy electronuclear Hamiltonian for LiY${}_{1-x}$Ho${}_x$F${}_4$
• Assessment of the RE(OH)3 Ising-like Magnetic Materials as Possible Candidates for the Study of Transverse-Field-Induced Quantum Phase Transitions
• Magnetic domain dynamics in an insulating quantum ferromagnet
• Dynamical Quantum Phase Transitions in presence of a spin bath
• Direct Measurement of Random Fields in the $LiH{o}_x{Y}_{1-x}{F}_4$ Crystal
• Absence of Domain Wall Roughening in a Transverse Field Ising Model with Long-Range Interactions
• Nonlinear susceptibility of a quantum spin glass under uniform transverse and random longitudinal magnetic fields
• A Gallery of Soft Modes: Theory and Experiment at a Ferromagnetic Quantum Phase Transition
• LiHoF4 as a spin-half non-standard quantum Ising system
• Dipolar Ising Model: Phases, Growth Laws and Universality
• Specific heat and non-linear susceptibility in spin glasses with random fields
• Hierarchy of correlations for the Ising model in the Majorana representation
• Quantum dynamics in strongly driven random dipolar magnets
• Magnetostatic modes and criticality in quantum-Ising materials
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results
• Off-Diagonal dipolar interactions in the mixed Ising--XY magnet $LiH{o}_{x}E{r}_{1-x}{F}_4$
• The Effect of Intrinsic Quantum Fluctuations on the Phase Diagram of Anisotropic Dipolar Magnets
• Perturbative approach to quantum tunneling and quantum interferences in spin clusters