Perturbative Quantum Monte Carlo Study of LiHoF4 in a Transverse Magnetic Field

Abstract

P.B. Chakraborty {\it et al.}, Phys. Rev. B {\bf 70}, 144411 (2004)) study of the LiHoF${}_4$ Ising magnetic material in an external transverse magnetic field $B_x$ show a discrepancy with the experimental results, even for small $B_x$ where quantum fluctuations are small. This discrepancy persists asymptotically close to the classical ferromagnet to paramagnet phase transition. In this paper, we numerically reinvestigate the temperature $T$, versus transverse field phase diagram of LiHoF${}_4$ in the regime of weak $B_x$. In this regime, starting from an effective low-energy spin-1/2 description of LiHoF${}_4$, we apply a cumulant expansion to derive an effective temperature-dependent classical Hamiltonian that incorporates perturbatively the small quantum fluctuations in the vicinity of the classical phase transition at $B_x=0$. Via this effective classical Hamiltonian, we study the $B_x-T$ phase diagram via classical Monte Carlo simulations. In particular, we investigate the influence on the phase diagram of various effects that may be at the source of the discrepancy between the previous QMC results and the experimental ones. For example, we consider two different ways of handling the long-range dipole-dipole interactions and explore how the $B_x-T$ phase diagram is modified when using different microscopic crystal field Hamiltonians. The main conclusion of our work is that we fully reproduce the previous QMC results at small $B_x$. Unfortunately, none of the modifications to the microscopic Hamiltonian that we explore are able to provide a $B_x-T$ phase diagram compatible with the experiments in the small semi-classical $B_x$ regime.

arXiv comment22 pages, 14 figures

References in corpus (23)

• Continuous Quantum Phase Transitions
• Entangled Quantum States of Magnetic Dipoles
• Critical Behavior of the Three-Dimensional Ising Spin Glass
• Thermodynamic Properties of the Dipolar Spin Ice Model
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Griffiths Singularities in the Disordered Phase of a Quantum Ising Spin Glass
• Quantum Phase Transition of a Magnet in a Spin Bath
• Quantum Griffiths Singularities in the Transverse-Field Ising Spin Glass
• Coherent Spin Oscillations in a Disordered Magnet
• Theory of the Magnetic phase diagram of LiHoF${}_4$
• Induced Random Fields in the LiHo${}_x$Y${}_{1-x}$F${}_4$ Quantum Ising Magnet in a Transverse Magnetic Field
• Ferromagnet in a continuously tuneable random field
• Quantum and Classical Glass Transitions in $LiH{o}_x{Y}_{1-x}{F}_4$
• Observation of Spin Glass Dynamics in Dilute LiHo${}_x$Y${}_{1-x}$F${}_4$
• Significance of the Hyperfine Interactions in the Phase Diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Quantum spin glass and the dipolar interaction
• Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo_xY_{1-x}F_4
• 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
• 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

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• Spin Glass Transition at Nonzero Temperature in a Disordered Dipolar Ising System: The Case of LiHoxY{1-x}F4
• 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)
• Emergence of mesoscale quantum phase transitions in a ferromagnet
• The ferromagnetic transition and domain structure in LiHoF4
• Experimental Phase Diagram and Dynamics of a Dilute Dipolar-Coupled Ising System
• Theory of magnon-polaritons in quantum Ising materials
• Limits to magnetic quantum criticality from nuclear spins
• Phase diagram of diluted Ising ferromagnet LiHo${}_x$Y${}_{1-x}$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
• A Gallery of Soft Modes: Theory and Experiment at a Ferromagnetic Quantum Phase Transition
• LiHoF4 as a spin-half non-standard quantum Ising system
• Quantum dynamics in strongly driven random dipolar magnets
• Cavity-Magnon-Polariton spectroscopy of strongly hybridized electro-nuclear spin excitations in LiHoF4
• Disorder Line and Incommensurate Floating Phases in the Quantum Ising Model on an Anisotropic Triangular Lattice
• Magnetostatic modes and criticality in quantum-Ising materials
• Thermodynamics of a Quantum Ising system coupled to a spin bath: Zero Temperature Results
• The Effect of Intrinsic Quantum Fluctuations on the Phase Diagram of Anisotropic Dipolar Magnets
• Off-Diagonal dipolar interactions in the mixed Ising--XY magnet $LiH{o}_{x}E{r}_{1-x}{F}_4$
• Perturbative approach to quantum tunneling and quantum interferences in spin clusters