The low-$T$ phase diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$

Abstract

The $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ compound is widely considered to be the archetypal dipolar Quantum Ising system, with longitudinal dipolar interactions $V_{ij}^{zz}$ between $\mathrm{Ho}$ spins $\{i,j\}$ competing with transverse field-induced tunneling, to give a T=0 quantum phase transition. By varying the $\mathrm{Ho}$ concentration x, the typical strength $V_0$ of $V_{ij}^{zz}$ can be varied over many orders of magnitude; and so can the transverse field $H_{\perp }$. A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, and valid at low and intermediate temperatures. For any such dipolar Quantum Ising system, the hyperfine interaction will dominate the physics at low temperatures, even if its strength $A_0<V_0$: one must therefore go beyond an electronic transverse field Quantum Ising model. We derive the full phase diagram of this system, including all nuclear levels, as a function of transverse field $H_{\perp }$, temperature $T$, and dipole concentration x. For $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ we predict a re-entrant critical field as a function of x. We also predict the phase diagram for x$=0.045$, and the behavior of the system in magnetic resonance and $\mu$SR experiments.

19 pages, 10 figures, predictions regarding magnetic resonance experiments are added, presentation improved

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• Existence of a Thermodynamic Spin-Glass Phase in the Zero-Concentration Limit of Anisotropic Dipolar Systems
• Probing strongly hybrid nuclear-electronic states in a model quantum ferromagnet
• Phase diagram of diluted Ising ferromagnet LiHo${}_x$Y${}_{1-x}$F${}_4$
• Random-field-induced disordering mechanism in a disordered ferromagnet: Between the Imry-Ma and the standard disordering mechanism
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• LiHoF4 as a spin-half non-standard quantum Ising system
• Quantum dynamics in strongly driven random dipolar magnets
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Magnetostatic modes and criticality in quantum-Ising materials
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• The Effect of Intrinsic Quantum Fluctuations on the Phase Diagram of Anisotropic Dipolar Magnets
• Off-Diagonal dipolar interactions in the mixed Ising--XY magnet $LiH{o}_{x}E{r}_{1-x}{F}_4$