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

References in corpus (4)

• Ferromagnet in a continuously tuneable random field
• 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
• Effective Spin-1/2 Description of Transverse-Field-Induced Random Fields in Dipolar Spin Glasses with Strong Single-Ion Anisotropy

Cited by in corpus (1)

• Low-temperature properties of the dilute dipolar magnet LiHo_xY_(1-x)F_4