The low-$T$ phase diagram of ${\rm LiHo_xY_{1-x}F_4}$

Details The low-$T$ phase diagram of ${\rm LiHo_xY_{1-x}F_4}$ The low-$T$ phase diagram of ${\rm LiHo_xY_{1-x}F_4}$

2008-01-18

arxiv.org/abs/0801.2889v2

Phys. Rev. B 78, 054438 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

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

Scientific paper

10.1103/PhysRevB.78.054438

The ${\rm LiHo_xY_{1-x}F_4}$ compound is widely considered to be the archetypal dipolar Quantum Ising system, with longitudinal dipolar interactions $V_{ij}^{zz}$ between ${\rm Ho}$ spins $\{i,j \}$ competing with transverse field-induced tunneling, to give a T=0 quantum phase transition. By varying the ${\rm Ho}$ 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 ${\rm LiHo_xY_{1-x}F_4}$ 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.

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