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

摘要: The ${\rm LiHo_xY_{1-x}F_4}$ compound is widely considered to be the archetypal dipolar Quantum Ising system, with longitudinal interactions $V_{ij}^{zz}$ between Ho}$ spins $\{i,j \}$ competing transverse field-induced tunneling, give a T=0 quantum phase transition. By varying concentration x, typical strength $V_0$ of can varied over many orders magnitude; and so field $H_{\perp}$. A new effective Hamiltonian derived, starting from electronuclear degrees freedom, valid at low intermediate temperatures. For any such hyperfine interaction will dominate physics temperatures, even if its $A_0 < V_0$: one must therefore go beyond an electronic model. We derive full diagram this including all nuclear levels, as function $H_{\perp}$, temperature $T$, dipole x. we predict re-entrant critical also for x$=0.045$, behavior system in magnetic resonance $\mu$SR experiments.