Derivation of the low- T phase diagram of LiHoxY1-xF4 : A dipolar quantum Ising magnet
Abstract
The LiHoxY1-xF4 compound is widely considered to be the archetypal dipolar quantum Ising system, with longitudinal dipolar interactions Vijzz between Ho spins {i,j} competing with transverse field induced tunneling, to give a T=0 quantum phase transition. By varying the Ho concentration x , the typical strength V0 of Vijzz can be varied over many orders of magnitude, and so can the transverse field H⊥ . A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, which is 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 A0<V0 : 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⊥ , temperature T , and dipole concentration x . For LiHoxY1-xF4 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 muon-spin-relaxation experiments.
- Publication:
-
Physical Review B
- Pub Date:
- August 2008
- DOI:
- 10.1103/PhysRevB.78.054438
- arXiv:
- arXiv:0801.2889
- Bibcode:
- 2008PhRvB..78e4438S
- Keywords:
-
- 75.50.Lk;
- 75.10.Nr;
- 75.10.Jm;
- 75.30.Gw;
- Spin glasses and other random magnets;
- Spin-glass and other random models;
- Quantized spin models;
- Magnetic anisotropy;
- Condensed Matter - Strongly Correlated Electrons;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 19 pages, 10 figures, predictions regarding magnetic resonance experiments are added, presentation improved