Is LiHoF4 a Quantum Magnet? Moshe Schechter UBC Philip Stamp Bitko, Rosenbaum, Aeppli PRL 77, 940 (1996) Wu, Bitko, Rosenbaum, Aeppli PRL 71, 1919 (1993) LiHoxY1-xF4

Outline Low energy effective Hamiltonian 3 energy scales, J,A,Δ Ht renormalizes interaction, classical Ising Transverse hyperfine interaction restores quantum Ising model at high Ht

Transverse Field Ising Model Mean Field Classical phase transition Fluctuations lower energy of unpolarized state Quantum Phase transition

Ho atom in LiHoF Crystal 4 J=8, Ground state doublet, <Jz> = 5.4 Neglecting h.f. interactions: transverse field Ising model, with Hyperfine interaction is important! Ground state splits to 8 equidistant states, I=-7/2….7/2 Effective H: -7/2 7/2 -7/2 7/2

Dipolar smaller than hyperfine Eigenstate: Ground state polarized: Map to classical Ising - renormalized spin! 2 energy scales: PM FM

Dipolar larger than hyperfine Or T=0: no phase transition! PM FM

Transverse hyperfine: Quantum transition flips nuclear spin, splitting of , High order perturbation – small for Ht<Δ! 7/2 -7/2 -7/2 7/2

Conclusions 3 energy scales: J,A,Δ. LiHoF4 of the same order. Longitudinal hf  Ht<Δ renormalizes spins. Can change J continuously. Ωc>Tc, since T~J, Ω~Δ. Ht≈Δ  Quantum behavior due to transverse h.f. Transverse field Ising model, BUT: J(Ht,A), Ω(A,Δ,Ht). Applicable also to spin glass state. Significant effect on the dynamics

Diluted systems Dilution introduces disorder and frustration, therefore glass J<<A limit is fulfilled, classical up to H_t=min{A,~0.1Delta} Corresponds to T=