1. 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

2. 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

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

4. Ho atom in LiHoF Crystal4
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

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

6. Dipolar larger than hyperfineOr
T=0: no phase transition! PM FM

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

8. 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

9. 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=