Theory of the magnetic phase diagram ofLiHoF4

Abstract

The properties of LiHoF4 are believed to be well described by a long-range dipolar Ising model. We go beyond mean-field theory and calculate the phase diagram of the Ising model in a transverse field using a quantum Monte Carlo method. The relevant Ising degrees of freedom are obtained using a non-perturbative projection onto the low-lying crystal field eigenstates. We explicitly take the domain structure into account, and the strength of the near-neighbor exchange interaction is obtained as a fitting parameter. The on-site hyperfine interaction is approximately taken into account through a renormalization of the transverse applied magnetic field. Finally, we propose a spectroscopy experiment to precisely measure the most important parameter controlling the location of the phase boundary.

Collective Phenomena in the LiHoxY1−xF4Quantum Ising Magnet: Recent Progress and Open Questions

“…The ground state doublet is split by B x , with an energy ∆(B x ) between the two states. Meanwhile, the excited |ψ e singlet state remains more than 10 K above the split doublet [20,21]. Consequently, the J i operators can be projected onto the two-dimensional subspace of the two lowest energy eigenstates via the relationship J µ i = C µ0 + ν=x,y,z C µν (B x )σ ν i , hence providing a description in terms of effective pseudospin-1/2 operators [20,21].…”

“…An early Monte Carlo simulation using free boundary conditions for rather small system sizes found a critical temperature of 1.89 K [23]. To obtain better accuracy with long range dipolar interactions, there are two standard approaches that can be implemented: Ewald summation [19,21,24,25,26,27] and cavity methods [20,28]. An early Monte Carlo simulation using the Ewald summation method to a dipolar Ising ferromagnet on a body-centered lattice was carried out by Xu et al [24,25].…”

“…Also, for thick samples, a branched pattern is predicted in the domain structure for [3,5]. The minimal microscopic Hamiltonian in the presence of a transverse magnetic field B = B xx can be written as [20]:…”

“…Consequently, the J i operators can be projected onto the two-dimensional subspace of the two lowest energy eigenstates via the relationship J µ i = C µ0 + ν=x,y,z C µν (B x )σ ν i , hence providing a description in terms of effective pseudospin-1/2 operators [20,21]. The strongest effective interaction is ∝ (C zz ) 2 L zz ij σ z i σ z j and, to an accuracy of a few percent [20,21], the effective model can be written (up to a field dependent constant) as…”

An ultra-low temperature scanning Hall probe microscope for magnetic imaging below 40 mK

“…12 One aspect of LiHoF 4 which makes it such an interesting material is remarkably well defined and relatively simple microscopic Hamiltonian. 13,14 A recent theme of investigation is the effect of transverse magnetic field on the hardness of this ferromagnet, observed via bulk magnetization measurements taken at 100 mK. 15 A logical complement would be therefore to directly image how the domain structure is modified during this process.…”