Low-temperature properties of the dilute dipolar magnetLiHoxY1−xF4

Abstract

We analyze recent experiments on the dilute rare-earth compound LiHoxY1−xF4 in the context of an effective Ising dipolar model. Using a Monte Carlo method we calculate the low-temperature behavior of the specific heat and linear susceptibility, and compare our results to measurements. In our model the susceptibility follows a Curie-Weiss law at high temperature, χ ∼ 1/(T − Tcw), with a Curie-Weiss temperature that scales with dilution, Tcw ∼ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, Cmax(T ) ∼ x, in disagreement with recent experiments. Experimental studies do not reach a consensus on the functional form of these quantities, and in particular we do not see reported scalings of the form χ ∼ T −0.75 and χ ∼ exp (−T /T0). Furthermore we calculate the ground state magnetization as a function of dilution, and re-examine the phase diagram around the critical dilution xc = 0.24 ± 0.03. We find that the spin glass susceptibility for the Ising model does not diverge below xc, while recent experiments give strong evidence for a stable spin-glass phase in LiHo0.167Y0.833F4.

Nonmonotonic residual entropy in diluted spin ice: A comparison between Monte Carlo simulations of diluted dipolar spin ice models and experimental results

“…We note in passing that such an approximation has recently been shown to describe quantitatively quite well the variation of the critical ferromagnetic temperature in Ho 3+ substituted by Y 3+ in LiHo 1−x Y x F 4 . 51,52 In practice, the microscopic J ν 's and D in Eq. …”

“…Presently, we do not have a good suggestion as to what may cause such a sudden (in terms of "just" going from x = 1.7 to x = 1.8) and large discrepancy between experiments and Monte Carlo data. A possible mechanism includes the development of a dipolar Ising spin glass state [38][39][40][41]43 inhibiting thermal equilibrium in the experiments. However, this should not be at play at temperatures as high as 1 K as we would naively expect the thermodynamic spin glass transition temperature to be below 200 mK or so for those two concentrations.…”

“…The study of site-diluted spin ices may thus offer a unique opportunity to investigate quantitatively the effect of random disorder in a strongly correlated (classical) spin liquid state. Such an endeavor should be achievable by noting, for example, the quantitative progress made in describing the thermodynamic properties of the LiHo 1−x Y x F 4 dipolar Ising system, both in the diluted-ferromagnetic regime 39,40 as well as the dipolar spin glass regime. 38 A neutron scattering study shows no sign of long-range ordering in Ho 2−x Y x Ti 2 O 7 down to 30 mK for x = 0.3 and x = 1.0.…”

“…27 The close ionic radius of Y 3+ with that of Dy 3+ and Ho 3+ allow for a substitution causing negligible local lattice deformation and strain, 6 similarly to the situation in the LiHo 1−x Y x F 4 dipolar Ising ferromagnet. [38][39][40][41][42][43] In such a situation, the substitution of Dy 3+ /Ho 3+ by Y 3+ in Dy 2−x Y x Ti 2 O 7 and Ho 2−x Y x Ti 2 O 7 can thus be viewed as the mere removal of the Dy 3+ /Ho 3+ magnetic species. The study of site-diluted spin ices may thus offer a unique opportunity to investigate quantitatively the effect of random disorder in a strongly correlated (classical) spin liquid state.…”

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

“…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].…”