Phase diagram of the dilute magnetLiHoxY1−xF4

Abstract

We study the effective long-range Ising dipole model with a local exchange interaction appropriate for the dilute magnetic compound LiHoxY1−xF4. Our calculations yield a value of 0.12 K for the nearest neighbor exchange interaction. Using a Monte Carlo method we calculate the phase boundary Tc(x) between the ferromagnetic and paramagnetic phases. We demonstrate that the experimentally observed linear decrease in Tc with dilution is not the simple mean-field result, but a combination of the effects of fluctuations, the exchange interaction and the hyperfine coupling. Furthermore, we find a critical dilution xc = 0.21(2), below which there is no ordering. In agreement with recent Monte Carlo simulations on a similar model, we find no evidence of the experimentally observed freezing of the glassy state in our calculation. We apply the theory of Stephen and Aharony to LiHoxY1−xF4 and find that the theory does predict a finite-temperature freezing of the spin glass. Reasons for the discrepancies are discussed. The rare-earth compound LiHo x Y 1−x F 4 has been widely used as a model magnet displaying a wide range of phenomena. At T c =1.53 K the predominant longrange dipolar interaction causes a second order classical phase transition to a ferromagnetic state [1]. By applying a transverse magnetic field the order can be destroyed in a T=0 quantum phase transition at about 4.9 T[2]. Positional disorder can be introduced by substituting the magnetic Ho 3+ ions with non-magnetic Y 3+ ions. The disorder has been shown to cause a transition to glassy behavior at high dilution [3].A main attraction of LiHo x Y 1−x F 4 is that the microscopic model is well-known [3,4]. The ground state of the Ho 3+ ion in the crystal field is an Ising doublet, with the first excited state 11 K above the ground state. At the temperature range we consider here (T < 1.5 K) LiHoF 4 should be a very good realization of a dipolar Ising modelwhere J is the dipolar coupling constant, J ex the nearestneighbor exchange constant, r ij the interspin distance and z ij the interspin distance along the Ising axis. The summation is done over all Ho 3+ ions, which form a tetragonal Bravais lattice with four ions per unit cell. When diluted, a fraction x of the sites are occupied by non-magnetic Yttrium and not included in the above sum. The size of the unit cell is (1, 1, 2.077) in units of a = 5.175Å. If we express the interspin distance in units of a, then the dipolar coupling constant J = (gµ B /2) 2 /a 3 = 0.214K [4]. The exchange coupling J ex has been experimentally determined to about half of the nearest-neighbor dipolar coupling [5]. In our calculation we have neglected the next nearest neighbor exchange interaction, which was found to be about 5% of the nearestneighbor dipolar coupling [5]. In addition, we have left out the hyperfine coupling between the nuclear and electronic spins as well as the random fields generated by the breaking of crystal symmetries due to the dilution. The effects of these terms on our results will be discussed.

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.…”

Low-temperature properties of the dilute dipolar magnetLiHoxY1−xF4

“…where we have used a dipolar coupling constant J = 0.214 K and a nearest-neighbor (nn) exchange coupling J ex = 0.12 K. 5 The interspin distance is r ij , with a component z ij along the Ising axis. The magnetic Ho 3+ ions sit on a tetragonal lattice with four ions per unit cell.…”