Induced Random Fields in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>LiHo</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">Y</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">F</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>Quantum Ising Magnet in a Transverse Magnetic Field

2008

Phys. Rev. B

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.

Section: Discussionmentioning

confidence: 99%

“…14,15,16,17 Yet a non-perturabative calculation beyond mean-field of several fundamental properties such as the specific heat and linear susceptibility is lacking even for the first-order model described by Eq. (1).…”

Section: Introductionmentioning

confidence: 99%

Low-temperature properties of the dilute dipolar magnetLiHoxY1−xF4

Biltmo

2008

Phys. Rev. B

“…Indeed, the experimental procedure for creating such a random field Ising system is convoluted and typically considers a diluted Ising antiferromagnet in a uniform longitudinal field B z [66,67]. Analytical [33,62,63,64,65] and numerical [62,63,64] studies have shown, rather convincingly, that the presence of B x -induced random fields h z i can explain the two aforementioned puzzles observed in LiHo x Y 1−x F 4 in nonzero B x , in both the diluted FM regime and in the SG regime. In particular, the B x -induced random fields h z i eliminate the divergence of the nonlinear susceptibility χ 3 in the spin glass regime x 0.25 [32,62,64].…”

Section: Transverse Field and Random Field Effects In Lihomentioning

confidence: 99%

“…(2) when the occupation factor i = 1 [62,63], the transverse field B x induces not only quantum fluctuations, but also random fields [43,44,47], h z i , that couple linearly to theẑ component of σ i [32,33,62,63,64,65]. There are two key physical ingredients responsible for these random fields.…”

Section: Transverse Field and Random Field Effects In Lihomentioning

confidence: 99%

Collective Phenomena in the LiHo_xY_1−xF₄Quantum Ising Magnet: Recent Progress and Open Questions

Gingras

2011

J. Phys.: Conf. Ser.

Abstract. In LiHo x Y 1−x F 4 , the magnetic Holmium Ho 3+ ions behave as effective Ising spins that can point parallel or antiparallel to the crystalline c-axis. The predominant inter-Ho 3+ interaction is dipolar, while the Y 3+ ions are non-magnetic. The application of a magnetic field B x transverse to the c-axis Ising direction leads to quantum spin-flip fluctuations, making this material a rare physical realization of the celebrated transverse field Ising model. The problems of classical and transverse-field-induced quantum phase transitions in LiHo x Y 1−x F 4 in the dipolar ferromagnetic (x = 1), diluted ferromagnetic (0.25 x < 1) and highly diluted x 0.25 dipolar spin glass regimes have attracted much experimental and theoretical interest over the past twenty-five years. Two questions have received particular attention: (i) is there an antiglass (quantum disordered) phase at low Ho 3+ concentration and (ii) what is the mechanism responsible for the fast B x -induced destruction of the ferromagnetic (0.25 x < 1) and spin glass (x 0.25) phases? This paper reviews some of the recent theoretical and experimental progress in our understanding of the collective phenomena at play in LiHo x Y 1−x F 4 , in both zero and nonzero B x .

“…In particular, it should not be a cause of the spin-glass freezing. Another effect omitted in our simulation is the generation of random magnetic fields due to the dilution, which breaks the crystalline symmetry [20,21,22]. However, the effect of this term should be to increase fluctuations and lower the critical temperature for both the ferromagnetic and the spin-glass phase.…”

mentioning

confidence: 99%

Phase diagram of the dilute magnetLiHoxY1−xF4

Biltmo

2007

Phys. Rev. B

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.