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.
We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of "semi-frustrated" systems (Heisenberg models with ferromagnetic couplings Jz(r) < 0 along the z-axis and antiferromagnetic couplings Jxy(r) = −Jz(r) in the xyplane, for arbitrary distances r) the sign problem present for algorithms operating in the z-basis can be solved within a recent "operator-loop" formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of exp(−βH) to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated ("merons") and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. 83, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.
7 and show that it decays with a stretched exponential followed by a very slow long-time tail. In a Monte Carlo simulation governed by Metropolis dynamics we show that surface effects and a very low level of stuffed spins (0.30%)-magnetic Dy ions substituted for non-magnetic Ti ions-cause these signatures in the relaxation. In addition, we find evidence that the rapidly diverging experimental timescale is due to a temperature-dependent attempt rate proportional to the monopole density.The exceptional physical properties of the spin-ice materials arise from the underlying pyrochlore lattice of corner-sharing tetrahedra and crystal-field effects, which constrain the magnetic moments of the rare-earth ions to point along the axis connecting the centres of the two neighbouring tetrahedra 1 . As a result, the spin-ice materials are highly frustrated and possess a ground state containing a large residual entropy similar to water ice 2 . The thermodynamic properties of the spin-ice materials have been very successfully modelled by the Hamiltonian for Ising spins interacting through dipolar and exchange interactions 3,4 ,where r nn = 3.5 Å, D = 1.41 K and J = 3.72 K, and the moments S, of unit length, are forced to point along the local 111 axes. Recently, it was realized that the fundamental excitations are magnetic charges, commonly referred to as monopoles 5,6 that are created by overturning a spin in the highly degenerate spin-ice ground state, where two spins point in and two point out of each tetrahedron. The motion of magnetic monopoles has been observed experimentally through the generation of monopole currents by the application of a magnetic field 7 , and muon spin rotation 8 , which is a subject of recent controversy 9 . Monte Carlo simulations of a Coulomb gas of monopoles 10 and the dipolar spin-ice model 11 , equation (1), agree well with experimental results down to 1 K, below which the observed dynamics become much slower in the experiments than in the simulations [11][12][13][14][15][16][17] . In this study we find that significant corrections to the ideal model in equation (1) are necessary to accurately model the motion of magnetic monopoles in the real material. Similarly to electrical conductors and semiconductors, in which local impurities can decrease the conductivity, or introduce new states in the bandgap, we find that a small amount of extra spins and surface effects change the flow of magnetic monopoles. Experimental access to the properties of the magnetic monopoles is provided through the dynamic correlation function C(t ) = M (0)M (t ) , where M (t ) is the time-dependent magnetization of the sample. To study these excitations we therefore scrutinize the low-temperature dynamics of Dy 2 Ti 2 O 7 . In particular, we measure C(t ) by two independent methods using custom designed superconducting quantum interference device (SQUID) circuits. In the direct field-quench measurement we apply a small field of 5 mOe to the sample and directly observe the decay of the magnetization. In the second met...
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.
The stochastic series expansion quantum Monte Carlo method is used to study thin ferromagnetic films, described by a Heisenberg model including local anisotropies. The magnetization curve is calculated, and the results compared to Schwinger boson and many-body Green's function calculations. A transverse field is introduced in order to study the reorientation effect, in which the magnetization changes from out-of-plane to in-plane. Since the approximate theoretical approaches above differ significantly from each other, and the Monte Carlo method is free of systematic errors, the calculation provides an unbiased check of the approximate treatments. By studying quantum spin models with local anisotropies, varying spin size, and a transverse field, we also demonstrate the general applicability of the recent cluster-loop formulation of the stochastic series expansion quantum Monte Carlo method.Comment: 9 pages, 12 figure
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