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

Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past fifteen years as exemplars of high frustration in three dimensions. Recent experimental developments aimed at interrogating anew the low-temperature properties of these systems, in particular whether the predicted transition to long-range order occurs, behoove researchers to scrutinize our current dipolar spin ice model description of these materials. In this work we do so by combining extensive Monte Carlo simulations and mean-field theory calculations to analyze data from previous magnetization, elastic neutron scattering and specific heat measurements on the paradigmatic Dy2Ti2O7 spin ice material. In the present work, we also reconsider the possible importance of the nuclear specific heat, Cnuc, in Dy2Ti2O7. We find that Cnuc is not entirely negligible below a temperature ∼ 0.5 K and must therefore be taken into account in a quantitative analysis of the calorimetric data of this compound below that temperature. We find that in this material, small effective spin-spin exchange interactions compete with the magnetostatic dipolar interaction responsible for the main spin ice phenomenology. This causes an unexpected "refrustration" of the long-range order that would be expected from the incompletely self-screened dipolar interaction and which positions the material at the boundary between two competing classical long-range ordered ground states. This allows for the manifestation of new physical low-temperature phenomena in Dy2Ti2O7, as exposed by recent specific heat measurements. We show that among the four most likely causes for the observed upturn of the specific heat at low temperature -an exchange-induced transition to long-range order, quantum non-Ising (transverse) terms in the effective spin Hamiltonian, the nuclear hyperfine contribution and random disorder -only the last appears to be reasonably able to explain the calorimetric data.

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 .

We present 1/N Schwinger boson and quantum Monte Carlo calculations of the magnetization and NMR relaxation rate for the two-dimensional ferromagnetic Heisenberg model representing a quantum Hall system at filling factor ν = 1. Comparing the analytic and numerical calculations, we find that the SU(N ) version of Schwinger boson theory gives accurate results for the magnetization at low temperatures, whereas the O(N ) model works well at higher temperatures.PACS numbers: 73.40.Hm,75.40.Mg,76.50.+g,75.30.Ds Two-dimensional quantum magnets have received particular attention in recent years because of advances in materials synthesis associated with high-temperature superconductivity, thin films and surfaces, and semiconductor quantum wells. It has recently come to be appreciated that two-dimensional electron gases in quantum wells subjected to strong magnetic fields in the quantum Hall regime are novel itinerant ferromagnets. The strong external magnetic field quenches the orbital kinetic energy but couples only very weakly to the spin degrees of freedom allowing low energy spin fluctuations to survive.Two-dimensional ferromagnets exhibit novel topological defects referred to as skyrmions by analogy with the corresponding objects in the Skyrme model in nuclear physics. What is unique about quantum Hall ferromagnets [1,2] is that these defects carry fermion charge and hence their ground state density can be controlled by moving the filling factor away from ν = 1. The combination of low energy spin fluctuations and these topological defects dramatically alters the NMR spectrum [3,2] and the specific heat [4].With the advent of NMR and magnetoabsorption measurements in quantum Hall systems, it is now possible to measure the temperature dependence of the electron magnetization. Recent theoretical work [5] has evaluated the magnetization of this quantum critical system at ν = 1 using SU(N ) and O(N ) formulations of mean field theory (with N = ∞). In this paper we present analytic results for the 1/N corrections to the magnetization and compare them with extensive quantum Monte Carlo simulations. We also present numerical results for the NMR relaxation rate 1/T 1 . In addition to their relevance to 2D quantum ferromagnets in general and QHE magnets in particular, these results provide new information on the level of accuracy of large N expansion methods and show a highly non-trivial difference in the behavior of the SU(N ) and O(N ) models.Low energy spin fluctuations in quantum Hall ferromagnets at ν = 1 are expected to be well described by the Heisenberg model [5]. The large N approach to this model is a systematic expansion around a mean field theory for N = ∞ and has the advantage of being equally valid at all temperatures T . Furthermore, even at the mean field level this approach correctly captures the fact that arbitrarily small thermal fluctuations destroy the long range order in two dimensions. An alternative microscopic approach which includes spin-wave corrections to the electronic self-energy has also recen...