Phase diagram of the dilute magnet LiHo_xY_{1-x}F_4

We study the effective long-range Ising dipole model with a local exchange interaction appropriate for the dilute magnetic compound LiHo_{x}Y_{1-x}F_4. 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 T_c(x) between the ferromagnetic and paramagnetic phases. We demonstrate that the experimentally observed linear decrease in T_c 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 x_c=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 LiHo_{x}Y_{1-x}F_4 and find that the theory does predict a finite-temperature freezing of the spin glass. Reasons for the discrepancies are discussed.Comment: 5 pages, 4 figure

Ground state of the random-bond spin-1 Heisenberg chain

Stochastic series expansion quantum Monte Carlo is used to study the ground state of the antiferromagnetic spin-1 Heisenberg chain with bond disorder. Typical spin- and string-correlations functions behave in accordance with real-space renormalization group predictions for the random-singlet phase. The average string-correlation function decays algebraically with an exponent of -0.378(6), in very good agreement with the prediction of $-(3-\sqrt{5})/2\simeq -0.382$, while the average spin-correlation function is found to decay with an exponent of about -1, quite different from the expected value of -2. By implementing the concept of directed loops for the spin-1 chain we show that autocorrelation times can be reduced by up to two orders of magnitude.Comment: 9 pages, 10 figure

Low-temperature properties of the dilute dipolar magnet LiHo_xY_(1-x)F_4

We analyze recent experiments on the dilute rare-earth compound LiHo_xY_(1-x)F_4 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, chi ~ 1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, C_max(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 chi ~ T^-0.75 and chi ~ exp(-T/T_0). Furthermore we calculate the ground state magnetization as a function of dilution, and re-examine the phase diagram around the critical dilution x_c=0.24(3). We find that the spin glass susceptibility for the Ising model does not diverge below x_c, while recent experiments give strong evidence for a stable spin-glass phase in LiHo_0.167Y_0.833F_4.Comment: 6 pages, 9 figure

Quantum Monte Carlo simulation of thin magnetic films

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

LiHoF4_4: Cuboidal Demagnetizing Factor in an Ising Ferromagnet

The demagnetizing factor has an important effect on the physics of ferromagnets. For cuboidal samples it depends on susceptibility and the historic problem of determining this function continues to generate theoretical and experimental challenges. To test a recent theory, we measure the magnetic susceptibility of the Ising dipolar ferromagnet LiHoF$_4$, using samples of varying aspect ratio, and we reconsider the demagnetizing transformation necessary to obtain the intrinsic material susceptibility. Our experimental results confirm that the microscopic details of the material significantly affect the transformation, as predicted. In particular, we find that the uniaxial Ising spins require a demagnetizing transformation that differs from the one needed for Heisenberg spins and that use of the wrong demagnetizing transformation would result in unacceptably large errors in the measured physical properties of the system. Our results further shed light on the origin of the mysterious `flat' susceptibility of ordered ferromagnets by demonstrating that the intrinsic susceptibility of the ordered ferromagnetic phase is infinite, regardless of sample shape.Comment: 8 pages, 4 figure

The spectral theorem of many-body Green's function theory when there are zero eigenvalues of the matrix governing the equations of motion

In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever the matrix governing the equations of motion for the commutator Green's functions has zero eigenvalues. We show that a singular-value decomposition of this matrix allows one to reformulate the problem in terms of a smaller set of Green's functions with an associated matrix having no zero eigenvalues, thus eliminating the need for the anti-commutator Green's functions. The procedure is quite general and easy to apply. It is illustrated for the field-induced reorientation of the magnetization of a ferromagnetic Heisenberg monolayer and it is expected to work for more complicated cases as well.Comment: 4 pages, 1 figure, accepted for publication in Physical Review B (16. May 2003

Disorder Induced Quantum Phase Transition in Random-Exchange Spin-1/2 Chains

We investigate the effect of quenched bond-disorder on the anisotropic spin-1/2 (XXZ) chain as a model for disorder induced quantum phase transitions. We find non-universal behavior of the average correlation functions for weak disorder, followed by a quantum phase transition into a strongly disordered phase with only short-range xy-correlations. We find no evidence for the universal strong-disorder fixed point predicted by the real-space renormalization group, suggesting a qualitatively different view of the relationship between quantum fluctuations and disorder.Comment: 4 pages, 4 postscript figures, needs RevTeX

The ferromagnetic transition and domain structure in LiHoF4

Using Monte Carlo simulations we confirm that the rare-earth compound LiHoF4 is a very good realization of a dipolar Ising model. With only one free parameter our calculations for the magnetization, specific heat and inverse susceptibility match experimental data at a quantitative level in the single Kelvin temperature range, including the ferromagnetic transition at 1.53 K. Using parallel tempering methods and reaching system sizes up to 32000 dipoles with periodic boundary conditions we are able to give strong direct evidence of the logarithmic corrections predicted in renormalization group theory. Due to the long range and angular dependence of the dipolar model sample shape and domains play a crucial role in the ordered state. We go beyond Griffiths's theorem and consider surface corrections arising in finite macroscopic samples leading to a theory of magnetic domains. We predict that the ground-state domain structure for cylinders with a demagnetization factor N>0 consists of thin parallel sheets of opposite magnetization, with a width depending on the demagnetization factor.Comment: 5 pages, 9 figure