78 research outputs found
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 , 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
LiHoF: 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, 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
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