82 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
Reduction of the sign problem using the meron-cluster approach
The sign problem in quantum Monte Carlo calculations is analyzed using the
meron-cluster solution. The concept of merons can be used to solve the sign
problem for a limited class of models. Here we show that the method can be used
to \textit{reduce} the sign problem in a wider class of models. We investigate
how the meron solution evolves between a point in parameter space where it
eliminates the sign problem and a point where it does not affect the sign
problem at all. In this intermediate regime the merons can be used to reduce
the sign problem. The average sign still decreases exponentially with system
size and inverse temperature but with a different prefactor. The sign exhibits
the slowest decrease in the vicinity of points where the meron-cluster solution
eliminates the sign problem. We have used stochastic series expansion quantum
Monte Carlo combined with the concept of directed loops.Comment: 8 pages, 9 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
Screening and the Pinch Point Paradox in Spin Ice
Spin ice may be considered to be a model system for the investigation of pinch point scattering. We present very-high-resolution numerical simulations and an analytical theory of the pinch point profiles of the near-neighbor and dipolar spin ice models and find these to be in excellent agreement with each other and with existing theory. Most importantly, the pinch points of the dipolar spin ice model are infinitely sharp, as a result of unscreened dipolar fields. These results are compared to polarized neutron scattering measurements of the pinch point profiles in
Ho
2
Ti
2
O
7
, considered to be an accurate realization of dipolar spin ice. In contrast to the numerical and analytical results, the experimental pinch point profiles are shown to be broadened in a manner that is quantitatively consistent with fully screened dipolar fields. This striking paradox is not easily resolved: Possible resolutions implicate quantum fluctuations or fundamental corrections to the theory of simulation or polarized neutron scattering. We further discuss our results in the context of spin ice's role as a model Coulomb fluid
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
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
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
Hybrid Quantum-Classical Monte-Carlo Study of a Molecule-Based Magnet
Using a Monte Carlo (MC) method, we study an effective model for the
Fe(II)Fe(III) bimetallic oxalates. Within a hybrid quantum-classical MC
algorithm, the Heisenberg S=2 and spins on the Fe(II) and Fe(III)
sites are updated using a quantum MC loop while the Ising-like orbital angular
momenta on the Fe(II) sites are updated using a single-spin classical MC flip.
The effective field acting on the orbital angular momenta depends on the
quantum state of the system. We find that the mean-field phase diagram for the
model is surprisingly robust with respect to fluctuations. In particular, the
region displaying two compensation points shifts and shrinks but remains
finite.Comment: 8 pages, 7 figure
Special temperatures in frustrated ferromagnets
The description and detection of unconventional magnetic states, such as spin liquids, is a recurring topic in condensed matter physics. While much of the efforts have traditionally been directed at geometrically frustrated antiferromagnets, recent studies reveal that systems featuring competing antiferromagnetic and ferromagnetic interactions are also promising candidate materials. We find that this competition leads to the notion of special temperatures, analogous to those of gases, at which the competing interactions balance, and the system is quasi-ideal. Although induced by weak perturbing interactions, these special temperatures are surprisingly high and constitute an accessible experimental diagnostic of eventual order or spin-liquid properties. The well characterised Hamiltonian and extended low-temperature susceptibility measurement of the canonical frustrated ferromagnet Dy2Ti2O7 enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this class of magnets include kapellasite Cu3Zn(OH)6Cl2 and the spinel GeCo2O4
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