13 research outputs found
Ill-Behaved Convergence of a Model of the Gd3Ga5O12 Garnet Antiferromagnet with Truncated Magnetic Dipole-Dipole Interactions
Previous studies have found that calculations which consider long-range
magnetic dipolar interactions truncated at a finite cut-off distance Rc predict
spurious (unphysical) long-range ordered phases for Ising and Heisenberg
systems on the pyrochlore lattice. In this paper we show that, similar to these
two cases, calculations that use truncated dipolar interactions to model the
Gd3Ga5O12 garnet antiferromagnet also predict unphysical phases with
incommensurate ordering wave vector q_ord that is very sensitive to the dipolar
cut-off distance Rc.Comment: 7 pages, 2 color figures; Proceedings of the HFM2006 conference, to
appear in a special issue of J. Phys.: Condens. Matte
Quantum spin fluctuations in the dipolar Heisenberg-like rare earth pyrochlores
The magnetic pyrochlore oxide materials of general chemical formula R2Ti2O7
and R2Sn2O7 (R = rare earth) display a host of interesting physical behaviours
depending on the flavour of rare earth ion. These properties depend on the
value of the total magnetic moment, the crystal field interactions at each rare
earth site and the complex interplay between magnetic exchange and long-range
dipole-dipole interactions. This work focuses on the low temperature physics of
the dipolar isotropic frustrated antiferromagnetic pyrochlore materials.
Candidate magnetic ground states are numerically determined at zero temperature
and the role of quantum spin fluctuations around these states are studied using
a Holstein-Primakoff spin wave expansion to order 1/S. The results indicate the
strong stability of the proposed classical ground states against quantum
fluctuations. The inclusion of long range dipole interactions causes a
restoration of symmetry and a suppression of the observed anisotropy gap
leading to an increase in quantum fluctuations in the ground state when
compared to a model with truncated dipole interactions. The system retains most
of its classical character and there is little deviation from the fully ordered
moment at zero temperature.Comment: Latex2e, 18 pages, 4 figures, IOP forma
The Spin Liquid State of the Tb2Ti2O7 Pyrochlore Antiferromagnet: A Puzzling State of Affairs
The pyrochlore antiferromagnet Tb2Ti2O7 has proven to be an enigma to
experimentalists and theorists working on frustrated magnetic systems. The
experimentally determined energy level structure suggests a local Ising
antiferromagnet at low temperatures, T < 10 K. An appropriate model then
predicts a long-range ordered Q = 0 state below approximately 2 K. However,
muon spin resonance experiments reveal a paramagnetic structure down to tens of
milli-Kelvin. The importance of fluctuations out of the ground state effective
Ising doublet has been recently understood, for the measured paramagnetic
correlations can not be described without including the higher crystal field
states. However, these fluctuations treated within the random phase
approximation (RPA) fail to account for the lack of ordering in this system
below 2 K. In this work, we briefly review the experimental evidence for the
collective paramagnetic state of Tb2Ti2O7. The basic theoretical picture for
this system is discussed, where results from classical spin models are used to
motivate the investigation of quantum effects to lowest order via the RPA.
Avenues for future experimental and theoretical work on Tb2Ti2O7 are presented.Comment: Latex2e,6 pages, IOP format, introduction shortened and other minor
corrections, replaced with published version in the Proceedings of the Highly
Frustrated Magnetism 2003 Conference, Grenobl
Proposal for a [111] Magnetization Plateau in the Spin Liquid State of Tb2Ti2O7
Despite a Curie-Weiss temperature K, the Tb2Ti2O7
pyrochlore magnetic material lacks long range magnetic order down to at least
mK. It has recently been proposed that the low temperature
collective paramagnetic or spin liquid regime of this material may be akin to a
spin ice state subject to both thermal and quantum fluctuations a {\it
quantum spin ice} (QSI) of sorts. Here we explore the effect of a magnetic
field along the direction on the QSI state. To do so, we
investigate the magnetic properties of a microscopic model of Tb2Ti2O7 in an
independent tetrahedron approximation in a finite along . Such
a model describes semi-quantitatively the collective paramagnetic regime where
nontrivial spin correlations start to develop at the shortest lengthscale, that
is over a single tetrahedron, but where no long range order is yet present. Our
results show that a magnetization plateau develops at low temperatures as the
system develops ferromagnetic spin-ice-like "two-in/two-out"
correlations at the shortest lengthscale. From these results, we are led to
propose that the observation of such a [111] magnetization plateau in Tb2Ti2O7
would provide compelling evidence for a QSI at in this material and
help guide the development of a theory for the origin of its spin liquid state.Comment: 6 pages, 3 figure
Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice material
Spin ices, frustrated magnetic materials analogous to common water ice, are
exemplars of high frustration in three dimensions. Recent experimental studies
of the low-temperature properties of the paradigmatic DyTiO spin
ice material, in particular whether the predicted transition to long-range
order occurs, raise questions as per the currently accepted microscopic model
of this system. In this work, we combine Monte Carlo simulations and mean-field
theory calculations to analyze data from magnetization, elastic neutron
scattering and specific heat measurements on DyTiO. We also
reconsider the possible importance of the nuclear specific heat, ,
in DyTiO. We find that is not entirely negligible
below a temperature K and must be taken into account in a
quantitative analysis of the calorimetric data of this compound below that
temperature. We find that small effective 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 DyTiO,
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.Comment: 24 pages, 18 figures. To appear in Physical Review
Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb2Ti2O7, pyrochlore antiferromagnet
Highly frustrated antiferromagnets composed of magnetic rare-earth moments
are currently attracting much experimental and theoretical interest. Rare-earth
ions generally have small exchange interactions and large magnetic moments.
This makes it necessary to understand in detail the role of long-range magnetic
dipole-dipole interactions in these systems, in particular in the context of
spin-spin correlations that develop in the paramagnetic phase, but are often
unable to condense into a conventional long-range magnetic ordered phase. This
scenario is most dramatically emphasized in the frustrated pyrochlore
antiferromagnet material Tb2Ti207 which does not order down to 50 mK despite an
antiferromagnetic Curie-Weiss temperature Tcw ~ -20 K. In this paper we report
results from mean-field theory calculations of the paramagnetic elastic
neutron-scattering in highly frustrated magnetic systems with long-range
dipole-dipole interactions, focusing on the Tb2Ti207 system. Modeling Tb2Ti207
as an antiferromagnetic Ising pyrochlore, we find that the mean-field
paramagnetic scattering is inconsistent with the experimentally observed
results. Through simple symmetry arguments we demonstrate that the observed
paramagnetic correlations in Tb2Ti207 are precluded from being generated by any
spin Hamiltonian that considers only Ising spins, but are qualitatively
consistent with Heisenberg-like moments. Explicit calculations of the
paramagnetic scattering pattern for both Ising and Heisenberg models,
which include finite single-ion anisotropy, support these claims. We offer
suggestions for reconciling the need to restore spin isotropy with the Ising
like structure suggested by the single-ion properties of Tb3+.Comment: Revtex4, 18 pages, 3 eps figures (2 color figures). Change in title
and emphasis on Tb2Ti2O7 only. Spin-ice material removed, to appear in a
later publicatio
Absence of anomalous negative lattice-expansion for polycrystalline sample of Tb2Ti2O7
High resolution X-ray powder-diffraction experiments on a well-characterized
polycrystalline sample of the spin liquid Tb2Ti2O7 reveal that it shows normal
positive thermal-expansion above 4 K, which does not agree with the intriguing
anomalous negative thermal-expansion due to a magneto-elastic coupling reported
for a single crystal sample below 20 K. We also performed a Rietveld profile
refinement of a powder-diffraction pattern taken at a room temperature, and
confirmed that it is consistent with the fully ordered cubic pyrochlore
structure.Comment: 2 pages, 3 figure
Understanding Paramagnetic Spin Correlations in the Spin-Liquid Pyrochlore Tb2Ti2O7
Recent elastic and inelastic neutron scattering studies of the highly
frustrated pyrochlore antiferromagnet Tb2Ti2O7 have shown some very intriguing
features that cannot be modeled by the local classical Ising model,
naively expected to describe this system at low temperatures. Using the random
phase approximation to take into account fluctuations between the ground state
doublet and the first excited doublet, we successfully describe the elastic
neutron scattering pattern and dispersion relations in Tb2Ti2O7,
semi-quantitatively consistent with experimental observations.Comment: revtex4, 4 pages, 1 Color+ 2 BW figure
Refrustration and competing orders in the prototypical Dy₂ Ti₂ O₇ spin ice material
Spin ices, frustrated magnetic materials analogous to common water ice, have emerged over the past 15 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, diffuse neutron scattering, and specific-heat measurements on the paradigmatic Dy2 Ti2 O7 spin ice material. In this work, we also reconsider the possible importance of the nuclear specific heat C nuc in Dy 2 Ti 2 O 7 . We find that C nuc 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 Dy 2 Ti 2 O 7 , 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. </p