75 research outputs found
Neutron scattering study on spin correlations and fluctuations in the transition-metal-based magnetic quasicrystal Zn-Fe-Sc
Spin correlations and fluctuations in the 3d-transition-metal-based
icosahedral quasicrystal Zn-Fe-Sc have been investigated by neutron scattering
using polycrystalline samples. Magnetic diffuse scattering has been observed in
the elastic experiment at low temperatures, indicating development of static
short-range-spin correlations. In addition, the inelastic scattering experiment
detects a -independent quasielastic signal ascribed to single-site
relaxational spin fluctuations. Above the macroscopic freezing temperature
K, the spin relaxation rate shows Arrhenius-type behavior,
indicating thermally activated relaxation process. In contrast, the relaxation
rate remains finite even at the lowest temperature, suggesting a certain
quantum origin for the spin fluctuations below .Comment: To be published in Phys. Rev.
Magnetic properties of the Ag-In-rare-earth 1/1 approximants
We have performed magnetic susceptibility and neutron scattering measurements
on polycrystalline Ag-In-RE (RE: rare-earth) 1/1 approximants. In the magnetic
susceptibility measurements, for most of the RE elements, inverse
susceptibility shows linear behaviour in a wide temperature range, confirming
well localized isotropic moments for the RE ions. Exceptionally for the
light RE elements, such as Ce and Pr, non-linear behaviour was observed,
possibly due to significant crystalline field splitting or valence fluctuation.
For RE = Tb, the susceptibility measurement clearly shows a bifurcation of the
field-cooled and zero-field-cooled susceptibility at ~K,
suggesting a spin-glass-like freezing. On the other hand, neutron scattering
measurements detect significant development of short-range antiferromagnetic
spin correlations in elastic channel, which accompanied by a broad peak at
~meV in inelastic scattering spectrum. These features have
striking similarity to those in the Zn-Mg-Tb quasicrystals, suggesting that the
short-range spin freezing behaviour is due to local high symmetry clusters
commonly seen in both the systems.Comment: 14 pages, 12 figure
Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling
We investigate exact eigenstates of tight-binding models on the planar
rhombic Penrose tiling. We consider a vertex model with hopping along the edges
and the diagonals of the rhombi. For the wave functions, we employ an ansatz,
first introduced by Sutherland, which is based on the arrow decoration that
encodes the matching rules of the tiling. Exact eigenstates are constructed for
particular values of the hopping parameters and the eigenenergy. By a
generalized ansatz that exploits the inflation symmetry of the tiling, we show
that the corresponding eigenenergies are infinitely degenerate. Generalizations
and applications to other systems are outlined.Comment: 24 pages, REVTeX, 13 PostScript figures include
Pure point diffraction and cut and project schemes for measures: The smooth case
We present cut and project formalism based on measures and continuous weight
functions of sufficiently fast decay. The emerging measures are strongly almost
periodic. The corresponding dynamical systems are compact groups and
homomorphic images of the underlying torus. In particular, they are strictly
ergodic with pure point spectrum and continuous eigenfunctions. Their
diffraction can be calculated explicitly. Our results cover and extend
corresponding earlier results on dense Dirac combs and continuous weight
functions with compact support. They also mark a clear difference in terms of
factor maps between the case of continuous and non-continuous weight functions.Comment: 30 page
Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems
We study energy spectra, eigenstates and quantum diffusion for one- and
two-dimensional quasiperiodic tight-binding models. As our one-dimensional
model system we choose the silver mean or `octonacci' chain. The
two-dimensional labyrinth tiling, which is related to the octagonal tiling, is
derived from a product of two octonacci chains. This makes it possible to treat
rather large systems numerically. For the octonacci chain, one finds singular
continuous energy spectra and critical eigenstates which is the typical
behaviour for one-dimensional Schr"odinger operators based on substitution
sequences. The energy spectra for the labyrinth tiling can, depending on the
strength of the quasiperiodic modulation, be either band-like or fractal-like.
However, the eigenstates are multifractal. The temporal spreading of a
wavepacket is described in terms of the autocorrelation function C(t) and the
mean square displacement d(t). In all cases, we observe power laws for C(t) and
d(t) with exponents -delta and beta, respectively. For the octonacci chain,
0<delta<1, whereas for the labyrinth tiling a crossover is observed from
delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the
multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both
systems. Moreover, we find that the behaviour of C(t) and d(t) is independent
of the shape and the location of the initial wavepacket. We use our results to
check several relations between the diffusion exponent beta and the fractal
dimensions of energy spectra and eigenstates that were proposed in the
literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new
results adde
Generalized Inverse Participation Numbers in Metallic-Mean Quasiperiodic Systems
From the quantum mechanical point of view, the electronic characteristics of
quasicrystals are determined by the nature of their eigenstates. A practicable
way to obtain information about the properties of these wave functions is
studying the scaling behavior of the generalized inverse participation numbers
with the system size . In particular, we
investigate -dimensional quasiperiodic models based on different
metallic-mean quasiperiodic sequences. We obtain the eigenstates of the
one-dimensional metallic-mean chains by numerical calculations for a
tight-binding model. Higher dimensional solutions of the associated generalized
labyrinth tiling are then constructed by a product approach from the
one-dimensional solutions. Numerical results suggest that the relation
holds for these models. Using the
product structure of the labyrinth tiling we prove that this relation is always
satisfied for the silver-mean model and that the scaling exponents approach
this relation for large system sizes also for the other metallic-mean systems.Comment: 7 pages, 3 figure
Atomic dynamics of the i-ScZnMg and its 1/1 approximant phase: experiment and simulation
International audienceQuasicrystals are long range ordered materials which lack translational invariance so that the study of their physical properties remains a challenging problem. In order to study the respective influence of the local order and of the long range order (periodic or quasiperiodic) on lattice dynamics, we have carried out inelastic x-ray and neutron scattering experiments on single grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant. Besides the overall similarities and the existence of a pseudo gap in the transverse dispersion relation, marked differences are observed, the pseudo gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of pseudo Brillouin zone in the quasicrystal. These results are compared to simulations on atomic models and using oscillating pair potentials which have been fitted against ab-initio data. The simulated response function reproduces both the dispersion relation but also the observed intensity distribution in the measured spectra. The partial vibrational density of states, projected on the cluster shells, is computed from this model
- …