5,456 research outputs found
Asymptotically Optimal Tests when Parameters are Estimated
The main purpose of this paper is to provide an asymptotically optimal test.
The proposed statistic is of Neyman-Pearson-type when the parameters are
estimated with a particular kind of estimators. It is shown that the proposed
estimators enable us to achieve this end. Two particular cases, AR(1) and ARCH
models were studied and the asymptotic power function was derived
Theory of Scanning Tunneling Microscopy
This lecture has been given at the 45th Spring School: Computing Solids:
Models, Ab-initio Methods and Supercomputing organized at the Forschungszentrum
J\"ulich. The goal of this manuscript is to review the basics behind the theory
accompanying Scanning Tunneling Microscopy.Comment: 38 pages, 45th IFF Spring School: Computing Solids: Models, Ab-initio
Methods and Supercomputing organized at the research center of Juelic
Mapping the magnetic exchange interactions from first principles: Anisotropy anomaly and application to Fe, Ni, and Co
Mapping the magnetic exchange interactions from model Hamiltonian to density
functional theory is a crucial step in multi-scale modeling calculations.
Considering the usual magnetic force theorem but with arbitrary rotational
angles of the spin moments, a spurious anisotropy in the standard mapping
procedure is shown to occur provided by bilinear-like contributions of high
order spin interactions. The evaluation of this anisotropy gives a hint on the
strength of non-bilinear terms characterizing the system under investigation.Comment: 11 pages, 1 figur
Impact of single atomic defects and vacancies on the magnetic anisotropy energy of CoPt thin films
The impact of surface vacancies and single adatoms on the magnetic properties
of tetragonal {\bf{L1}} CoPt thin films is investigated from first
principles. We consider Co and Fe single adatoms deposited on a Pt-terminated
thin film while a Pt adatom is assumed to be supported by a Co-terminated film.
The vacancy is injected in the top-surface layer of the films with both types
of termination. After finding the most stable location of the defects, we
discuss their magnetic properties tight to those of the substrate and
investigate the magnetic crystalline anisotropy energy (MAE). Previous
simulations [Brahimi et al. J. Phys.: Condens. Matter. \textbf{28}, 496002
(2016)] predicted a large out-of-plane surface MAE for the Pt-terminated CoPt
films (4 meV per f.u.) in contrast to in-plane surface MAE for Co-terminated
films (-1 meV per f.u.). Here, we find that the surface MAE is significantly
modified upon the presence of the atomic defects. All investigated defects
induce an in-plane MAE, which is large enough for Fe adatom and Pt vacancy to
switch the surface MAE from out-of-plane to in-plane for the Pt-terminated
films. Interestingly, among the investigated defects Pt vacancy has the largest
effect on the MAE in contrast to Co vacancy, which induced the smallest but
still significant effect. This behavior is explained in terms of the orbital
moment anisotropy of the thin films
Giant perpendicular magnetic anisotropy energies in CoPt thin films: Impact of reduced dimensionality and imperfections
The impact of reduced dimensionality on the magnetic properties of the
tetragonal L1 CoPt alloy is investigated from ab-initio considering
several kinds of surface defects. By exploring the dependence of the
magnetocrystalline anisotropy energy (MAE) on the thickness of CoPt thin films,
we demonstrate the crucial role of the chemical nature of the surface. For
instance, Pt-terminated thin films exhibit huge MAEs which can be 1000% larger
than those of Co-terminated films. Besides the perfect thin films, we
scrutinize the effect of defective surfaces such as stacking faults or
anti-sites on the surface layers. Both types of defects reduce considerably the
MAE with respect to the one obtained for Pt-terminated thin films. A detailed
analysis of the electronic structure of the thin films is provided with a
careful comparison to the CoPt bulk case. The behavior of the MAEs is then
related to the location of the different virtual bound states utilising second
order perturbation theory.Comment: 10 pages, 7 figures, accepted in Journal of Physics: Condensed Matte
Insights into the orbital magnetism of noncollinear magnetic systems
The orbital magnetic moment is usually associated with the relativistic
spin-orbit interaction, but recently it has been shown that noncollinear
magnetic structures can also be its driving force. This is important not only
for magnetic skyrmions, but also for other noncollinear structures, either
bulk-like or at the nanoscale, with consequences regarding their experimental
detection. In this work we present a minimal model that contains the effects of
both the relativistic spin-orbit interaction and of magnetic noncollinearity on
the orbital magnetism. A hierarchy of models is discussed in a step-by-step
fashion, highlighting the role of time-reversal symmetry breaking for
translational and spin and orbital angular motions. Couplings of spin-orbit and
orbit-orbit type are identified as arising from the magnetic noncollinearity.
We recover the atomic contribution to the orbital magnetic moment, and a
nonlocal one due to the presence of circulating bound currents, exploring
different balances between the kinetic energy, the spin exchange interaction,
and the relativistic spin-orbit interaction. The connection to the scalar spin
chirality is examined. The orbital magnetism driven by magnetic noncollinearity
is mostly unexplored, and the presented model contributes to laying its
groundwork
Exchange coupling in transition-metal nano-clusters on Cu(001) and Cu(111) surfaces
We present results of density-functional calculations on the magnetic
properties of Cr, Mn, Fe and Co nano-clusters (1 to 9 atoms large) supported on
Cu(001) and Cu(111). The inter-atomic exchange coupling is found to depend on
competing mechanisms, namely ferromagnetic double exchange and
antiferromagnetic kinetic exchange. Hybridization-induced broadening of the
resonances is shown to be important for the coupling strength. The cluster
shape is found to weaken the coupling via a mechanism that comprises the
different orientation of the atomic d-orbitals and the strength of
nearest-neighbour hopping. Especially in Fe clusters, a correlation of binding
energy and exchange coupling is also revealed
Nonlocal orbital magnetism of 3d adatoms deposited on the Pt(111) surface
The orbital magnetic moment is still surprisingly not well understood, in
contrast to the spin part. Its description in finite systems, such as isolated
atoms and molecules, is not problematic, but it was only recently that a
rigorous picture was provided for extended systems. Here we focus on an
intermediate class of systems: magnetic adatoms placed on a non-magnetic
surface. We show that the essential quantity is the ground-state charge current
density, in the presence of spin-orbit coupling, and set out its
first-principles description. This is illustrated by studying the magnetism of
the surface Pt electrons, induced by the presence of Cr, Mn, Fe, Co and Ni
adatoms. A physically appealing partition of the charge current is introduced.
This reveals that there is an important nonlocal contribution to the orbital
moments of the Pt atoms, extending three times as far from each magnetic adatom
as the induced spin and local orbital moments. We find that it is as sizable as
the latter, and attribute its origin to a spin-orbital susceptibility of the Pt
surface, different from the one responsible for the formation of the local
orbital moments.Comment: 6 pages, 3 figures, submitte
New Entropy Estimator with an Application to Test of Normality
In the present paper we propose a new estimator of entropy based on smooth
estimators of quantile density. The consistency and asymptotic distribution of
the proposed estimates are obtained. As a consequence, a new test of normality
is proposed. A small power comparison is provided. A simulation study for the
comparison, in terms of mean squared error, of all estimators under study is
performed
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