296 research outputs found
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
Multiple-scattering approach for multi-spin chiral magnetic interactions: Application to the one- and two-dimensional Rashba electron gas
Various multi-spin magnetic exchange interactions (MEI) of chiral nature have
been recently unveiled. Owing to their potential impact on the realisation of
twisted spin-textures, their implication in spintronics or quantum computing is
very promising. Here, I address the long-range behavior of multi-spin MEI on
the basis of a multiple-scattering formalism implementable in Green functions
based methods. I consider the impact of spin-orbit coupling (SOC) as described
in the one- (1D) and two-dimensional (2D) Rashba model, from which the
analytical forms of the four- and six-spin interactions are extracted and
compared to the bilinear isotropic, anisotropic and Dzyaloshinskii-Moriya
interactions (DMI). Similarly to the DMI between two sites and , there
is a four-spin chiral vector perpendicular to the bond connecting the two
sites. The oscillatory behavior of the MEI and their decay as function of
interatomic distances are analysed and quantified for the Rashba surfaces
states characterizing Au surfaces. The interplay of beating effects and
strength of SOC gives rise to a wide parameter space where chiral MEI are more
prominent than the isotropic ones. The multi-spin interactions for a plaquette
of magnetic moments decay like
simplifying to for
equidistant atoms, where is the dimension of the mediating electrons,
the Fermi wave vector, the perimeter of the plaquette while is the
product of interatomic distances. This recovers the behavior of the bilinear
MEI, , and shows that increasing the perimeter of the
plaquette weakens the MEI. More important, the power-law pertaining to the
distance-dependent 1D MEI is insensitive to the number of atoms in the
plaquette in contrast to the linear dependence associated with the 2D MEI
Non-collinear magnetism induced by frustration in transition-metal nanostructures deposited on surfaces
How does magnetism behave when the physical dimension is reduced to the size
of nanostructures? The multiplicity of magnetic states in these systems can be
very rich, in that their properties depend on the atomic species, the cluster
size, shape and symmetry or choice of the substrate. Small variations of the
cluster parameters may change the properties dramatically. Research in this
field has gained much by the many novel experimental methods and techniques
exhibiting atomic resolution. Here I review the ab-initio approach, focusing on
recent calculations on magnetic frustration and occurrence of non-collinear
magnetism in antiferromagnetic nanostructures deposited on surfaces.Comment: 45 pages, topical review, Updated from the Psi-k scientific highlight
of the month N.106 (2011
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
The chiral biquadratic pair interaction
Magnetic interactions underpin a plethora of magnetic states of matter, hence
playing a central role both in fundamental physics and for future spintronic
and quantum computation devices. The Dzyaloshinskii-Moriya interaction, being
chiral and driven by relativistic effects, leads to the stabilization of
highly-noncollinear spin textures such as skyrmions, which thanks to their
topological nature are promising building blocks for magnetic data storage and
processing elements. Here, we reveal and study a new chiral pair interaction,
which is the biquadratic equivalent of the Dzyaloshinskii-Moriya interaction.
First, we derive this interaction and its guiding principles from a microscopic
model. Second, we study its properties in the simplest prototypical systems,
magnetic dimers deposited on various substrates, resorting to systematic
first-principles calculations. Lastly, we discuss its importance and
implications not only for magnetic dimers but also for extended systems, namely
one-dimensional spin spirals and complex two-dimensional magnetic structures,
such as a nanoskyrmion lattice
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