Theory of magnetic transition metal nanoclusters on surfaces [Elektronische Ressource] / vorgelegt von Samir Lounis

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• Physik

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• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2007
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 3 Mo

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Theory of Magnetic Transition
Metal Nanoclusters on Surfaces
Von der Fakultät für Mathematik, Informatik und Naturwissenschaften
der Rheinisch-Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines Doktors
der Naturwissenschaften genehmigte Dissertation
vorgelegt von
Magister in Physik
Samir Lounis
aus Larbàa Nath Irathen (Algeria)
Berichter: Universitätsprofessor Dr. S. Blügel
Univ Dr. P. H. Dederichs
Tag der mündlichen Prüfung: 17.04.2007
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar."The task is not so much to see what nobody has seen yet, but to
think what nobody has thought yet about that everybody sees"
A. Schopenhauerv
Abstract
The question how magnetism behaves when the dimension of materials is reduced to
increasingly smaller sizes has attracted much research and led to the development of the
field of magnetic nanostructures. This research has been fueled by the technological po-
tentialofthesesystemsforthefieldofhigh-densitymagneticstoragemediaandhasbeen
accelerated by the many novel experimental methods and techniques developed exhibit-
ing atomic resolution. This thesis is motivated by the quest for the understanding and
the exploration of complex magnetism provided by atomic scale magnetic clusters de-
posited on surfaces or embedded in the bulk. The nature of magnetism in these systems
can be very rich, in that the properties depend on the atomic species, the cluster size,
shapeandsymmetryorchoiceofthesubstrate.Smallvariationsoftheclusterparameter
may change the properties dramatically. Particularly rich and particularly challenging
for experiment and theory is the behavior of clusters with competing magnetic inter-
actions either between the cluster atoms or between the cluster and the substrate. In
both cases magnetic frustration can lead to non-collinear magnetic structures for which
the magnetic quantization axis changes from atom to atom.
This thesis sheds light onto these systems from a theoretical perspective. Use is
made of the density functional theory (DFT), the most successful material specific the-
ory for describing electronic and derived properties from first-principles. Acting within
this framework, we have developed and implemented the treatment of non-collinear
magnetism into the Jülich version of the full-potential Korringa-Kohn-Rostoker Green
Function (KKR-GF) method. The KKR-GF method provides several advantages com-
pared to other first-principles methods. Based on solving the Dyson equation it allows
an elegant treatment of non-periodic systems such as impurities and clusters in bulk
or on surfaces. Electronic, magnetic properties and the observables provided by exper-
imental techniques such as x-ray, scanning tunneling microscopy and spectroscopy can
be accessed with the KKR-GF method.
Firstly, the method was applied to 3d transition-metal clusters on different ferro-
magnetic surfaces. Different types of magnetic clusters where selected. Clusters of Fe,
Co, Ni atoms are ferromagnetic and thus magnetically collinear. In order to investigate
magnetic frustration due to competing interactions within the ad-cluster we consid-
ered a (001) oriented surface of fcc metals, a topology which usually does not lead
to non-collinear magnetism. We tuned the strength of the magnetic coupling between
the ad-clusters and the ferromagnetic surface by varying the substrate from the case of
Ni(001) with a rather weak hybridization of the Ni d-states with the adatom d-states
to the case of Fe /Cu(001) with a much stronger hybridization due to the larger3ML
extend of the Fe wavefunctions. On Ni(001), the interaction between the Cr- as well as
the Mn-dimer adatoms is of antiferromagnetic nature, which is in competition with the
interaction with the substrate atoms. If we allow the magnetism to be non-collinear,
the moments rotate such the Cr-(Mn) adatom moments are aligned antiparallel to each
other and are basically perpendicular to the substrate moments. However, the weak
AF(FM) interaction with the substrate causes a slight tilting towards the substrate,
◦ ◦ ◦leading to an angle of 94.2 (72.6 ) instead of 90 . After performing total energy calcu-
lations we find that for Cr-dimer the ground state is collinear whereas the Mn-dimer
prefers the non-collinear configuration as ground state. The Heisenberg model is shownvi
to be good for the prediction of local energy minima but not for describing the magnetic
ground state. Bigger clusters are found to be magnetically collinear. These calculations
were extended to 3d multimers on Fe /Cu(001). Here the strong hybridization with3ML
the substrate leads to a collinear AF coupling of both Cr adatoms to the substrate
Fe atoms while the Mn-dimer is non-collinear. The ground states for both trimers are
non-collinear. All neighboring Cr (Mn) moments in the compact tetramer are antifer-
romagnetically aligned in-plane, with the directions slightly tilted towards (outwards
from) the substrate to gain some exchange interaction energy. Note that among differ-
ent shapes of tetramers the non-collinear compact Cr-tetramer appeared to be the most
stable one. The second type of frustration was investigated employing a Ni(111) sur-
face, a surface with a triangular lattice of atoms, were both kind of competing magnetic
interactions occur: intra-cluster magnetic frustration and cluster-substrate in-
teraction.ThemagneticconfigurationsforcompactCrorMnad-trimersareverysimilar
to the expected topological non-collinear configuration of a free frustrated trimer (an-
◦gle of 120 between successive adatoms). Additional trimers shapes considered have
collinear ground states with very small energy differences, in particular for Mn, with
respect to the non-collinear local minimum. Among the investigated tetramers only the
compact ones are Ferrimagnetic. Parity of number of adatoms in finite antiferromag-
netic nanowires is shown to be crucial in predicting whether the magnetic ground state
is non-collinear or collinear. We show that nanochains with an even number of adatoms
are always magnetically non-collinear while an odd number of adatoms leads under
given conditions to a collinear ferrimagnetic ground state.
In the second part of the thesis we applied the KKR-GF method to reveal experi-
mental issues related to scanning tunneling microscopy (STM). Hence, we investigated
the scattering of a two-dimensional surface state at adatoms. Here it is shown theo-
retically for some special cases as well as experimentally (STM) that any attractive
potential should lead to a localized state. With a systematic study, including sp as well
as d adatoms on or in the surface, we demonstrate that the cited statement, that any
attractive potential should lead to a localized state, is not correct. Indeed, we derive a
better criteria based on the scattering length of the adatom.
Atlast,weshowthatFermisurfacescanbeimagedthroughSTM.TheFermisurface
is one of the most important properties in metals as they determine many transport
properties as well as long-ranged interactions. The new effect is explained by means of
scattering of electrons at subsurface impurities. Since the electrons propagate away from
the impurities with velocity vectors perpendicular to the Fermi surface, flat regions on
this surface focus the electrons in special space-angle directions, leading in real space
to highly symmetric STM spots around the impurity.vii
Non-collinear magnetic structure of a Mn-trimer deposited on the surface of
Ni(001).
Real space imaging of the Fermi surface of Cu(111) by STM, simulated with the
KKR-GF method, considering a buried Co impurity as local probe.ix
Contents
1 Introduction 1
2 Density Functional Theory 7
2.1 Born-Oppenheimer Approximation . . . . . . . . . . . . . . . . . 8
2.2 Hohenberg-Kohn Theorems . . . . . . . . . . . . . . . . . . . . . 8
2.3 The Kohn-Sham Ansatz . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 The Local Spin Density Approximation . . . . . . . . . . . . . . . 11
2.5 Non-collinear Spin Density . . . . . . . . . . . . . . . . . . . . . . 12
3 The KKR Green Function Method 15
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Green Function Method . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Single-Site Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Multiple-Scattering Theory . . . . . . . . . . . . . . . . . . . . . . 21
3.5 Multiple-Scattering: The Green Function Approach . . . . . . . . 23
3.6 Description of the Full Potential . . . . . . . . . . . . . . . . . . 25
3.7 Self-Consistency Algorithm . . . . . . . . . . . . . . . . . . . . . . 27
4 KKR for Non-collinear Magnetism 31
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Non-collinear KKR Formalism . . . . . . . . . . . . . . . . . . . . 33
4.3 Rotation Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4 Host Green Functions and t-matrices . . . . . . . . . . . . . . . . 37
4.4.1 Screened (tight-binding) KKR Method . . . . . . . . . . . 39
4.4.2 Two-DimensionalSystems:Finite-ThicknessSlabsandHalf-
Infinite Crystals . . . . . . . . . . . . . . . . . . . . . . . 40x Contents
4.5 t-matrix for Perturbed Atoms . . . . . . . . . . . . . . . . . . . . 41
4.6