Dissertationen
https://kobra.uni-kassel.de:443/handle/123456789/2012010940259
Wed, 01 Dec 2021 11:35:54 GMT2021-12-01T11:35:54ZA new perspective to strongly-interacting lattice fermions in the framework of density functional theory
https://kobra.uni-kassel.de:443/handle/123456789/12409
Die in dieser Arbeit formulierte Theorie betrachtet das Vielteilchenproblem wechselwirkender Fermionen auf einem Gitter aus einem neuen Blickwinkel.
Wed, 01 Jan 2020 00:00:00 GMThttps://kobra.uni-kassel.de:443/handle/123456789/124092020-01-01T00:00:00ZMüller, TobiasDie in dieser Arbeit formulierte Theorie betrachtet das Vielteilchenproblem wechselwirkender Fermionen auf einem Gitter aus einem neuen Blickwinkel.Energy landscapes and dynamics of magnetic nanostructures: disorder, structure, and magnetic field effects
https://kobra.uni-kassel.de:443/handle/123456789/12403
The static and dynamic magnetic properties of two-dimensional ensembles of dipole-coupled magnetic nanoparticles (NPs) are investigated from a theoretical perspective. Particular emphasis is put on the correlations between the geometrical arrangements of the NPs, their inherent structural disorder, and the cooperative magnetic dynamics of the nanostructures as a whole. To this aim a significant number of representative two-dimensional NP ensembles with different structural geometries and degrees of disorder are considered. The interaction- energy landscapes (ELs) of the ensembles are characterized and analyzed systematically by calculating the local minima and connecting first-order saddle points and by deriving the corresponding disconnectivity graphs and kinetic networks. In this way, a microscopic understanding of the dominant relaxation processes, their interrelations and the resulting dynamics is achieved.
The study shows that the topology of the ELs changes as a function of disorder in a most profound way. Weakly disordered square and triangular ensembles are found to be good structure seekers with a relaxation dynamics that is funnelled towards the ground state. In contrast, the ELs of strongly disordered ensembles are very rough, with a much larger number of low-energy local minima, which are separated by large energy barriers that tend to increase as the energy of the metastable states decreases. Furthermore, the study shows that the transition from weak to strong disorder has a drastic impact on the stochastic Markovian dynamics. While the relaxation dynamics in weakly disordered square and triangular ensembles follows a stretched exponential law with a single characteristic time scale, strongly disordered ensembles show a much more intricate dynamics that includes nontrivial phenomena such as multiple time scales, trapping and possibly ergodicity breaking.
The consequences of applying external magnetic fields on the cooperative magnetic behavior of NP ensembles and the role of the structural arrangement and disorder on the magnetic-field response of the nanostructures are determined. The anisotropy of the field- induced changes in the dominant magnetic configurations and in the interaction-energy landscapes are quantified. One observes that weakly disordered square and triangular ensembles remain good structure seekers as the external magnetic field is increased, whereas strongly disordered ensembles show a transition from bad to good structure-seeking behavior.
Furthermore, it is shown how the different ensemble geometries can be distinguished on the basis of the experimentally accessible hysteresis loops. For example, square ensembles have wasp-waisted hysteresis loops with a small remanence and a small coercivity, triangular ensembles have pot-belly-shaped loops with a large remanence and a small coercivity, and random ensembles have step-like loops with a large remanence and a large coercivity.
The correlation between nanostructure geometry and collective behavior is understood in further detail by showing how different NP arrangements have very different EL topologies, even if the degree of structural disorder remains small. NP ensembles arranged on lattices with a high rotational symmetry, such as square, triangular, and honeycomb lattices, are found to be very good structure seekers with fast and unhindered relaxation dynamics. In contrast, ensembles with more complex or less symmetric underlying geometries, such as kagome, rectangular, and orthorhombic lattices, show significantly rougher energy landscapes with larger energy barriers and slower dynamics. Especially the results on the kagome lattice demonstrate that geometric frustrations have a major impact on the ELs of nanostructures, which is as important as the frustrations resulting from strong structural disorder.
The goals and limitations of harmonic transition-state theory (HTST) in the context of magnetic systems are investigated by considering a small magnetic NP with cubic magne- tocrystalline anisotropy. The transition rates obtained from HTST are compared with the ones obtained from propagating the Landau-Lifshitz-Gilbert equation. The calculations indicate that HTST provides a good approximation of the transition rates at low temperatures and for large values of the Gilbert damping parameter. In addition, it is demonstrated that HTST breaks down in the small damping regime as a result of dissipative effects, recrossing trajectories, and multi-barrier transitions.
The dissertation is concluded by pointing out some of the possible extensions of this work and its implications for current open problems.
Wed, 01 Jan 2020 00:00:00 GMThttps://kobra.uni-kassel.de:443/handle/123456789/124032020-01-01T00:00:00ZGallina, DavidThe static and dynamic magnetic properties of two-dimensional ensembles of dipole-coupled magnetic nanoparticles (NPs) are investigated from a theoretical perspective. Particular emphasis is put on the correlations between the geometrical arrangements of the NPs, their inherent structural disorder, and the cooperative magnetic dynamics of the nanostructures as a whole. To this aim a significant number of representative two-dimensional NP ensembles with different structural geometries and degrees of disorder are considered. The interaction- energy landscapes (ELs) of the ensembles are characterized and analyzed systematically by calculating the local minima and connecting first-order saddle points and by deriving the corresponding disconnectivity graphs and kinetic networks. In this way, a microscopic understanding of the dominant relaxation processes, their interrelations and the resulting dynamics is achieved.
The study shows that the topology of the ELs changes as a function of disorder in a most profound way. Weakly disordered square and triangular ensembles are found to be good structure seekers with a relaxation dynamics that is funnelled towards the ground state. In contrast, the ELs of strongly disordered ensembles are very rough, with a much larger number of low-energy local minima, which are separated by large energy barriers that tend to increase as the energy of the metastable states decreases. Furthermore, the study shows that the transition from weak to strong disorder has a drastic impact on the stochastic Markovian dynamics. While the relaxation dynamics in weakly disordered square and triangular ensembles follows a stretched exponential law with a single characteristic time scale, strongly disordered ensembles show a much more intricate dynamics that includes nontrivial phenomena such as multiple time scales, trapping and possibly ergodicity breaking.
The consequences of applying external magnetic fields on the cooperative magnetic behavior of NP ensembles and the role of the structural arrangement and disorder on the magnetic-field response of the nanostructures are determined. The anisotropy of the field- induced changes in the dominant magnetic configurations and in the interaction-energy landscapes are quantified. One observes that weakly disordered square and triangular ensembles remain good structure seekers as the external magnetic field is increased, whereas strongly disordered ensembles show a transition from bad to good structure-seeking behavior.
Furthermore, it is shown how the different ensemble geometries can be distinguished on the basis of the experimentally accessible hysteresis loops. For example, square ensembles have wasp-waisted hysteresis loops with a small remanence and a small coercivity, triangular ensembles have pot-belly-shaped loops with a large remanence and a small coercivity, and random ensembles have step-like loops with a large remanence and a large coercivity.
The correlation between nanostructure geometry and collective behavior is understood in further detail by showing how different NP arrangements have very different EL topologies, even if the degree of structural disorder remains small. NP ensembles arranged on lattices with a high rotational symmetry, such as square, triangular, and honeycomb lattices, are found to be very good structure seekers with fast and unhindered relaxation dynamics. In contrast, ensembles with more complex or less symmetric underlying geometries, such as kagome, rectangular, and orthorhombic lattices, show significantly rougher energy landscapes with larger energy barriers and slower dynamics. Especially the results on the kagome lattice demonstrate that geometric frustrations have a major impact on the ELs of nanostructures, which is as important as the frustrations resulting from strong structural disorder.
The goals and limitations of harmonic transition-state theory (HTST) in the context of magnetic systems are investigated by considering a small magnetic NP with cubic magne- tocrystalline anisotropy. The transition rates obtained from HTST are compared with the ones obtained from propagating the Landau-Lifshitz-Gilbert equation. The calculations indicate that HTST provides a good approximation of the transition rates at low temperatures and for large values of the Gilbert damping parameter. In addition, it is demonstrated that HTST breaks down in the small damping regime as a result of dissipative effects, recrossing trajectories, and multi-barrier transitions.
The dissertation is concluded by pointing out some of the possible extensions of this work and its implications for current open problems.First-principles electronic theory of non-collinear magnetic order in transition-metal nanowires
https://kobra.uni-kassel.de:443/handle/123456789/2015052748393
The structural, electronic and magnetic properties of one-dimensional 3d transition-metal (TM)
monoatomic chains having linear, zigzag and ladder geometries are investigated in the frame-work of
first-principles density-functional theory. The stability of long-range magnetic order along the
nanowires is determined by computing the corresponding frozen-magnon dispersion relations as a
function of the 'spin-wave' vector q.
First, we show that the ground-state magnetic orders of V, Mn and Fe linear chains at the equilibrium
interatomic distances are non-collinear (NC) spin-density waves (SDWs) with characteristic equilibrium
wave vectors q that depend on the composition and interatomic distance. The electronic and
magnetic properties of these novel spin-spiral structures are discussed from a local perspective
by analyzing the spin-polarized electronic densities of states, the local magnetic moments and the
spin-density distributions for representative values q. Second, we investigate the stability
of NC spin arrangements in Fe zigzag chains and ladders. We find that the non-collinear SDWs are
remarkably stable in the biatomic chains (square ladder), whereas ferromagnetic order (q =0)
dominates in zigzag chains (triangular ladders). The different magnetic structures are interpreted in terms of the
corresponding effective exchange interactions J(ij) between the local
magnetic moments μ(i) and μ(j) at atoms i and j.
The effective couplings are derived by fitting a classical Heisenberg model to the
ab initio magnon dispersion relations. In addition they are analyzed in the
framework of general magnetic phase diagrams having arbitrary first, second,
and third nearest-neighbor (NN) interactions J(ij).
The effect of external electric fields (EFs) on the stability of NC magnetic order has been
quantified for representative monoatomic free-standing and deposited chains. We find that an
external EF, which is applied perpendicular to the chains, favors non-collinear order in V chains,
whereas it stabilizes the ferromagnetic (FM) order in Fe chains. Moreover, our calculations reveal a change
in the magnetic order of V chains deposited on the Cu(110) surface in the presence of external EFs.
In this case the NC spiral order, which was unstable in the absence of EF, becomes the most
favorable one when perpendicular fields of the order of 0.1 V/Å are applied.
As a final application of the theory we study the magnetic interactions within monoatomic TM chains deposited
on graphene sheets. One observes that even weak chain substrate hybridizations can
modify the magnetic order. Mn and Fe chains show incommensurable NC spin configurations. Remarkably, V chains
show a transition from a spiral magnetic order in the freestanding geometry to FM order when they are deposited
on a graphene sheet. Some TM-terminated zigzag graphene-nanoribbons, for example V and Fe
terminated nanoribbons, also show NC spin configurations. Finally, the magnetic anisotropy energies (MAEs) of TM
chains on graphene are investigated. It is shown that Co and Fe chains exhibit significant MAEs and orbital
magnetic moments with in-plane easy magnetization axis. The remarkable changes in the magnetic properties of chains
on graphene are correlated to charge transfers from the TMs to NN carbon atoms.
Goals and limitations of this study and the resulting perspectives of future investigations are
discussed.
Wed, 27 May 2015 00:00:00 GMThttps://kobra.uni-kassel.de:443/handle/123456789/20150527483932015-05-27T00:00:00ZTanveer, MuhammadThe structural, electronic and magnetic properties of one-dimensional 3d transition-metal (TM)
monoatomic chains having linear, zigzag and ladder geometries are investigated in the frame-work of
first-principles density-functional theory. The stability of long-range magnetic order along the
nanowires is determined by computing the corresponding frozen-magnon dispersion relations as a
function of the 'spin-wave' vector q.
First, we show that the ground-state magnetic orders of V, Mn and Fe linear chains at the equilibrium
interatomic distances are non-collinear (NC) spin-density waves (SDWs) with characteristic equilibrium
wave vectors q that depend on the composition and interatomic distance. The electronic and
magnetic properties of these novel spin-spiral structures are discussed from a local perspective
by analyzing the spin-polarized electronic densities of states, the local magnetic moments and the
spin-density distributions for representative values q. Second, we investigate the stability
of NC spin arrangements in Fe zigzag chains and ladders. We find that the non-collinear SDWs are
remarkably stable in the biatomic chains (square ladder), whereas ferromagnetic order (q =0)
dominates in zigzag chains (triangular ladders). The different magnetic structures are interpreted in terms of the
corresponding effective exchange interactions J(ij) between the local
magnetic moments μ(i) and μ(j) at atoms i and j.
The effective couplings are derived by fitting a classical Heisenberg model to the
ab initio magnon dispersion relations. In addition they are analyzed in the
framework of general magnetic phase diagrams having arbitrary first, second,
and third nearest-neighbor (NN) interactions J(ij).
The effect of external electric fields (EFs) on the stability of NC magnetic order has been
quantified for representative monoatomic free-standing and deposited chains. We find that an
external EF, which is applied perpendicular to the chains, favors non-collinear order in V chains,
whereas it stabilizes the ferromagnetic (FM) order in Fe chains. Moreover, our calculations reveal a change
in the magnetic order of V chains deposited on the Cu(110) surface in the presence of external EFs.
In this case the NC spiral order, which was unstable in the absence of EF, becomes the most
favorable one when perpendicular fields of the order of 0.1 V/Å are applied.
As a final application of the theory we study the magnetic interactions within monoatomic TM chains deposited
on graphene sheets. One observes that even weak chain substrate hybridizations can
modify the magnetic order. Mn and Fe chains show incommensurable NC spin configurations. Remarkably, V chains
show a transition from a spiral magnetic order in the freestanding geometry to FM order when they are deposited
on a graphene sheet. Some TM-terminated zigzag graphene-nanoribbons, for example V and Fe
terminated nanoribbons, also show NC spin configurations. Finally, the magnetic anisotropy energies (MAEs) of TM
chains on graphene are investigated. It is shown that Co and Fe chains exhibit significant MAEs and orbital
magnetic moments with in-plane easy magnetization axis. The remarkable changes in the magnetic properties of chains
on graphene are correlated to charge transfers from the TMs to NN carbon atoms.
Goals and limitations of this study and the resulting perspectives of future investigations are
discussed.Magnetic interactions between transition metal impurities and clusters mediated by low-dimensional metallic hosts: A first principles theoretical investigation
https://kobra.uni-kassel.de:443/handle/123456789/2015033147887
The magnetic properties and interactions between transition metal (TM) impurities and clusters in low-dimensional metallic hosts are studied using a first principles
theoretical method. In the first part of this work, the effect of magnetic order in 3d-5d systems is addressed from the perspective of its influence on the enhancement of the magnetic anisotropy energy (MAE). In the second part, the possibility of using external electric fields (EFs) to control the magnetic properties and interactions between nanoparticles deposited at noble metal surfaces is investigated.
The inﬂuence of 3d composition and magnetic order on the spin polarization of the
substrate and its consequences on the MAE are analyzed for the case of 3d impurities
in one- and two-dimensional polarizable hosts. It is shown that the MAE and easy-
axis of monoatomic free standing 3d-Pt wires is mainly determined by the atomic
spin-orbit (SO) coupling contributions. The competition between ferromagnetic (FM) and antiferromagnetic (AF) order in FePtn wires is studied in detail for n=1-4 as a function of the relative position between Fe atoms. Our results show an oscillatory behavior of the magnetic polarization of Pt atoms as a function of their distance from the magnetic
impurities, which can be correlated to a long-ranged magnetic coupling of the Fe
atoms. Exceptionally large variations of the induced spin and orbital moments at the
Pt atoms are found as a function of concentration and magnetic order. Along with
a violation of the third Hund’s rule at the Fe sites, these variations result in a non
trivial behavior of the MAE.
In the case of TM impurities and dimers at the Cu(111), the effects of surface charging
and applied EFs on the magnetic properties and substrate-mediated magnetic interactions have been investigated. The modifications of the surface electronic structure, impurity local moments and magnetic exchange coupling as a result of the EF-induced metallic screening and charge rearrangements are analysed. In a ﬁrst study, the properties of surface substitutional Co and Fe impurities are investigated as a function of
the external charge per surface atom q. At large inter-impurity distances the effective magnetic exchange coupling ∆E between impurities shows RKKY-like oscillations
as a function of the distance which are not signiﬁcantly affected by the considered values of q. For distances r < 10 Å, important modifications in the magnitude of ∆E, involving changes from FM to AF coupling, are found depending non-monotonously on the value and polarity of q. The interaction energies are analysed from a local perspective. In a second study, the interplay between external EF effects, internal magnetic order and substrate-mediated magnetic coupling has been investigated for Mn dimers on Cu(111). Our calculations show that EF (∼ 1eV/Å) can induce a switching from AF to FM ground-state magnetic order within single Mn dimers. The relative coupling between a pair of dimers also shows RKKY-like oscillations as a function of the inter-dimer distance. Their effective magnetic exchange interaction
is found to depend significantly on the magnetic order within the Mn dimers and on
their relative orientation on the surface. The dependence of the substrate-mediated
interaction on the magnetic state of the dimers is qualitatively explained in terms
of the differences in the scattering of surface electrons. At short inter-dimer distances, the ground-state conﬁguration is determined by an interplay between exchange interactions and EF effects. These results demonstrate that external surface charging and applied EFs offer remarkable possibilities of manipulating the sign and strength of the magnetic coupling of surface supported nanoparticles.
Tue, 31 Mar 2015 00:00:00 GMThttps://kobra.uni-kassel.de:443/handle/123456789/20150331478872015-03-31T00:00:00ZJuárez Reyes, Lucila MaitreyaThe magnetic properties and interactions between transition metal (TM) impurities and clusters in low-dimensional metallic hosts are studied using a first principles
theoretical method. In the first part of this work, the effect of magnetic order in 3d-5d systems is addressed from the perspective of its influence on the enhancement of the magnetic anisotropy energy (MAE). In the second part, the possibility of using external electric fields (EFs) to control the magnetic properties and interactions between nanoparticles deposited at noble metal surfaces is investigated.
The inﬂuence of 3d composition and magnetic order on the spin polarization of the
substrate and its consequences on the MAE are analyzed for the case of 3d impurities
in one- and two-dimensional polarizable hosts. It is shown that the MAE and easy-
axis of monoatomic free standing 3d-Pt wires is mainly determined by the atomic
spin-orbit (SO) coupling contributions. The competition between ferromagnetic (FM) and antiferromagnetic (AF) order in FePtn wires is studied in detail for n=1-4 as a function of the relative position between Fe atoms. Our results show an oscillatory behavior of the magnetic polarization of Pt atoms as a function of their distance from the magnetic
impurities, which can be correlated to a long-ranged magnetic coupling of the Fe
atoms. Exceptionally large variations of the induced spin and orbital moments at the
Pt atoms are found as a function of concentration and magnetic order. Along with
a violation of the third Hund’s rule at the Fe sites, these variations result in a non
trivial behavior of the MAE.
In the case of TM impurities and dimers at the Cu(111), the effects of surface charging
and applied EFs on the magnetic properties and substrate-mediated magnetic interactions have been investigated. The modifications of the surface electronic structure, impurity local moments and magnetic exchange coupling as a result of the EF-induced metallic screening and charge rearrangements are analysed. In a ﬁrst study, the properties of surface substitutional Co and Fe impurities are investigated as a function of
the external charge per surface atom q. At large inter-impurity distances the effective magnetic exchange coupling ∆E between impurities shows RKKY-like oscillations
as a function of the distance which are not signiﬁcantly affected by the considered values of q. For distances r < 10 Å, important modifications in the magnitude of ∆E, involving changes from FM to AF coupling, are found depending non-monotonously on the value and polarity of q. The interaction energies are analysed from a local perspective. In a second study, the interplay between external EF effects, internal magnetic order and substrate-mediated magnetic coupling has been investigated for Mn dimers on Cu(111). Our calculations show that EF (∼ 1eV/Å) can induce a switching from AF to FM ground-state magnetic order within single Mn dimers. The relative coupling between a pair of dimers also shows RKKY-like oscillations as a function of the inter-dimer distance. Their effective magnetic exchange interaction
is found to depend significantly on the magnetic order within the Mn dimers and on
their relative orientation on the surface. The dependence of the substrate-mediated
interaction on the magnetic state of the dimers is qualitatively explained in terms
of the differences in the scattering of surface electrons. At short inter-dimer distances, the ground-state conﬁguration is determined by an interplay between exchange interactions and EF effects. These results demonstrate that external surface charging and applied EFs offer remarkable possibilities of manipulating the sign and strength of the magnetic coupling of surface supported nanoparticles.