DOCSLIB.ORG

Spin and Orbital Contributions to the Magnetic Moment of Transition Metal Clusters and Complexes

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spin and Orbital Contributions to the Magnetic Moment of Transition Metal Clusters and Complexes Technische Universität Kaiserslautern Fachbereich Chemie SPIN AND ORBITAL CONTRIBUTIONS TO THE MAGNETIC MOMENT OF TRANSITION METAL CLUSTERS AND COMPLEXES Am Fachbereich Chemie der Technischen Universität Kaiserslautern zur Erlangung des akademischen Grades "Doktor der Naturwissenschaften" genehmigte Dissertation (D386) vorgelegt von Dipl.-Chem. Jennifer Meyer Betreuer: Prof. Dr. G. Niedner-Schatteburg Tag der wissenschaftlichen Aussprache: 10. Juli 2014 Technische Universität Kaiserslautern Der experimentelle Teil der vorliegenden Arbeit wurde in der Zeit von November 2009 bis April 2014 im Fachbereich Chemie der Technischen Universität Kaiserslautern unter der Betreuung von Prof. Dr. G. Niedner-Schatteburg angefertigt. Datum des Antrags der Eröffnung des Promotionsverfahrens: 07.05.2014 Tag der wissenschaftlichen Aussprache: 10.07.2014 Promotionskommission: Vorsitzender Prof. Dr. W. Thiel 1. Berichterstatter Prof. Dr. G. Niedner-Schatteburg 2. Berichterstatter Prof. Dr. M. Gerhards für meine Familie Magnetes Geheimnis, erklär mir das! Kein größer Geheimnis als Lieb' und Hass. The magnet's mystery, explain that to me! No greater mystery but love and hate. Johann Wolfgang von Goethe CONTENT 1. Introduction ........................................................................................................................................................................................ 1 1.1 References ................................................................................................................................................................................. 4 2. Theoretical background ............................................................................................................................................................ 11 2.1 Classification of magnetic materials ......................................................................................................................... 11 2.1.1 Diamagnetism ......................................................................................................................................................... 12 2.1.2 Paramagnetism ...................................................................................................................................................... 12 2.1.3 Collective magnetism .......................................................................................................................................... 13 2.1.3.1 Ferromagnetism ................................................................................................................................... 14 2.1.3.2 Ferrimagnetism ..................................................................................................................................... 14 2.1.3.3 Antiferromagnetism ........................................................................................................................... 14 2.2 Magnetism of 3d transition metals ........................................................................................................................... 15 2.2.1 Magnetic domains ................................................................................................................................................ 18 2.3 Magnetism of nanoparticles and clusters ............................................................................................................. 19 2.3.1 Superparamagnetic ensemble ....................................................................................................................... 19 2.3.2 Magnetic moment of free clusters .............................................................................................................. 20 2.3.2.1 The Stern-Gerlach experiment ..................................................................................................... 20 2.3.2.2 Enhanced magnetic moments in small clusters .................................................................. 22 2.4 X-ray magnetic circular dichroism (XMCD) ........................................................................................................... 23 2.4.1 X-ray absorption .................................................................................................................................................... 23 2.4.2 Dipole selection rules ......................................................................................................................................... 26 2.4.3 Origin of the x-ray magnetic circular dichroism (XMCD) effect ................................................... 27 2.4.4 Sum rules ................................................................................................................................................................... 30 2.4.4.1 Intensity sum rule ................................................................................................................................ 30 2.4.4.2 Spin and orbital sum rule ................................................................................................................ 32 2.4.5 Summary of the XMCD effect ......................................................................................................................... 33 2.5 References .............................................................................................................................................................................. 34 3. Experimental methods - the GAMBIT setup ................................................................................................................. 37 3.1 Experimental setup ............................................................................................................................................................ 38 I 3.1.1 Laser vaporization source ................................................................................................................................. 38 3.1.2 Fourier Transform - Ion Cyclotron Resonance (FT-ICR) mass spectrometry ......................... 39 3.1.3 FT-ICR mass spectrometer with cryogenic trap .................................................................................... 42 3.1.4 Synchrotron radiation......................................................................................................................................... 44 3.1.5 Total Ion Yield spectroscopy of isolated clusters ................................................................................. 46 3.1.6 Collisional cooling ................................................................................................................................................. 49 3.2 Data acquisition & analysis ............................................................................................................................................ 51 3.2.1 Data acquisition ..................................................................................................................................................... 51 3.2.2 Data analysis ............................................................................................................................................................ 56 3.2.3 Application of sum rules.................................................................................................................................... 56 3.2.4 Scaling of experimental magnetic moments .......................................................................................... 59 3.3 References .............................................................................................................................................................................. 64 3.4 Supplement ............................................................................................................................................................................ 67 3.4.1 Publication - J. Electron Spectroscopy and related Phenomena, 2011, 184, 113 .............. 67 3.4.1.0 Abstract ..................................................................................................................................................... 68 3.4.1.1 Introduction ............................................................................................................................................ 69 3.4.1.2 Experimental setup ............................................................................................................................. 70 3.4.1.3 Results and discussion ...................................................................................................................... 74 3.4.1.4 Summary .................................................................................................................................................. 79 3.4.1.5 Acknowledgement .............................................................................................................................. 80 3.4.1.6 References ............................................................................................................................................... 80 3.4.2 Draft - J. Electron Spectroscopy and related Phenomena, 2014, accepted .......................... 81 3.4.2.0 Abstract ..................................................................................................................................................... 82 3.4.2.1 Introduction ...........................................................................................................................................
Load more

Recommended publications
  • Flat Band Moirés
    European Physical Society Condensed Matter Division Flat Band Moirés Leni Bascones1, Dmitri Efetov2, Johannes Lischner3 1 Instituto de Ciencia de Materiales de Madrid, ICMM-CSIC 2 Institute of Photonic Sciences ICFO 3 Imperial College London Wednesday, September, 2nd 9:30-10:10 Correlated, insulating and superconducting States in twisted bilayer graphene Below the Magic Angle. Jeanie Lau (invited). 10:10-10:30 Flat band superconductivity in twisted bilayer graphene. Tero Heikkilä, T. Peltonen, A. Julku, R. Ojajärvi, L. Long, P. Törmä. 10:30-10:50 Band structure and insulating states driven by the Coulomb interactions in twisted bilayer graphene. Tommaso Cea, F. Guinea. 10:50-11:10 Interactions in magic-angle twisted bilayer graphene. María José Calderón, E. Bascones. 11:10-11:30 Evidence of weakly dispersive bands in twisted bilayer graphene from nano-ARPES. Simone Lisi, X. Lu, T. Benschop, T. A. de Jong, P. Stepanov, J. R. Duran, Fl. Margot, I. Cucchi, E. Cappelli, A. Hunter, A. Tamai, V. Kandyba, A. Giampietri, A. Barinov, Johannes Jobst, Vincent Stalman, M. Leeuwenhoek, K. Watanabe, T. Taniguchi, L. Rademaker, S. J. van der Molen, M. Allan, D. K. Efetov, F. Baumberger. 11:30-11:50 Marginal Fermi liquid in twisted bilayer graphene José González, T. Stauber. 11:50-12:10 Inconmensurability induced sub-ballistic states in twisted bilayer graphene. Miguel de Jesús Mestre Gonçalves, H. Z. Olyaei1, B. Amorim, R. Mondaini, P. Ribeiro, E. V. Castro. 12:10-12:30 Strain induced excitonic instability in twisted bilayer graphene. Héctor Ochoa. Thursday, September 3rd 9:30-10:10 Moiré physics and symmetry breaking in magnetically encapsulated van der Waals structures.
    [Show full text]
  • Performance Best Practices for Vmware Workstation Vmware Workstation 7.0
    Performance Best Practices for VMware Workstation VMware Workstation 7.0 This document supports the version of each product listed and supports all subsequent versions until the document is replaced by a new edition. To check for more recent editions of this document, see http://www.vmware.com/support/pubs. EN-000294-00 Performance Best Practices for VMware Workstation You can find the most up-to-date technical documentation on the VMware Web site at: http://www.vmware.com/support/ The VMware Web site also provides the latest product updates. If you have comments about this documentation, submit your feedback to: [email protected] Copyright © 2007–2009 VMware, Inc. All rights reserved. This product is protected by U.S. and international copyright and intellectual property laws. VMware products are covered by one or more patents listed at http://www.vmware.com/go/patents. VMware is a registered trademark or trademark of VMware, Inc. in the United States and/or other jurisdictions. All other marks and names mentioned herein may be trademarks of their respective companies. VMware, Inc. 3401 Hillview Ave. Palo Alto, CA 94304 www.vmware.com 2 VMware, Inc. Contents About This Book 5 Terminology 5 Intended Audience 5 Document Feedback 5 Technical Support and Education Resources 5 Online and Telephone Support 5 Support Offerings 5 VMware Professional Services 6 1 Hardware for VMware Workstation 7 CPUs for VMware Workstation 7 Hyperthreading 7 Hardware-Assisted Virtualization 7 Hardware-Assisted CPU Virtualization (Intel VT-x and AMD AMD-V)
    [Show full text]
  • Chapter 1. Origins of Mac OS X
    1 Chapter 1. Origins of Mac OS X "Most ideas come from previous ideas." Alan Curtis Kay The Mac OS X operating system represents a rather successful coming together of paradigms, ideologies, and technologies that have often resisted each other in the past. A good example is the cordial relationship that exists between the command-line and graphical interfaces in Mac OS X. The system is a result of the trials and tribulations of Apple and NeXT, as well as their user and developer communities. Mac OS X exemplifies how a capable system can result from the direct or indirect efforts of corporations, academic and research communities, the Open Source and Free Software movements, and, of course, individuals. Apple has been around since 1976, and many accounts of its history have been told. If the story of Apple as a company is fascinating, so is the technical history of Apple's operating systems. In this chapter,[1] we will trace the history of Mac OS X, discussing several technologies whose confluence eventually led to the modern-day Apple operating system. [1] This book's accompanying web site (www.osxbook.com) provides a more detailed technical history of all of Apple's operating systems. 1 2 2 1 1.1. Apple's Quest for the[2] Operating System [2] Whereas the word "the" is used here to designate prominence and desirability, it is an interesting coincidence that "THE" was the name of a multiprogramming system described by Edsger W. Dijkstra in a 1968 paper. It was March 1988. The Macintosh had been around for four years.
    [Show full text]
  • Zenon Manual Programming Interfaces
    zenon manual Programming interfaces v.7.11 ©2014 Ing. Punzenberger COPA-DATA GmbH All rights reserved. Distribution and/or reproduction of this document or parts thereof in any form are permitted solely with the written permission of the company COPA-DATA. The technical data contained herein has been provided solely for informational purposes and is not legally binding. Subject to change, technical or otherwise. Contents 1. Welcome to COPA-DATA help ...................................................................................................... 6 2. Programming interfaces ............................................................................................................... 6 3. Process Control Engine (PCE) ........................................................................................................ 9 3.1 The PCE Editor ............................................................................................................................................. 9 3.1.1 The Taskmanager ....................................................................................................................... 10 3.1.2 The editing area .......................................................................................................................... 10 3.1.3 The output window .................................................................................................................... 11 3.1.4 The menus of the PCE Editor .....................................................................................................
    [Show full text]
  • 1 Introduction 2 Spins As Quantized Magnetic Moments
    Spin 1 Introduction For the past few weeks you have been learning about the mathematical and algorithmic background of quantum computation. Over the course of the next couple of lectures, we'll discuss the physics of making measurements and performing qubit operations in an actual system. In particular we consider nuclear magnetic resonance (NMR). Before we get there, though, we'll discuss a very famous experiment by Stern and Gerlach. 2 Spins as quantized magnetic moments The quantum two level system is, in many ways, the simplest quantum system that displays interesting behavior (this is a very subjective statement!). Before diving into the physics of two-level systems, a little on the history of the canonical example: electron spin. In 1921, Stern proposed an experiment to distinguish between Larmor's classical theory of the atom and Sommerfeld's quantum theory. Each theory predicted that the atom should have a magnetic moment (i.e., it should act like a small bar magnet). However, Larmor predicted that this magnetic moment could be oriented along any direction in space, while Sommerfeld (with help from Bohr) predicted that the orientation could only be in one of two directions (in this case, aligned or anti-aligned with a magnetic field). Stern's idea was to use the fact that magnetic moments experience a linear force when placed in a magnetic field gradient. To see this, not that the potential energy of a magnetic dipole in a magnetic field is given by: U = −~µ · B~ Here, ~µ is the vector indicating the magnitude and direction of the magnetic moment.
    [Show full text]
  • Spin the Evidence of Intrinsic Angular Momentum Or Spin and Its
    Spin The evidence of intrinsic angular momentum or spin and its associated magnetic moment came through experiments by Stern and Gerlach and works of Goudsmit and Uhlenbeck. The spin is called intrinsic since, unlike orbital angular momentum which is extrinsic, it is carried by point particle in addition to its orbital angular momentum and has nothing to do with motion in space. The magnetic moment ~µ of silver atom was measured in 1922 experiment by Stern and Gerlach and its projection µz in the direction of magnetic fieldz ^ B (through which the silver beam was passed) was found to be just −|~µj and +j~µj instead of continuously varying between these two as limits. Classically, magnetic moment is proportional to the angular momentum (12) and, assuming this proportionality to survive in quantum mechanics, quan- tization of magnetic moment leads to quantization of corresponding angular momentum S, which we called spin, q q µ = g S ) µ = g ~ m (57) z 2m z z 2m s as is the case with orbital angular momentum, where the ratio q=2m is called Bohr mag- neton, µb and g is known as Lande-g factor or gyromagnetic factor. The g-factor is 1 for orbital angular momentum and hence corresponding magnetic moment is l µb (where l is integer orbital angular momentum quantum number). A surprising feature here is that spin magnetic moment is also µb instead of µb=2 as one would naively expect. So it turns out g = 2 for spin { an effect that can only be understood if linearization of Schr¨odinger equation is attempted i.e.
    [Show full text]
  • Operating System Architectures
    Operating System Architectures • Learning objectives: • Explain how OS functionality is orthogonal to where you place services relative to processor modes. • Describe some alternative ways to structure the operating system. • Operating systems evolve over time, but that evolution is frequently in terms of their architecture: how they structure functionality relative to protection boundaries. • We’ll review some of the basic architectures: • Executives • Monolithic kernels • Micro kernels • Exo kernels • Extensible operating systems 2/3/15 CS161 Spring 2015 1 OS Executives • Think MS-DOS: With no hardware protection, the OS is simply a set of services: • Live in memory • Applications can invoke them • Requires a software trap to invoke them. • Live in same address space as application 1-2-3 QBasic WP Applications Command Software Traps Operating System routlines 2/3/15 CS161 Spring 2015 2 Monolithic Operating System • Traditional architecture • Applications and operating system run in different address spaces. • Operating system runs in privileged mode; applications run in user mode. Applications Operating System file system processes networking Device drivers virtual memory 2/3/15 CS161 Spring 2015 3 Microkernels (late 80’s and on) • Put as little of OS as possible in privileged mode (the microkernel). • Implement most core OS services as user-level servers. • Only microkernel really knows about hardware • File system, device drivers, virtual memory all implemented in unprivileged servers. • Must use IPC (interprocess communication) to communicate among different servers. Applications Process Virtual management memory file system networking Microkernel 2/3/15 CS161 Spring 2015 4 Microkernels: Past and Present • Much research and debate in late 80’s early 90’s • Pioneering effort in Mach (CMU).
    [Show full text]
  • 7. Examples of Magnetic Energy Diagrams. P.1. April 16, 2002 7
    7. Examples of Magnetic Energy Diagrams. There are several very important cases of electron spin magnetic energy diagrams to examine in detail, because they appear repeatedly in many photochemical systems. The fundamental magnetic energy diagrams are those for a single electron spin at zero and high field and two correlated electron spins at zero and high field. The word correlated will be defined more precisely later, but for now we use it in the sense that the electron spins are correlated by electron exchange interactions and are thereby required to maintain a strict phase relationship. Under these circumstances, the terms singlet and triplet are meaningful in discussing magnetic resonance and chemical reactivity. From these fundamental cases the magnetic energy diagram for coupling of a single electron spin with a nuclear spin (we shall consider only couplings with nuclei with spin 1/2) at zero and high field and the coupling of two correlated electron spins with a nuclear spin are readily derived and extended to the more complicated (and more realistic) cases of couplings of electron spins to more than one nucleus or to magnetic moments generated from other sources (spin orbit coupling, spin lattice coupling, spin photon coupling, etc.). Magentic Energy Diagram for A Single Electron Spin and Two Coupled Electron Spins. Zero Field. Figure 14 displays the magnetic energy level diagram for the two fundamental cases of : (1) a single electron spin, a doublet or D state and (2) two correlated electron spins, which may be a triplet, T, or singlet, S state. In zero field (ignoring the electron exchange interaction and only considering the magnetic interactions) all of the magnetic energy levels are degenerate because there is no preferred orientation of the angular momentum and therefore no preferred orientation of the magnetic moment due to spin.
    [Show full text]
  • Access Control for the SPIN Extensible Operating System
    Access Control for the SPIN Extensible Operating System Robert Grimm Brian N. Bershad Dept. of Computer Science and Engineering University of Washington Seattle, WA 98195, U.S.A. Extensible systems, such as SPIN or Java, raise new se- on extensions and threads, are enforced at link time (when curity concerns. In these systems, code can be added to a an extension wants to link against other extensions) and at running system in almost arbitrary fashion, and it can inter- call time (when a thread wants to call an extension). Ac- act through low latency (but type safe) interfaces with other cess restrictions on objects are enforced by the extension code. Consequently, it is necessary to devise and apply that provides an object’s abstraction (if an extension is not security mechanisms that allow the expression of policies trusted to enforce access control on its objects but is ex- controlling an extension’s access to other extensions and its pected to do so, DTE can be used to prevent other exten- ability to extend, or override, the behavior of already exist- sions from linking against the untrusted extension). ing services. In the SPIN operating system [3, 4] built at the Due to the fine grained composition of extensions in University of Washington, we are experimenting with a ver- SPIN, it is important to minimize the performance overhead sion of domain and type enforcement (DTE) [1, 2] that has of call time access control. We are therefore exploring opti- been extended to address the security concerns of extensible mization that make it possible to avoid some dynamic ac- systems.
    [Show full text]
  • Relativistic Theory of Laser-Induced Magnetization Dynamics
    Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1558 Relativistic theory of laser-induced magnetization dynamics RITWIK MONDAL ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-513-0070-2 UPPSALA urn:nbn:se:uu:diva-315247 2017 Dissertation presented at Uppsala University to be publicly examined in Polhemsalen, Lägerhyddsvägen 1, Uppsala, Friday, 27 October 2017 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Paul- Antoine Hervieux (Université de Strasbourg). Abstract Mondal, R. 2017. Relativistic theory of laser-induced magnetization dynamics. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1558. 115 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0070-2. Ultrafast dynamical processes in magnetic systems have become the subject of intense research during the last two decades, initiated by the pioneering discovery of femtosecond laser-induced demagnetization in nickel. In this thesis, we develop theory for fast and ultrafast magnetization dynamics. In particular, we build relativistic theory to explain the magnetization dynamics observed at short timescales in pump-probe magneto-optical experiments and compute from first-principles the coherent laser-induced magnetization. In the developed relativistic theory, we start from the fundamental Dirac-Kohn-Sham equation that includes all relativistic effects related to spin and orbital magnetism as well as the magnetic exchange interaction and any external electromagnetic field. As it describes both particle and antiparticle, a separation between them is sought because we focus on low-energy excitations within the particle system. Doing so, we derive the extended Pauli Hamiltonian that captures all relativistic contributions in first order; the most significant one is the full spin- orbit interaction (gauge invariant and Hermitian).
    [Show full text]
  • Magnetism of Atoms and Ions
    Magnetism of Atoms and Ions Wulf Wulfhekel Physikalisches Institut, Karlsruhe Institute of Technology (KIT) Wolfgang Gaede Str. 1, D-76131 Karlsruhe 1 0. Overview Literature J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, 628 pages (2010). Very detailed Stephen J. Blundell, Magnetism in Condensed Matter, Oxford University Press, 256 pages (2001). Easy to read, gives a condensed overview C. Kittel, Introduction to Solid State Physics, John Whiley and Sons (2005). Solid state aspects 2 0. Overview Chapters of the two lectures 1. A quick refresh of quantum mechanics 2. The Hydrogen problem, orbital and spin angular momentum 3. Multi electron systems 4. Paramagnetism 5. Dynamics of magnetic moments and EPR 6. Crystal fields and zero field splitting 7. Magnetization curves with crystal fields 3 1. A quick refresh of quantum mechanics The equation of motion The Hamilton function: with T the kinetic energy and V the potential, q the positions and p the momenta gives the equations of motion: Hamiltonian gives second order differential equation of motion and thus p(t) and q(t) Initial conditions needed for Classical equations need information on the past! t p q 4 1. A quick refresh of quantum mechanics The Schrödinger equation Quantum mechanics replacement rules for Hamiltonian: Equation of motion transforms into Schrödinger equation: Schrödinger equation operates on wave function (complex field in space) and is of first order in time. Absolute square of the wave function is the probability density to find the particle at selected position and time. t Initial conditions needed for Schrödinger equation does not need information on the past! How is that possible? We know that the past influences the present! q 5 1.
    [Show full text]
  • Designing a Concurrent File Server
    Communicating Process Architectures 2012 1 P.H. Welch et al. (Eds.) Open Channel Publishing Ltd., 2012 c 2012 The authors and Open Channel Publishing Ltd. All rights reserved. Designing a Concurrent File Server James WHITEHEAD II Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom; [email protected] Abstract. In this paper we present a design and architecture for a concurrent file sys- tem server. This architecture is a compromise between the fully concurrent V6 UNIX implementation, and the simple sequential implementation in the MINIX operating system. The design of the server is made easier through the use of a disciplined model of concurrency, based on the CSP process algebra. By viewing the problem through this restricted lens, without traditional explicit locking mechanisms, we can construct the system as a process network of components with explicit connections and depen- dencies. This provides us with insight into the problem domain, and allows us to anal- yse the issues present in concurrent file system implementation. Keywords. file system, Go, CSP, UNIX, MINIX. Introduction Modern operating systems allow multiple users and programs to share the computing re- sources on a single machine. They also serve as an intermediary between programs and the physical computing hardware, such as persistent storage devices. In the UNIX family of op- erating systems, disk access is accomplished by interacting with files and directories through a hierarchical file system, using system calls. Managing access to the file system in a concurrent environment is a challenging problem. An implementation must ensure that a program cannot corrupt the state of the file system, or the data stored on disk.
    [Show full text]