The purpose of this work is to reveal the governing mechanisms responsible for the magnetic field-induced i) martensite reorientation in Ni2MnGa single crystals, ii) stress-assisted phase transformation in Ni2MnGa single crystals and iii) phase transformation in NiMnCoIn alloys. The ultimate goal of utilizing these mechanisms is to increase the actuation stress levels in magnetic shape memory alloys (MSMAs). Extensive experimental work on magneto-thermo-mechanical (MTM) characterization of these materials enabled us to i) better understand the ways to increase the actuation stress and strain and decrease the required magnetic field for actuation in MSMAs, ii) determine the effects of main MTM parameters on reversible magnetic field induced phase transformation, such as magnetocrystalline anisotropy energy (MAE), Zeeman energy (ZE), stress hysteresis, thermal hysteresis, critical stress for the stress induced phase transformation and crystal orientation, iii) find out the feasibility of employing polycrystal MSMAs, and iv) formulate a thermodynamical framework to capture the energetics of magnetic field-induced phase transformations in MSMAs. Magnetic shape memory properties of Ni2MnGa single crystals were characterized by monitoring magnetic field-induced strain (MFIS) as a function of compressive stress and stress-induced strain as a function of magnetic field. It is revealed that the selection of the operating temperature with respect to martensite start and Curie temperatures is critical in optimizing actuator performance. The actuation stress of 5 MPa and work output of 157 kJm−3 are obtained by the field-induced variant reorientation in NiMnGa alloys. Reversible and one-way stress-assisted field-induced phase transformations are observed in Ni2MnGa single crystals under low field magnitudes (<0.7T) and resulted in at least an order of magnitude higher actuation stress levels. It is very promising to provide higher work output levels and operating temperatures than variant reorientation mechanisms in NiMnGa alloys. Reversible field-induced phase transformation and shape memory characteristics of NiMnCoIn single crystals are also studied. Reversible field-induced phase transformation is observed only under high magnetic fields (>4T). Necessary magnetic and mechanical conditions, and materials design and selection guidelines are proposed to search for field-induced phase transformation in other ferromagnetic materials that undergo thermoelastic martensitic phase transformation.

The purpose of this work is to reveal the governing mechanisms responsible for the magnetic field-induced i) martensite reorientation in Ni2MnGa single crystals, ii) stress-assisted phase transformation in Ni2MnGa single crystals and iii) phase transformation in NiMnCoIn alloys. The ultimate goal of utilizing these mechanisms is to increase the actuation stress levels in magnetic shape memory alloys (MSMAs). Extensive experimental work on magneto-thermo-mechanical (MTM) characterization of these materials enabled us to i) better understand the ways to increase the actuation stress and strain and decrease the required magnetic field for actuation in MSMAs, ii) determine the effects of main MTM parameters on reversible magnetic field induced phase transformation, such as magnetocrystalline anisotropy energy (MAE), Zeeman energy (ZE), stress hysteresis, thermal hysteresis, critical stress for the stress induced phase transformation and crystal orientation, iii) find out the feasibility of employing polycrystal MSMAs, and iv) formulate a thermodynamical framework to capture the energetics of magnetic field-induced phase transformations in MSMAs. Magnetic shape memory properties of Ni2MnGa single crystals were characterized by monitoring magnetic field-induced strain (MFIS) as a function of compressive stress and stress-induced strain as a function of magnetic field. It is revealed that the selection of the operating temperature with respect to martensite start and Curie temperatures is critical in optimizing actuator performance. The actuation stress of 5 MPa and work output of 157 kJm−3 are obtained by the field-induced variant reorientation in NiMnGa alloys. Reversible and one-way stress-assisted field-induced phase transformations are observed in Ni2MnGa single crystals under low field magnitudes (<0.7T) and resulted in at least an order of magnitude higher actuation stress levels. It is very promising to provide higher work output levels and operating temperatures than variant reorientation mechanisms in NiMnGa alloys. Reversible field-induced phase transformation and shape memory characteristics of NiMnCoIn single crystals are also studied. Reversible field-induced phase transformation is observed only under high magnetic fields (>4T). Necessary magnetic and mechanical conditions, and materials design and selection guidelines are proposed to search for field-induced phase transformation in other ferromagnetic materials that undergo thermoelastic martensitic phase transformation.

The large magneto-crystalline anisotropy energy of the L10 phase has pushed the interest to the FePt nanoparticles to get smallest possible not superparamagnetic particles for magnetic data storage media. The DC magnetron sputtering process, in an inert gas atmosphere and subsequently ejection into high vacuum via differential pumping in addition with a newly constructed light furnace, allows us to have a predeposition annealing of FePt nanoparticles. The advantage compared to wet chemical process route is, that we can prevent the growing of particles on a substrate. In order to determine the experimentally hardly accessible temperature of the particles, the thermal history of the particles is rather calculated from the interaction with the light field along the flight path through the light furnace used for the in-flight annealing. The results obtained for the particle temperature are corroborated by experimental findings on the sintering of agglomerated particles and change in magnetic properties due to heating over the L10 stability temperature. The experiments reveal that the effect of the thermal treatment on both the structural and magnetic properties of the FePt nanoparticles strongly depends on the particles’ crystal structure. The magnetic behavior shows a size depending effective uniaxial magnetic anisotropy constant. This behavior is strongly correlated to the structure of the 5 nm to 8 nm L10 FePt particle.

Mit Hilfe der Dichtefunktionaltheorie wurden magnetische Eigenschaften an 3d Elementen und Legierungen und 5f Verbindungen untersucht. Dabei wurde auf die Wichtigkeit von Orbitalpolarisationskorrekturen eingegangen und diese näher erörtert. Im ersten Anwendungsteil wurden magnetische Momente und die Magnetokristalline Anisotropie Energie an 3d Elementen untersucht. Des Weiteren wurden FeCo Legierungen als mögliche Bestandteile in der Festplattenindustrie diskutiert. Im letzten Abschnitt wurden Uranverbindungen in Hinsicht auf Ihre Orbitalpolarisation untersucht.

Mit Hilfe der Dichtefunktionaltheorie wurden magnetische Eigenschaften an 3d Elementen und Legierungen und 5f Verbindungen untersucht. Dabei wurde auf die Wichtigkeit von Orbitalpolarisationskorrekturen eingegangen und diese näher erörtert. Im ersten Anwendungsteil wurden magnetische Momente und die Magnetokristalline Anisotropie Energie an 3d Elementen untersucht. Des Weiteren wurden FeCo Legierungen als mögliche Bestandteile in der Festplattenindustrie diskutiert. Im letzten Abschnitt wurden Uranverbindungen in Hinsicht auf Ihre Orbitalpolarisation untersucht.:1 Introduction 1 2 Theoretical Considerations 5 2.1 Quantum Mechanics Applied to Solids . . . . . . . . . . . . . . . 6 2.2 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 non-Relativistic DFT . . . . . . . . . . . . . . . . . . . . 7 2.2.1.1 Hohenberg and Kohn . . . . . . . . . . . . . . . 7 2.2.1.2 Kohn-Sham Equations . . . . . . . . . . . . . . 10 2.2.1.3 Local Density Approximation and More . . . . 12 2.2.2 Relativistic DFT . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 FPLO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Magneto-Crystalline Anisotropy Energy . . . . . . . . . . . . . . 18 2.5 Disorder within DFT . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Orbital Polarisation in DFT 23 3.1 Hund’s Rules in DFT . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 An Introduction to OPC and DFT . . . . . . . . . . . . . . . . . 25 3.2.1 OPC Brooks . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.2 OPC Eschrig . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Transition Metals 39 4.1 Fe, Co, and Ni . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.1.1 Calculational Details . . . . . . . . . . . . . . . . . . . . 40 4.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.2 Fe1−xCox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.2.2 Fixed Spin Moment Calculations . . . . . . . . . . . . . . 50 4.2.3 Epitaxial Bain Path . . . . . . . . . . . . . . . . . . . . . 51 4.2.4 Calculational Details . . . . . . . . . . . . . . . . . . . . 54 4.2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.6 LSDA vs. GGA . . . . . . . . . . . . . . . . . . . . . . . 69 4.2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5 Uranium Compounds 75 5.1 UX, with X = (N, P, As, Sb, O, S, Se, and Te) . . . . . . . . 77 5.1.1 UN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.1.2 UX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 UM2, with M = (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) 90 5.2.1 Calculational Details . . . . . . . . . . . . . . . . . . . . 90 5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.3 UAsSe, USb2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.3.1 Calculational Details . . . . . . . . . . . . . . . . . . . . 97 5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6 Summary and Outlook 101 A Definitions i A.1 Spherical Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . i A.2 Other Definitions Used in Text . . . . . . . . . . . . . . . . . . . ii B Input Parameters for the Racah Parameter iii B.1 d-Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii B.2 f-Shells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Biblography vi Acknowledgement xxiv Versicherung xxvii

Magnetic materials have many applications in technology. The magnetic properties of materials are therefore important to catalogue for future use. In this project, the magnetic properties of thin films of permalloy are investigated. Specifically, the goal is to find the perpendicular magnetic anisotropy energy (PMAE) of thin film geometries of permalloy of varying film thickness. The PMAE is computed with powerful parallel computers using density functional theory (DFT) as implemented in the open-source DFT package OpenMX. The project consists of two parts: Computations on the bulk system and computations on six thin film systems of varying thickness. The thin films are periodic in the basal plane (the permalloy has a tetragonal crystal structure). The easy axis of magnetization was found to be along the c-axis of the tetragonal structure, both for bulk and thin film geometries. For the thin film geometries, this corresponds to an out-of-plane easy axis. The PMAE of the thinnest thin film geometries (4-5 atomic layers) were several times greater than that of the bulk system. Thin films with one more layer of Fe than Ni have especially great PMAE. When comparing the results to another study, the magnetocrystalline anisotropy as computed in this project turned out to be more than two orders of magnitude greater than in the previous study. It is hypothesised that this is because of the differing crystal structure of permalloy used in the study.

The large magneto-crystalline anisotropy energy of the L10 phase has pushed the interest to the FePt nanoparticles to get smallest possible not superparamagnetic particles for magnetic data storage media. The DC magnetron sputtering process, in an inert gas atmosphere and subsequently ejection into high vacuum via differential pumping in addition with a newly constructed light furnace, allows us to have a predeposition annealing of FePt nanoparticles. The advantage compared to wet chemical process route is, that we can prevent the growing of particles on a substrate. In order to determine the experimentally hardly accessible temperature of the particles, the thermal history of the particles is rather calculated from the interaction with the light field along the flight path through the light furnace used for the in-flight annealing. The results obtained for the particle temperature are corroborated by experimental findings on the sintering of agglomerated particles and change in magnetic properties due to heating over the L10 stability temperature. The experiments reveal that the effect of the thermal treatment on both the structural and magnetic properties of the FePt nanoparticles strongly depends on the particles’ crystal structure. The magnetic behavior shows a size depending effective uniaxial magnetic anisotropy constant. This behavior is strongly correlated to the structure of the 5 nm to 8 nm L10 FePt particle.:Einleitung 1 Grundlagen 1.1 Eisen-Platin Nanopartikel 1.1.1 Das System Eisen-Platin 1.1.2 Die A1 - L10 Phasenumwandlung 1.1.3 Größeneinflüsse auf Phasenstabilität und strukturelle Allotropie 1.2 Magnetische Eigenschaften 1.2.1 Magnetokristalline Anisotropieenergie 1.2.2 Ummagnetisierungsverhalten nach Stoner-Wohlfarth (SW) 1.2.3 Ummagnetisierungsverhalten mit kubischer Anisotropie 1.2.4 Skalierungseffekte - Superparamagnetismus 1.2.5 Magnetische Wechselwirkungen zwischen Partikeln 1.3 Nanopartikelentstehung und Thermodynamik der Phasenbildung 1.3.1 Nukleation von Nanopartikeln aus der Gasphase 1.3.2 Partikelwachstum 1.4 Definition der Fragestellung 2 Experimentelles und Methoden 2.1 Das Nanopartikel-Depositions-System 2.2 Konstruktion und Aufbau des Lichtofens 2.2.1 Vermessung der Lichtofenleistung 2.2.2 Justage des Lichtofens 2.3 Optische Wärmebehandlung von Nanopartikeln 2.3.1 Wärmeströme 2.3.2 Absorptionsquerschnitt 2.3.3 Dielektrische Funktion 2.3.4 Schwarzkörperstrahlung 2.3.4.1 Beschreibung des Spektrums von Halogenlampen 2.3.4.2 Abstrahlungsleistung von Nanopartikeln 2.4 Berechnung der Partikeltemperatur 2.4.1 Optische Konstanten für L10-FePt Nanopartikel 2.4.2 Strahlungsverhalten freier Partikel 2.4.3 Numerische Berechnung der Partikelgeschwindigkeit 2.4.4 Experimentelle Bestimmung der Wärmekapazität von FePt 2.4.5 Bestimmung der Partikeltemperatur durch iterative Integration 2.4.6 Zusammenfassende Bewertung zum Optischen Heizen 2.5 Charakterisierung mittels TEM- und HRTEM-Analysen 2.5.1 Bestimmung der Größenverteilung 2.5.2 Bestimmung des Agglomerationsgrades 2.5.3 Auswertung der Kristallstruktur mittels HRTEM 2.6 Magnetisierungsmessungen 2.6.1 Magnetische Charakterisierung mittels VSM-Messungen 2.6.2 Messung der Hysterese-Schleife 2.6.3 Remanenzanalyse 3 Sintern von Partikeln 3.1 Optisches Heizen im Flug 3.2 Diskussion 4 Optimierung der Herstellungsparameter anhand HRTEM-Strukturanalyse 4.1 Einzelpartikel 4.1.1 Ungeheizte Einzelpartikel 4.1.2 Geheizte Einzelpartikel 4.2 Partikel-Agglomerate 4.2.1 Ungeheizte Agglomerate 4.2.2 Geheizte Agglomerate mit hohem Targetalter 4.2.3 Geheizte Agglomerate mit geringem Targetalter 4.3 Diskussion 5 Magnetische Eigenschaften geheizter Partikel 5.1 Einfluss der Wärmebehandlung auf die magnetische Hysterese 5.1.1 Überheizen kleiner Partikel 5.1.2 Überheizen großer Partikel 5.2 Magnetisierungsprozess 5.2.1 Messung des Remanenzverhaltens kleiner und großer Partikel 5.2.2 Temperaturabhängigkeit der Schaltfeldverteilung 5.3 Diskussion 6 Korrelation der effektiven Anisotropie mit der Partikelgrößenverteilung 6.1 Bestimmung der effektiven uniaxialen und kubischen Anisotropieverteilung 6.2 Korrelation der Partikelgröße mit der Anisotropie für kleine Partikel 6.3 Korrelation der Partikelgröße mit der Anisotropie für große Partikel 6.4 Diskussion 7 Zusammenfassung Literaturverzeichnis