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Effect of microstructure on the magnetic properties of transition metal implanted TiO2 filmsYildirim, Oguz 07 March 2016 (has links) (PDF)
The combined electronic, optic and magnetic properties of transition metal (TM) implanted ferromagnetic TiO2 is of interest for spintronic applications. The nature of the observed abundant ferromagnetism in such materials has been investigated for more than one and a half decades, yet still no clear explanation for its appearance can be given.
In this thesis, the origin of the ferromagnetic order in TM:TiO2 systems is studied by investigating the interplay between structural order, defects and incorporation of implanted ions within the host lattice. The defect properties of the host TiO2 are altered by preparing different microstructures of TiO2 (e.g. amorphous, polycrystalline anatase and epitaxial anatase). The difference in microstructure is also found to influence the incorporation of the implanted ions with the host lattice. The crystallographic incorporation of the implanted TM atoms is found only in crystalline films.
Moreover, it is observed that the suppression of the dopant related secondary phases can also be achieved by changing the microstructure. The obtained experimental results are compared with the existing theoretical frameworks, while the most relevant one describing our findings is elucidated. Based on this discussion, we propose an ideal microstructural candidate for a dilute magnetic oxide material based on our results. / Die kombinierten elektrischen, optischen und ferromagnetischen Eigenschaften von TiO2, welches mit einem Übergangsmetall (TM) dotiert wurde, sind für Anwendungen in der Spintronik von hoher Bedeutung. Obwohl dieses Material seit mehr als anderthalb Jahrzehnten untersucht wird, kann derzeit noch keine eindeutige Erklärung für den beobachteten Ferromagnetismus gegeben werden.
In dieser Arbeit wird die Ursache für die ferromagnetische Ordnung in TM:TiO2-Systemen untersucht, indem der Zusammenhang von struktureller Ordnung, Defekten und der Einlagerung der implantierten Ionen im Wirtsgitter analysiert wird. Durch die Verwendung unterschiedlicher Mikrostrukturen (z.B. amorphes, polykristalliner Anatas und epitaktischer Anatas) wurden auch die Defekteigenschaften des Wirts-Titanoxid variiert. Dabei zeigte sich ein Einfluss der unterschiedlichen Mikrostrukturen auf die Einlagerung der implantierten Atome in das Wirtsgitter. So konnte die Substitution von Ti-Atomen durch Atome des dotierten Übergangsmetalls nur in kristallinen Filmen beobachtet werden.
Weiterhin wurde herausgefunden, dass die vom Dotanden hervorgerufenen Sekundärphasen durch die initiale Mikrostruktur unterdrückt werden können. Die experimentellen Ergebnisse wurden mit aktuellen Theorien verglichen. Zusammenfassend wird ein Überblick über die wichtigsten Ergebnisse gegeben, auf Basis welcher eine optimale Mikrostruktur für ein verdünntes magnetisches Oxid vorgeschlagen wird.
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Controlled modulation of short- and long-range adhesion of microscale biogenic replicasGoodwin, William Brandon 27 May 2016 (has links)
The generation of nanostructured microscale assemblies with complex, three-dimensional (3-D) morphologies possessing multicomponent inorganic compositions tailored for adhesion is of considerable scientific and technological interest. This dissertation demonstrates that self-assembled 3-D organic templates of biogenic origin can be converted into replicas comprised of numerous other functional nanocrystalline inorganic materials and, further, how such replicas can tailored for adhesion. Nature provides a spectacular variety of biologically-assembled 3-D organic structures with intricate, hierarchical (macro-to-micro-to-nanoscale) morphologies designed for particle adhesion. The conformal coating of such structurally-complex biotemplates with synthetic materials provides a framework for chemical transformation of other, complex synthetic organic templates and the basis to study imparted adhesion properties. Three specific research thrusts are detailed in this document. First, freestanding magnetite (Fe3O4) replicas of bio-organic templates are synthesized via a layer-by-layer (LbL) wet chemical deposition process and subsequent morphology-preserving thermal treatments to allow for structures with tailorable long-range magnetic adhesion. Second, freestanding spinel ferrite replicas of bio-organic templates are synthesized (via LbL coating and thermal treatment) for grain size controlled long-range magnetic adhesion and short range van der Waals adhesion. The final research thrust focuses on the use of a low temperature (≤ 250°C) wet-chemical based process to convert bioorganic templates into magnetically-coated structures retaining both the size and morphology of the template. The rate-limiting kinetic mechanism(s) of the partial reduction of the inorganic coatings have been examined via quartz crystal microbalance analysis. The effects of the coating micro/nanostructure on magnetic behavior and on surface adhesion, have been investigated.
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Hyperjemné interakce v magnetitu a maghemitu / Hyperfine interactions in maghemite and magnetite particlesKřišťan, Petr January 2011 (has links)
Thesis is aimed at studying of magnetic iron oxide particles of submicron and nanoscale dimensions by means of nuclear magnetic resonance (NMR). 57 Fe NMR inves- tigations were carried out in composite bentonite/maghemite with respect to tempera- ture of calcination (Tcalc) during the sample preparation and in magnetite submicron powders with respect to various range of the particles size. One of the main findings is that increasing Tcalc improves resolution in the NMR spectra, which is most likely connected with higher degree of atomic ordering in the spinel structure. Evaluating the integral intensities of NMR spectra allowed us to determine the relative content of maghemite phase in particular samples of the series: the content rapidly grows for Tcalc up to ∼420 deg. An approach to distinguish signal from tetrahedral and octahedral irons was developed and tested on pure maghemite sample. Analysis based on vacancy- distribution models was performed in the spinel structure and the results were compared to the experiment. 57 Fe NMR spectra in submicron magnetite samples were found to differ markedly from spectrum of a single crystal. It was concluded that the investigated powders possess high amount of defects in the crystal structure or contain additional phase (probably closely related to the maghemite phase).
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Effect of microstructure on the magnetic properties of transition metal implanted TiO2 filmsYildirim, Oguz 24 February 2016 (has links)
The combined electronic, optic and magnetic properties of transition metal (TM) implanted ferromagnetic TiO2 is of interest for spintronic applications. The nature of the observed abundant ferromagnetism in such materials has been investigated for more than one and a half decades, yet still no clear explanation for its appearance can be given.
In this thesis, the origin of the ferromagnetic order in TM:TiO2 systems is studied by investigating the interplay between structural order, defects and incorporation of implanted ions within the host lattice. The defect properties of the host TiO2 are altered by preparing different microstructures of TiO2 (e.g. amorphous, polycrystalline anatase and epitaxial anatase). The difference in microstructure is also found to influence the incorporation of the implanted ions with the host lattice. The crystallographic incorporation of the implanted TM atoms is found only in crystalline films.
Moreover, it is observed that the suppression of the dopant related secondary phases can also be achieved by changing the microstructure. The obtained experimental results are compared with the existing theoretical frameworks, while the most relevant one describing our findings is elucidated. Based on this discussion, we propose an ideal microstructural candidate for a dilute magnetic oxide material based on our results.:1 Introduction 2
1.1 Spintronics 2
1.2 Dilute magnetic oxides 5
2 Fundamentals 13
2.1 Introduction 13
2.2 Magnetism in diluted magnetic oxides 13
2.2.1 Possible locations of dopant 3d ions in an oxide matrix 14
2.2.2 Mean field model 15
2.2.3 Bound magnetic polaron model 16
2.2.4 Charge transfer model 17
2.2.5 Ferromagnetism in undoped oxides 19
2.2.6 Extrinsic sources of ferromagnetism 20
2.3 Motivation 21
3 Experimental 24
3.1 Sample preparation 24
3.1.1 DC magnetron sputtering 24
3.1.2 Ion implantation 27
3.2 X-ray methods 29
3.2.1 X-ray diffraction 29
3.2.2 X-ray absorption 31
3.2.2.1 Synchrotron radiation 31
3.2.2.2 Physics of X-ray absorption 31
3.3 SQUID magnetometry 35
3.3.1 Avoiding magnetic contamination 37
3.4 Positron annihilation spectroscopy 38
4 TM Implantation into Different TiO2 Structures (TM = Co, Mn, V) 43
4.1 Experiments 43
4.2 Co+ implantation: from diluted paramagnetism to superparamagnetic clusters
45
4.2.1 Cluster-free Co+-implanted TiO2 thin films 45
4.2.1.1 Experiments 45
4.2.1.2 Structural properties 46
4.2.1.3 Implantation-induced structural defects 47
4.2.1.4 Magnetic properties 50
4.2.1.5 Local environment of implanted Co atoms 51
4.2.1.6 Summary 52
4.2.2 Revealing nano-clusters within Co+-implanted TiO2 thin films 54
4.2.2.1 Experiments 54
4.2.2.2 Structural properties 54
4.2.2.3 Magnetic properties 57
4.2.2.4 Local environment of implanted Co atoms 59
4.2.2.5 Summary 61
4.3 Mn+ implantation: from a non-magnet to a ferromagnet 63
4.3.1 Experiments 63
4.3.2 Relation between lattice damage and defects 64
4.3.3 Electrical transport properties 65
4.3.4 Local environment of implanted Mn atoms 66
4.3.5 Magnetic properties 67
4.3.6 Summary 69
4.4 V+-implanted TiO2 thin films 71
4.4.1 Experiments 71
4.4.2 Magnetic properties 71
4.4.3 Summary 74
5 The effect of the open volume defects on the magnetic properties of
V:TiO2 films prepared by doping during deposition 76
5.1 Experiments 76
5.2 Structural Properties 77
5.3 Investigation of the open volume defects 78
5.4 Magnetic, optical and electrical properties 79
5.5 Summary 81
6 Conclusions 84
6.1 Defects in TiO2 84
6.2 Formation of secondary phases 85
6.3 Evolution of the ferromagnetism in different microstructures of TiO2 87
7 Acknowledgments 91 / Die kombinierten elektrischen, optischen und ferromagnetischen Eigenschaften von TiO2, welches mit einem Übergangsmetall (TM) dotiert wurde, sind für Anwendungen in der Spintronik von hoher Bedeutung. Obwohl dieses Material seit mehr als anderthalb Jahrzehnten untersucht wird, kann derzeit noch keine eindeutige Erklärung für den beobachteten Ferromagnetismus gegeben werden.
In dieser Arbeit wird die Ursache für die ferromagnetische Ordnung in TM:TiO2-Systemen untersucht, indem der Zusammenhang von struktureller Ordnung, Defekten und der Einlagerung der implantierten Ionen im Wirtsgitter analysiert wird. Durch die Verwendung unterschiedlicher Mikrostrukturen (z.B. amorphes, polykristalliner Anatas und epitaktischer Anatas) wurden auch die Defekteigenschaften des Wirts-Titanoxid variiert. Dabei zeigte sich ein Einfluss der unterschiedlichen Mikrostrukturen auf die Einlagerung der implantierten Atome in das Wirtsgitter. So konnte die Substitution von Ti-Atomen durch Atome des dotierten Übergangsmetalls nur in kristallinen Filmen beobachtet werden.
Weiterhin wurde herausgefunden, dass die vom Dotanden hervorgerufenen Sekundärphasen durch die initiale Mikrostruktur unterdrückt werden können. Die experimentellen Ergebnisse wurden mit aktuellen Theorien verglichen. Zusammenfassend wird ein Überblick über die wichtigsten Ergebnisse gegeben, auf Basis welcher eine optimale Mikrostruktur für ein verdünntes magnetisches Oxid vorgeschlagen wird.:1 Introduction 2
1.1 Spintronics 2
1.2 Dilute magnetic oxides 5
2 Fundamentals 13
2.1 Introduction 13
2.2 Magnetism in diluted magnetic oxides 13
2.2.1 Possible locations of dopant 3d ions in an oxide matrix 14
2.2.2 Mean field model 15
2.2.3 Bound magnetic polaron model 16
2.2.4 Charge transfer model 17
2.2.5 Ferromagnetism in undoped oxides 19
2.2.6 Extrinsic sources of ferromagnetism 20
2.3 Motivation 21
3 Experimental 24
3.1 Sample preparation 24
3.1.1 DC magnetron sputtering 24
3.1.2 Ion implantation 27
3.2 X-ray methods 29
3.2.1 X-ray diffraction 29
3.2.2 X-ray absorption 31
3.2.2.1 Synchrotron radiation 31
3.2.2.2 Physics of X-ray absorption 31
3.3 SQUID magnetometry 35
3.3.1 Avoiding magnetic contamination 37
3.4 Positron annihilation spectroscopy 38
4 TM Implantation into Different TiO2 Structures (TM = Co, Mn, V) 43
4.1 Experiments 43
4.2 Co+ implantation: from diluted paramagnetism to superparamagnetic clusters
45
4.2.1 Cluster-free Co+-implanted TiO2 thin films 45
4.2.1.1 Experiments 45
4.2.1.2 Structural properties 46
4.2.1.3 Implantation-induced structural defects 47
4.2.1.4 Magnetic properties 50
4.2.1.5 Local environment of implanted Co atoms 51
4.2.1.6 Summary 52
4.2.2 Revealing nano-clusters within Co+-implanted TiO2 thin films 54
4.2.2.1 Experiments 54
4.2.2.2 Structural properties 54
4.2.2.3 Magnetic properties 57
4.2.2.4 Local environment of implanted Co atoms 59
4.2.2.5 Summary 61
4.3 Mn+ implantation: from a non-magnet to a ferromagnet 63
4.3.1 Experiments 63
4.3.2 Relation between lattice damage and defects 64
4.3.3 Electrical transport properties 65
4.3.4 Local environment of implanted Mn atoms 66
4.3.5 Magnetic properties 67
4.3.6 Summary 69
4.4 V+-implanted TiO2 thin films 71
4.4.1 Experiments 71
4.4.2 Magnetic properties 71
4.4.3 Summary 74
5 The effect of the open volume defects on the magnetic properties of
V:TiO2 films prepared by doping during deposition 76
5.1 Experiments 76
5.2 Structural Properties 77
5.3 Investigation of the open volume defects 78
5.4 Magnetic, optical and electrical properties 79
5.5 Summary 81
6 Conclusions 84
6.1 Defects in TiO2 84
6.2 Formation of secondary phases 85
6.3 Evolution of the ferromagnetism in different microstructures of TiO2 87
7 Acknowledgments 91
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Neutron Scattering Studies of Magnetic Oxides based on Triangular MotifsFritsch, Katharina 04 1900 (has links)
<p>The following dissertation presents neutron scattering studies on three specific magnetic insulating oxide materials whose lattice is based on triangular structural motifs. Each of the three materials studied, LuCoGaO<sub>4</sub>, Co<sub>3</sub>V<sub>2</sub>O<sub>8</sub> and Tb<sub>2</sub>Ti<sub>2</sub>O<sub>7</sub>, displays an interesting disordered ground state that is reached by different mechanisms: site disorder, geometric frustration, and quantum fluctuations induced by a transverse magnetic field. The main focus of this work is the characterization of the resulting magnetic ground states and magnetic excitations within these systems.</p> <p>Chapters 3, 4 and 5 contain original work in the form of six research articles that have either been published or have been prepared for publication in peer-reviewed journals.</p> <p>Chapter 3 describes studies of the quasi two-dimensional triangular layered antiferromagnet LuCoGaO<sub>4</sub>. This material is found to exhibit a spin glass ground state as a result of geometrical frustration and site disorder inherent in this system. Below the freezing temperature, this system exhibits static, two-dimensional correlations consistent with frozen short-range correlated regions in the plane of the bilayers that extend over roughly five unit cells. The dynamic correlations reveal typical spin glass behavior upon cooling. Furthermore, a resonant gapped spin-wave-like excitation is observed, that can be related to the anisotropy in the system. Such an excitation is relatively uncommon in spin glasses and has been studied for the first time in such detail.</p> <p>Chapter 4 is concerned with the study of the kagome staircase system Co<sub>3</sub>V<sub>2</sub>O<sub>8</sub>. While prone to geometrical frustration due to its underlying kagome structural motif, this material is characterized by predominantly ferromagnetic interactions that lead to an unfrustrated, ferromagnetic ground state. In this chapter, departures from this conventional ground state by different disordering mechanisms are investigated. The first part focuses on the effects of site disorder by introducing quenched nonmagnetic impurities into the system. The growth of single crystals of (Co<sub>1-x</sub>Mg<sub>x</sub>)<sub>3</sub>V<sub>2</sub>O<sub>8</sub> is reported. These crystals reveal that the ferromagnetic ground state is very sensitive to doping, and show that a low doping concentration of 19% leads to a suppression of the ferromagnetic ground state below 1.5 K. This could be understood as percolation problem on the quasi two-dimensional kagome lattice including site and bond percolation. The second part focuses on the influence of a transverse magnetic field on the ground state of Ising spins, introducing quantum fluctuations that lead to quantum phase transitions at ~6.25, 7 and 13 T. The observed quantum phase transitions are characterized by distinct changes in the magnetic structure and their associated spin excitation spectra.</p> <p>Chapter 5 presents studies on the pyrochlore antiferromagnet Tb<sub>2</sub>Ti<sub>2</sub>O<sub>7</sub>, which is a proposed spin liquid candidate but whose actual ground state is still the topic of current debate. The ground state of Tb<sub>2</sub>Ti<sub>2</sub>O<sub>7</sub> was revisited by neutron scattering measurements, revealing a new phase in the low temperature low field phase diagram that can be described as a frozen antiferromagnetic spin ice that exhibits distinct elastic and inelastic scattering features.</p> / Doctor of Philosophy (PhD)
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Fundamental Properties of Functional Magnetic MaterialsWikberg, Magnus January 2010 (has links)
Magnetic properties of powders, thin films and single crystals have been investigated using magnetometry methods. This thesis provides analysis and conclusions that are supported by the results obtained from spectroscopic and diffraction measurements as well as from theoretical calculations. First, the magnetic behavior of transition metal (TM) doped ZnO with respect to doping, growth conditions and post annealing has been studied. Our findings indicate that the magnetic behavior stems from small clusters or precipitates of the dopant, with ferromagnetic or antiferromagnetic interactions. At the lowest dopant concentrations, the estimated cluster sizes are too small for high resolution imaging. Still, the clusters may be sufficiently large to generate a finite spontaneous magnetization even at room temperature and could easily be misinterpreted as an intrinsic ferromagnetic state of the TM:ZnO compound. Second, influence of lattice strain on both magnetic moment and anisotropy has been investigated for epitaxial MnAs thin films grown on GaAs substrates. The obtained magnetic moments and anisotropy values are higher than for bulk MnAs. The enhanced values are caused by highly strained local areas that have a stronger dependence on the in-plane axis strain than out-of plane axis strain. Finally, spin glass behavior in Li-layered oxides, used for battery applications, and a double perovskite material has been investigated. For both Li(NiCoMn)O2 and (Sr,La)MnWO6, a mixed-valence of one of the transition metal ions creates competing ferromagnetic and antiferromagnetic interactions resulting in a low temperature three-dimensional (3D) spin glass state. Additionally, Li(NiCoMn)O2 with large cationic mixing exhibits a percolating ferrimagnetic spin order in the high temperature region and coexists with a two-dimensional (2D) frustrated spin state in the mid temperature region. This is one of the rare observations where a dimensional crossover from 2D to 3D spin frustration appears in a reentrant material. / Felaktigt tryckt som Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 720
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Investigação das propriedades magnéticas de amostras de IrO2 e Co:IrO2 sintetizadas via método de PechiniDreifus, Driele Von 31 August 2010 (has links)
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Previous issue date: 2010-08-31 / Financiadora de Estudos e Projetos / In this work the magnetic properties of iridium oxide synthesized via Pechini s method and doped with different concentrations of cobalt were studied. The proposal was to investigate the possibility of applying it as a diluted magnetic oxide (DMO1). The samples were characterized by x-ray diffraction to study the structural features by Rietveld refinement, which indicated that there is no inconsistency between the observed intensities and the calculated profile. The samples were characterized by magnetization measurements as a function of temperature and applied magnetic field. A paramagnetic behavior was observed in samples doped with low Co concentrations. However, a small change in the magnetism appears in samples with concentrations up to 10 mol% of Co. A new metamagnetic phase was observed for samples with 25% and 30% in mol of Co. / Neste trabalho foram estudadas as propriedades magnéticas do óxido de irídio sintetizado via método de Pechini e dopado com diferentes concentrações de Co, com a proposta de investigar a possibilidade de aplicá-lo como um Óxido Diluído Magnético (DMO, sigla em inglês) 1. As amostras foram caracterizadas por medidas de difração de raios-x através de refinamento Rietveld, indicando que não há incompatibilidade entre as intensidades observadas e as do perfil calculado. Além disso, foram realizadas medidas de magnetização em função da temperatura e do campo magnético aplicado. Foi observado comportamento paramagnético em amostras dopadas com baixas concentrações de Co, entretanto, uma pequena mudança no magnetismo das amostras começou a aparecer em amostras com concentrações de Co a partir de 10 mol%, ficando evidente em altas concentrações de dopante, 25% e 30% em mol, uma fase metamagnética.
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Exchange Spring Behaviour in Magnetic OxidesRoy, Debangsu January 2012 (has links) (PDF)
When a permanent magnet is considered for an application, the quantity that quantifies the usability of that material is the magnetic energy product (BH)max. In today’s world, rare earth transition metal permanent magnets like Nd-Fe-B, Sm-Co possesses the maximum magnetic energy product. But still for the industrial application, the ferrite permanent magnets are the primary choice over these rare transition metal magnets. Thus, in the present context, the magnetic energy product of the low cost ferrite system makes it unsuitable for the high magnetic energy application. In this regard, exchange spring magnets which combine the magnetization of the soft phase and coercivity of the hard magnetic phases become important in enhancing the magnetic energy product of the system. In this thesis, the exchange spring behaviour is reported for the first time in hard/soft oxide nanocomposites by microstructural tailoring of hard Barium Ferrite and soft Nickel Zinc Ferrite particles. We have analyzed the magnetization reversal and its correlation with the coercivity mechanism in the Ni0.8Zn0.2Fe2O4/BaFe12O19 exchange spring systems. Using this exchange spring concept, we could enhance the magnetic energy product in Iron Oxide/ Barium Calcium Ferrite nanocomposites compared to the bare hard ferrite by ~13%. The presence of the exchange interaction in this nanocomposite is confirmed by the Henkel plot. Moreover, a detailed Reitveld study, magnetization loop and corresponding variation of the magnetic energy product, Henkel plot analysis and First Order Reversal Curve analysis are performed on nanocomposites of hard Strontium Ferrite and soft Cobalt Ferrite. We have proved the exchange spring behaviour in this composite. In addition, we could successfully tailor the magnetization behaviour of the soft Cobalt Ferrite- hard Strontium Ferrite nanocomposite from non exchange spring behaviour to exchange spring behaviour, by tuning the size of the soft Cobalt Ferrite in the Cobalt Ferrite/Strontium Ferrite nanocomposite. The relative strength of the interaction governing the magnetization process in the composites has been studied using Henkel plot and First Order Reversal Curve method. The FORC method has been utilized to understand the magnetization reversal behaviour as well as the extent of the irreversible magnetization present in both the nanocomposites, having smaller and larger particle size of the Cobalt Ferrite. It has been found that for the all the studied composites, the pinning is the dominant process for magnetization reversal. The detailed structural analysis using thin film XRD, angle dependent magnetic hysteresis and remanent coercivity measurement, coercivity mechanism by micromagnetic analysis and First Order Reversal Curve analysis are performed for thin films of Strontium Ferrite which are grown on c-plane alumina using Pulsed Laser Deposition (PLD) at two different oxygen partial pressures. The magnetic easy directions of both the films lie in the out of plane direction where as the in plane direction corresponds to the magnetic hard direction. Depending on the oxygen partial pressure during deposition, the magnetization reversal changes from S-W type reversal to Kondorsky kind of reversal. Thus, the growth parameter for the Strontium Ferrite single layer which will be used further as a hard layer for realizing oxide exchange spring in oxide multilayer, is optimized. The details of the magnetic and structural properties are analyzed for Nickel Zinc Ferrite thin film grown on (100) MgAl2O4. We have obtained an epitaxial growth of Nickel Zinc Ferrite by tuning the growth parameters of PLD deposition. The ferromagnetic resonance and the angle dependent hysteresis loop suggest that, the magnetic easy direction for the soft Nickel Zinc Ferrite lie in the film plane whereas the out of plane direction is the magnetic hard direction. Using the growth condition of respective Nickel Zinc Ferrite and Strontium Ferrite, we have realized the exchange spring behaviour for the first time in the trilayer structure of SrFe12O19 (20 nm)/Ni0.8Zn0.2Fe2O4(20 nm)/ SrFe12O19 (20 nm) grown on c-plane alumina (Al2O3) using PLD. The FORC distribution for this trilayer structure shows the single switching behaviour, corresponding to the exchange spring behaviour. The reversible ridge measurement shows that the reversible and the irreversible part of the magnetizations are not coupled with each other.
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