In this work, stretchable magnetic sensorics is successfully established by combining metallic thin films revealing a giant magnetoresistance effect with elastomeric materials. Stretchability of the magnetic nanomembranes is achieved by specific morphologic features (e.g. wrinkles), which accommodate the applied tensile deformation while maintaining the electrical and magnetic integrity of the sensor device. The entire development, from the demonstration of the world-wide first elastically stretchable magnetic sensor to the realization of a technology platform for robust, ready-to-use elastic magnetoelectronics with fully strain invariant properties, is described. The prepared soft giant magnetoresistive devices exhibit the same sensing performance as on conventional rigid supports, but can be stretched uniaxially or biaxially reaching strains of up to 270% and endure over 1,000 stretching cycles without fatigue. The comprehensive magnetoelectrical characterization upon tensile deformation is correlated with in-depth structural investigations of the sensor morphology transitions during stretching. With their unique mechanical properties, the elastic magnetoresistive sensor elements readily conform to ubiquitous objects of arbitrary shapes including the human skin. This feature leads electronic skin systems beyond imitating the characteristics of its natural archetype and extends their cognition to static and dynamic magnetic fields that by no means can be perceived by human beings naturally. Various application fields of stretchable magnetoelectronics are proposed and realized throughout this work. The developed sensor platform can equip soft electronic systems with navigation, orientation, motion tracking and touchless control capabilities. A variety of novel technologies, like smart textiles, soft robotics and actuators, active medical implants and soft consumer electronics will benefit from these new magnetic functionalities.

In this work, stretchable magnetic sensorics is successfully established by combining metallic thin films revealing a giant magnetoresistance effect with elastomeric materials. Stretchability of the magnetic nanomembranes is achieved by specific morphologic features (e.g. wrinkles), which accommodate the applied tensile deformation while maintaining the electrical and magnetic integrity of the sensor device. The entire development, from the demonstration of the world-wide first elastically stretchable magnetic sensor to the realization of a technology platform for robust, ready-to-use elastic magnetoelectronics with fully strain invariant properties, is described. The prepared soft giant magnetoresistive devices exhibit the same sensing performance as on conventional rigid supports, but can be stretched uniaxially or biaxially reaching strains of up to 270% and endure over 1,000 stretching cycles without fatigue. The comprehensive magnetoelectrical characterization upon tensile deformation is correlated with in-depth structural investigations of the sensor morphology transitions during stretching. With their unique mechanical properties, the elastic magnetoresistive sensor elements readily conform to ubiquitous objects of arbitrary shapes including the human skin. This feature leads electronic skin systems beyond imitating the characteristics of its natural archetype and extends their cognition to static and dynamic magnetic fields that by no means can be perceived by human beings naturally. Various application fields of stretchable magnetoelectronics are proposed and realized throughout this work. The developed sensor platform can equip soft electronic systems with navigation, orientation, motion tracking and touchless control capabilities. A variety of novel technologies, like smart textiles, soft robotics and actuators, active medical implants and soft consumer electronics will benefit from these new magnetic functionalities.:Outline List of abbreviations 7 1. INTRODUCTION 1.1 Motivation and scope of this work 8 1.1.1 A brief review on stretchable electronics 8 1.1.2 Stretchable magnetic sensorics 10 1.2 Technological approach 11 1.3 State-of-the-art 12 2. THEORETICAL BACKGROUND 2.1 Magnetic coupling phenomena in layered structures 14 2.1.1 Magnetic interlayer exchange coupling 14 2.1.2 Exchange bias 15 2.1.3 Orange peel coupling 16 2.2 Giant magnetoresistance 17 2.2.1 Electronic transport through ferromagnets 17 2.2.2 The GMR effect 19 2.2.3 GMR multilayers 20 2.2.4 Spin valves 21 2.3 Theory of elasticity 22 2.3.1 Elastomeric materials 22 2.3.2 Stress and strain 23 2.3.3 Rubber elasticity 25 2.3.4 The Poisson effect 26 2.3.5 Viscoelasticity 27 2.3.6 Bending strain in a stiff film on a flexible support 27 2.4 Approaches to stretchable electronic systems 28 2.4.1 Microcrack formation 28 2.4.2 Meanders and compliant patterns 29 2.4.3 Surface wrinkling 30 2.4.4 Rigid islands 32 3. METHODS & MATERIALS 3.1 Sample fabrication 34 3.1.1 Polydimethylsiloxane (PDMS) 34 3.1.2 PDMS film preparation 35 3.1.3 Lithographic structuring on the PDMS surface. 36 3.1.4 Magnetic thin film deposition 38 3.1.5 GMR layer stacks 40 3.1.6 Mechanically induced pre-strain 43 3.1.7 Methods and materials for the direct transfer of GMR sensors 45 3.1.8 Materials used for imperceptible GMR sensors 47 3.2 Characterization 48 3.2.1 GMR characterization setup with in situ stretching capability 48 3.2.2 Sample mounting 50 3.2.3 Electrical contacting of stretchable sensor devices 51 3.2.4 Customized demonstrator electronics 52 3.2.5 Microscopic investigation techniques 53 4. RESULTS & DISCUSSION 4.1 GMR multilayer structures on PDMS 54 4.1.1 Pre-characterization 54 4.1.2 Thermally induced wrinkling 55 4.1.3 Self-healing effect 57 4.1.4 Demonstrator: Magnetic detection on a curved surface 60 4.1.5 Sensitivity enhancement 61 4.1.6 GMR sensors in circumferential geometry 64 4.1.7 Stretchability test 67 4.2 Stretchable spin valves 69 4.2.1 Random wrinkles and periodic fracture 70 4.2.2 GMR characterization 73 4.2.3 Stretching of spin valves 74 4.2.4 Microcrack formation mechanism 76 4.3 Direct transfer printing of GMR sensorics 81 4.3.1 The direct transfer printing process 82 4.3.2 Direct transfer of GMR microsensor arrays 84 4.3.3 Direct transfer of compliant meander shaped GMR sensors 86 4.4 Imperceptible magnetoelectronics 89 4.4.1 GMR multilayers on ultra-thin PET membranes 89 4.4.2 Imperceptible GMR sensor skin 92 4.4.3 Demonstrator: Fingertip magnetic proximity sensor 93 4.4.4 Ultra-stretchable GMR sensors 94 4.4.5 Biaxial stretchability 99 4.4.6 Demonstrator: Dynamic detection of diaphragm inflation 101 5. CONCLUSIONS & OUTLOOK 5.1 Achievements 102 5.2 Outlook 104 5.2.1 Further development steps 104 5.2.2 Prospective applications. 105 5.3 Technological impact: flexible Bi Hall sensorics 106 5.3.1 Application potential 106 5.3.2 Thin and flexible Hall probes 107 5.3.3 Continuative works and improvements 108 5.4 Activities on technology transfer and public relations 108 Appendix References 110 Selbständigkeitserklärung 119 Acknowledgements 120 Curriculum Vitae 121 Scientific publications, contributions, patents, grants & prizes 122

The work presented in this thesis encompasses the design, development, realization and testing of novel magnetoelectric thin film elements that do not rely on ferromagnets, but are based entirely on magnetoelectric antiferromagnets such as Cr2O3. Thin film spintronic elements, and in particular magnetoelectric transducers, are crucial building blocks of high efficiency data processing schemes that could complement conventional electronic data processing in the future. Recent developments in magnetoelectrics have revealed, that exchange biased systems are ill-suited to electric field induced switching of magnetization due to the strong coupling of their ferromagnetic layer to magnetic fields. Therefore, ferromagnet-free magnetoelectric elements are proposed here in an effort to mitigate the practical problems associated with existing exchange biased magnetoelectric elements. This goal is achieved by establishing an all-electric read-out method for the antiferromagnetic order parameter of thin films, which allows to omit the ferromagnet from conventional exchange biased magnetoelectric elements. The resulting ferromagnet-free magnetoelectric elements show greatly reduced writing thresholds, enabled operation at room temperature and do not require a pulsed magnetic field, all of which is in contrast to state-of-the-art exchange biased magnetoelectric systems. The novel all-electric read-out method of the magnetic field-invariant magnetization of antiferromagnets, so-called spinning-current anomalous Hall magnetometry, can be widely employed in other areas of thin film magnetism. Its high precision and its sensitivity to previously invisible phenomena make it a promising tool for various aspects of thin solid films. Based on this technique, a deep understanding could be generated as to what physical mechanisms drive the antiferromagnetic ordering in thin films of magnetoelectric antiferromagnets. As spinning-current anomalous Hall magnetometry is an integral probe of the magnetic properties in thin films, it offers no intrinsic scale sensitivity. In order to harness its great precision for scale related information, a statistical framework was developed, which links macroscopic measurements with microscopic properties such as the antiferromagnetic domain size.

The work presented in this thesis encompasses the design, development, realization and testing of novel magnetoelectric thin film elements that do not rely on ferromagnets, but are based entirely on magnetoelectric antiferromagnets such as Cr2O3. Thin film spintronic elements, and in particular magnetoelectric transducers, are crucial building blocks of high efficiency data processing schemes that could complement conventional electronic data processing in the future. Recent developments in magnetoelectrics have revealed, that exchange biased systems are ill-suited to electric field induced switching of magnetization due to the strong coupling of their ferromagnetic layer to magnetic fields. Therefore, ferromagnet-free magnetoelectric elements are proposed here in an effort to mitigate the practical problems associated with existing exchange biased magnetoelectric elements. This goal is achieved by establishing an all-electric read-out method for the antiferromagnetic order parameter of thin films, which allows to omit the ferromagnet from conventional exchange biased magnetoelectric elements. The resulting ferromagnet-free magnetoelectric elements show greatly reduced writing thresholds, enabled operation at room temperature and do not require a pulsed magnetic field, all of which is in contrast to state-of-the-art exchange biased magnetoelectric systems. The novel all-electric read-out method of the magnetic field-invariant magnetization of antiferromagnets, so-called spinning-current anomalous Hall magnetometry, can be widely employed in other areas of thin film magnetism. Its high precision and its sensitivity to previously invisible phenomena make it a promising tool for various aspects of thin solid films. Based on this technique, a deep understanding could be generated as to what physical mechanisms drive the antiferromagnetic ordering in thin films of magnetoelectric antiferromagnets. As spinning-current anomalous Hall magnetometry is an integral probe of the magnetic properties in thin films, it offers no intrinsic scale sensitivity. In order to harness its great precision for scale related information, a statistical framework was developed, which links macroscopic measurements with microscopic properties such as the antiferromagnetic domain size.:TABLE OF CONTENTS Abbreviations 9 1 Introduction 11 1.1 Motivation 11 1.2 Objectives 12 1.3 Organization of the thesis 13 2 Background 15 2.1 History of magnetoelectric coupling 15 2.2 Long range magnetic ordering 16 2.2.1 Magnetic order parameter and field susceptibility 17 2.2.2 Magnetic proximity effect 19 2.2.3 Exchange bias 20 2.3 Phenomenology of magnetoelectric coupling 21 2.3.1 The linear magnetoelectric effect 21 2.3.2 Magnetoelectric pressure on the antiferromagnetic order parameter 22 2.3.3 Switching the antiferromagnetic order parameter 23 2.4 Realized magnetoelectric thin film elements 24 2.4.1 BiFeO3/CoFe system 24 2.4.2 Cr2O3/Co/Pt system 25 3 Experimental methods 27 3.1 Development of ferromagnet free magnetoelectric elements 28 3.1.1 The substrate 29 3.1.2 The Cr2O3 bulk and top surface 31 3.1.3 The V2O3 or Pt bottom electrodes 33 3.1.4 Epitaxial relationships 34 3.1.5 The Cr2O3 bottom interface 39 3.1.6 Twinning of Cr2O3 39 3.1.7 Hall crosses and patterning processes 43 3.2 Magnetotransport measurements 44 3.2.1 Hall effects 45 3.2.2 Anomalous Hall effect 46 3.2.3 Magnetoelectric writing 47 3.2.4 All electric read out 49 3.3 The experimental setup 50 3.3.1 Temperature control 50 3.3.2 Magnetic field control 51 4 Spinning-current anomalous Hall magnetometry 53 4.1 Characteristics of the technique 53 4.1.1 Operational principle 53 4.1.2 Advantages 55 4.1.3 Magnetic hysteresis loops and field-invariant magnetization 55 4.1.4 Measurement of field-invariant magnetization 56 4.1.5 Limitations 58 4.2 Application of SCAHM to Cr2O3(0001) thin films 59 4.2.1 Criticality and distribution of the antiferromagnetic phase transition 61 4.2.2 Evaluation of the magnetic proximity effect 64 4.3 SCAHM with thin metallic antiferromagnetic IrMn films 65 4.3.1 [Pt/Co]4/IrMn exchange bias system 65 4.3.2 Isolated antiferromagnetic IrMn thin films 67 5 Magnetoelectric performance 69 5.1 Magnetoelectric field cooling 69 5.2 The gate bias voltage 71 5.3 Isothermal binary magnetoelectric writing in Cr2O3 72 6 Order parameter selection in magnetoelectric antiferromagnets 77 6.1 Uncompensated magnetic moment 77 6.2 Extrinsic causes for broken sublattice equivalence 81 6.3 The V2O3 gate electrode 83 7 Measurement of microscopic properties with an integral probe 87 7.1 Interentity magnetic exchange coupling 87 7.2 Ensemble formalism for the entity size determination 90 7.3 Estimation of the entity sizes 94 7.4 Microscopic confirmation of the ensemble model 97 8 Summary and Outlook 101 8.1 Goal-related achievements 101 8.1.1 All-electric read-out of the AF order parameter 101 8.1.2 Electric field induced writing of the AF order parameter 102 8.2 Further achievements 103 8.2.1 Foreseen impact of SCAHM on thin film magnetism 103 8.2.2 Practical optimization routes of magnetoelectric Cr2O3 systems 104 8.2.3 Theoretical work 105 8.3 Future directions 105 8.3.1 Development of Cr2O3-based magnetoelectric systems 105 8.3.2 Applications of SCAHM 106 References 107 Erklärung 113 Acknowledgements 115 Curriculum Vitae 117 Scientific publications, contributions, patents 119