Spin-torque nano-oscillators (STNOs) are prospective successors of transistor-based emitters and receivers of radio-frequency signals in commonly used remote communication systems. In comparison to the conventional electronic oscillators, STNOs offer the advantage of being tunable over a wide range of frequencies simply by adjusting the applied current, the smaller lateral size (up to 50 times) and the lower power consumption as the lateral size of the device is reduced. It has already been demonstrated that the output signal characteristics of STNOs are compatible with the requirements for applications: they can provide output powers in the µW range, frequencies of the order of GHz, quality factors Q (equal to df/f, where f is the frequency, and df is the linewidth) up to several thousands (e.g., 3 200), and can be integrated into Phase-Locked Loop (PLL) circuits. The most promising type of spin-torque oscillators is the hybrid geometry STNOs utilizing an in-plane magnetized fixed layer, an out-of-plane magnetized free layer and the MgO tunnel barrier as a spacer. This geometry maximizes the output power, since the full parallel-to-antiparallel resistance variation can be exploited in the limit of large magnetization precession angle (i.e., when the magnetization oscillates fully within the plane of the STNO stack). Moreover, the considered hybrid geometry allows for the reduction of the critical currents, enables functionality regardless of the applied magnetic or current history and requires a simplified fabrication process in comparison to the opposite hybrid geometry, consisting of an in-plane magnetized free layer and an out-of-plane reference layer, which requires an additional read-out layer. Simultaneously, the choice of the spacer material in considered STNOs is motivated by the increase of both the output power (via large magnetoresistance ratios) and the power conversion rate ('output power to input power' ratio), compared to their fully metallic counterparts. Despite the many advantages of MgO-based hybrid geometry STNOs, unexplained issues related to the physics behind their principle of operation remained. In this thesis, the main focus is put on the two key aspects related to the out-of-plane steady-state precession in hybrid STNOs: the precession mechanism (combined with the analysis of the influence of the bias dependence of the tunnel magnetoresistance) and the zero-field oscillations stabilized by an in-plane shape anisotropy. State-of-the-art theoretical studies demonstrated that stable precession in hybrid geometry STNOs can only be sustained if the in-plane component of the spin-transfer torque (STT) exhibits an asymmetric dependence on the angle between the free and the polarizing layer (which is true for fully metallic devices, but not for the MgO-based magnetic tunnel junctions (MTJs)). Nevertheless, recent experimental reports showed that spin-transfer driven dynamics can also be sustained in MgO-based STNOs with this particular configuration. In this thesis, a phenomenological and straightforward mechanism responsible for sustaining the dynamics in considered system is suggested. The mechanism is based on the fact that, in MgO-based MTJs, the strong cosine-type angular dependence of the tunnel magnetoresistance, at constant applied current, translates into an angle-dependent voltage component, which results in an angle-dependent spin-transfer torque giving a rise to the angular asymmetry of the in-plane STT and, thus, enabling steady-state precession to be sustained. Subsequently, the bias dependence of the tunnel magnetoresistance (TMR), which has been so far neglected in similar calculations, is taken into account. According to the results of analytical and numerical studies, the TMR bias dependence brings about a gradual quenching of the dynamics at large applied currents. The theoretical model yields trends confirming our experimental results. The most important conclusion regarding to this part of the thesis is that, while the angular dependence of the tunnel magnetoresistance introduces an angular asymmetry for the in-plane spin transfer torque parameter (which helps maintain steady-state precession), the bias dependence of the resistance works to reduce this asymmetry. Thus, these two mechanisms allow us to tune the asymmetry of the in-plane STT as function of current and to control the dynamical response of the actual device. Except for the precession mechanism, the thesis is also focused on the issue of zero-field oscillations, which would be especially desirable from the point of view of potential applications. According to the state-of-the-art theoretical studies, for hybrid geometry devices with circular cross-section (i.e., exhibiting no other anisotropy terms), current-driven dynamics cannot be excited at zero applied field. Indeed, zero-field oscillations have only been experimentally observed for systems having the free layer magnetization slightly tilted from the normal to the plane, which has usually been achieved by introducing an in-plane shape anisotropy. In the thesis, the influence of the in-plane shape anisotropy of the MTJ on zero-field dynamics in the hybrid geometry MgO-based STNOs is analytically and numerically investigated. In agreement with the previous reports, no zero-field dynamics for circular nano-pillars is observed; however, according to the numerical data, an additional in-plane anisotropy smaller than the effective out-of-plane anisotropy of the free layer enables zero-field steady-state precession. Accordingly, the lack of an in-plane anisotropy component (e.g., for circular cross-section nano-pillars), or the presence of an in-plane shape anisotropy equal or greater than the out-of-plane effective anisotropy, inhibits the stabilization of dynamics in the free layer at zero field. The results of analytical and numerical studies and the general trends identified in the corresponding experimental data are found to be in excellent qualitative agreement.:1. Introduction 1.1. Short history of magnetotransport applications 1.2. Spin-transfer torque induced effects and devices 1.3. Goals of the thesis 2. Fundamentals 2.1. Electronic transport in single transition metal layers 2.2. Tunnel magnetoresistance (TMR) 2.2.1. Electronic transport in magnetic tunnel junctions 2.2.2. Tunnel magnetoresistance versus structural properties of the multilayer 2.2.3. Bias voltage and temperature dependence of tunnel magnetoresistance 2.2.4. Angular dependence of tunnel magnetoresistance 2.3. Spin-transfer torque in GMR/TMR structures 2.3.1. Spin-transfer torque 2.3.2. Landau-Lifshitz-Gilbert (LLG) equation 2.3.3. LLG equation and spin-transfer torques 2.3.4. Bias voltage dependence of spin-transfer torques in MTJs 2.3.5. Angular dependence of spin-transfer torque 2.4. Spin-torque-based phenomena 2.4.1. Current-induced switching 2.4.2. Current-induced dynamics 3. Experimental 3.1. General characteristics of MgO-based magnetic tunnel junctions 3.2. STNO samples 3.2.1. Samples by AIST (Tsukuba, Japan) 3.2.2. Samples by HZDR / SINGULUS (Dresden / Kahl am Main, Germany) 3.3. Magnetotransport measurements 3.3.1. Experimental setup and data analysis 3.3.2. Experimental results 3.4. Aspects to be explained 4 Numerical and analytical calculations 4.1 Out-of-plane steady-state precession in hybrid geometry STNO 4.1.1 Angular dependence of tunnel magnetoresistance as a mechanism of stable precession 4.1.2. Influence of the bias dependence of tunnel magnetoresistance 4.1.3. Comparison with the experimental data 4.1.4. Comparison with the GMR-type counterpart 4.1.5. Summary 4.2. Zero-field dynamics in hybrid geometry STNO stabilized by in-plane shape anisotropy 4.2.1. Effect of the in-plane shape anisotropy 4.2.2. Zero-field dynamics 4.2.3. Summary 5. Conclusions 6. Outlook Appendix Bibliography

Understanding how biological cells organize to form complex functional tissues is a question of key interest at the interface between biology and physics. The liver is a model system for a complex three-dimensional epithelial tissue, which performs many vital functions. Recent advances in imaging methods provide access to experimental data at the subcellular level. Structural details of individual cells in bulk tissues can be resolved, which prompts for new analysis methods. In this thesis, we use concepts from soft matter physics to elucidate and quantify structural properties of mouse liver tissue. Epithelial cells are structurally anisotropic and possess a distinct apico-basal cell polarity that can be characterized, in most cases, by a vector. For the parenchymal cells of the liver (hepatocytes), however, this is not possible. We therefore develop a general method to characterize the distribution of membrane-bound proteins in cells using a multipole decomposition. We first verify that simple epithelial cells of the kidney are of vectorial cell polarity type and then show that hepatocytes are of second order (nematic) cell polarity type. We propose a method to quantify orientational order in curved geometries and reveal lobule-level patterns of aligned cell polarity axes in the liver. These lobule-level patterns follow, on average, streamlines defined by the locations of larger vessels running through the tissue. We show that this characterizes the liver as a nematic liquid crystal with biaxial order. We use the quantification of orientational order to investigate the effect of specific knock-down of the adhesion protein Integrin ß-1. Building upon these observations, we study a model of nematic interactions. We find that interactions among neighboring cells alone cannot account for the observed ordering patterns. Instead, coupling to an external field yields cell polarity fields that closely resemble the experimental data. Furthermore, we analyze the structural properties of the two transport networks present in the liver (sinusoids and bile canaliculi) and identify a nematic alignment between the anisotropy of the sinusoid network and the nematic cell polarity of hepatocytes. We propose a minimal lattice-based model that captures essential characteristics of network organization in the liver by local rules. In conclusion, using data analysis and minimal theoretical models, we found that the liver constitutes an example of a living biaxial liquid crystal.:1. Introduction 1 1.1. From molecules to cells, tissues and organisms: multi-scale hierarchical organization in animals 1 1.2. The liver as a model system of complex three-dimensional tissue 2 1.3. Biology of tissues 5 1.4. Physics of tissues 9 1.4.1. Continuum descriptions 11 1.4.2. Discrete models 11 1.4.3. Two-dimensional case study: planar cell polarity in the fly wing 15 1.4.4. Challenges of three-dimensional models for liver tissue 16 1.5. Liquids, crystals and liquid crystals 16 1.5.1. The uniaxial nematic order parameter 19 1.5.2. The biaxial nematic ordering tensor 21 1.5.3. Continuum theory of nematic order 23 1.5.4. Smectic order 25 1.6. Three-dimensional imaging of liver tissue 26 1.7. Overview of the thesis 28 2. Characterizing cellular anisotropy 31 2.1. Classifying protein distributions on cell surfaces 31 2.1.1. Mode expansion to characterize distributions on the unit sphere 31 2.1.2. Vectorial and nematic classes of surface distributions 33 2.1.3. Cell polarity on non-spherical surfaces 34 2.2. Cell polarity in kidney and liver tissues 36 2.2.1. Kidney cells exhibit vectorial polarity 36 2.2.2. Hepatocytes exhibit nematic polarity 37 2.3. Local network anisotropy 40 2.4. Summary 41 3. Order parameters for tissue organization 43 3.1. Orientational order: quantifying biaxial phases 43 3.1.1. Biaxial nematic order parameters 45 3.1.2. Co-orientational order parameters 51 3.1.3. Invariants of moment tensors 52 3.1.4. Relation between these three schemes 53 3.1.5. Example: nematic coupling to an external field 55 3.2. A tissue-level reference field 59 3.3. Orientational order in inhomogeneous systems 62 3.4. Positional order: identifying signatures of smectic and columnar order 64 3.5. Summary 67 4. The liver lobule exhibits biaxial liquid-crystal order 69 4.1. Coarse-graining reveals nematic cell polarity patterns on the lobulelevel 69 4.2. Coarse-grained patterns match tissue-level reference field 73 4.3. Apical and basal nematic cell polarity are anti-correlated 74 4.4. Co-orientational order: nematic cell polarity is aligned with network anisotropy 76 4.5. RNAi knock-down perturbs orientational order in liver tissue 78 4.6. Signatures of smectic order in liver tissue 81 4.7. Summary 86 5. Effective models for cell and network polarity coordination 89 5.1. Discretization of a uniaxial nematic free energy 89 5.2. Discretization of a biaxial nematic free energy 91 5.3. Application to cell polarity organization in liver tissue 92 5.3.1. Spatial profile of orientational order in liver tissue 93 5.3.2. Orientational order from neighbor-interactions and boundary conditions 94 5.3.3. Orientational order from coupling to an external field 99 5.4. Biaxial interaction model 101 5.5. Summary 105 6. Network self-organization in a liver-inspired lattice model 107 6.1. Cubic lattice geometry motivated by liver tissue 107 6.2. Effective energy for local network segment interactions 110 6.3. Characterizing network structures in the cubic lattice geometry 113 6.4. Local interaction rules generate macroscopic network structures 115 6.5. Effect of mutual repulsion between unlike segment types on network structure 118 6.6. Summary 121 7. Discussion and Outlook 123 A. Appendix 127 A.1. Mean field theory fo the isotropic-uniaxial nematic transition 127 A.2. Distortions of the Mollweide projection 129 A.3. Shape parameters for basal membrane around hepatocytes 130 A.4. Randomized control for network segment anisotropies 130 A.5. The dihedral symmetry group D2h 131 A.6. Relation between orientational order parameters and elements of the super-tensor 134 A.7. Formal separation of molecular asymmetry and orientation 134 A.8. Order parameters under action of axes permutation 137 A.9. Minimal integrity basis for symmetric traceless tensors 139 A.10. Discretization of distortion free energy on cubic lattice 141 A.11. Metropolis Algorithm for uniaxial cell polarity coordination 142 A.12. States in the zero-noise limit of the nearest-neighbor interaction model 143 A.13. Metropolis Algorithm for network self-organization 144 A.14. Structural quantifications for varying values of mutual network segment repulsion 146 A.15. Structural quantifications for varying values of self-attraction of network segments 148 A.16. Structural quantifications for varying values of cell demand 150 Bibliography 152 Acknowledgements 175

We utilize the exact factorization of the electron-nuclear wave function [Abedi et al., PRL 105 123002 (2010)] to illuminate several aspects of laser-driven molecular dynamics in intense femtosecond laser pulses. Above factorization allows for a splitting of the full molecular wave function and leads to a time-dependent Schrödinger equation for the nuclear subsystem alone which is exact in the sense that the absolute square of the corresponding, purely nuclear, wave function yields the exact nuclear N-body density of the full electron-nuclear system. As one remarkable feature, this factorization provides the exact classical force, the force which contains the highest amount of electron-nuclear correlations that can be retained in the quantum-classical limit of the electron-nuclear system. We re-evaluate the classical limit of the nuclear Schrödinger equation from the perspective of the exact factorization, and address the long-standing question of the validity of the popular quantum-classical surface hopping approach in laserdriven cases. In particular, our access to the exact classical force allows for an elaborate evaluation of the various and completely different potential energy surfaces frequently applied in surface hopping calculations. The highlight of this work consists in a generalization of the exact factorization and its application to the laser-driven molecular wave function in the Floquet picture, where the molecule and the laser form an united quantum system exhibiting its own Hilbert space. This particular factorization enables us to establish an analytic connection between the exact nuclear force and Floquet potential energy surfaces. Complementing above topics, we combine different well-known and proven methods to give a systematic study of molecular dissociation mechanisms for the complicated electric fields provided by modern attosecond laser technology.:Contents Introduction 1 The exact factorization of time-dependent wave functions 1.1 Concern and state of the art 1.2 The exact factorization of the electron-nuclear wave function 1.3 The generalized exact factorization 1.4 The exact factorization for coupled harmonic oscillators 1.5 The exact factorization for a single particle with spin 1.6 The exact factorization of the laser-driven electron-nuclear wave function in the Floquet picture 1.7 Summary and conclusion 2 Quantum-classical molecular dynamics from an exact factorization perspective 2.1 Concern and state of the art 2.2 The exact nuclear TDSE 2.3 The Wigner-Moyal equation for the nuclear TDSE and its classical limit 2.4 The Bohmian formulation of the nuclear TDSE and its classical limit 2.5 Comparative calculations 2.5.1 Scenario 1: stationary states 2.5.2 Scenario 2: laser-driven dynamics 2.6 Summary and conclusion 3 Surface hopping in laser-driven molecular dynamics 3.1 Concern and state of the art 3.2 Surface hopping 3.3 Quantum-classical dynamics on the EPES 3.4 The benchmark model and its potential energy surfaces 3.5 Surface hopping in laser-driven molecular dynamics 3.6 Summary and conclusion 4 Beyond the limit of the Floquet picture: molecular dissociation in few-cycle laser pulses 4.1 Concern and state of the art 4.2 Theoretical few-cycle pulses 4.3 Calculation of dissociation probabilities 4.4 Dissociation in few-cycle pulses 4.4.1 Dissociation in half-cycle pulses 4.4.2 Dissociation in few-cycle pulses 4.5 Dissociation in realistic attosecond pulses 4.6 Summary and conclusion Outlook Appendices A List of abbreviations B Numerical details C Calculating electronic observables within quantum-classical molecular dynamics D Ionization in few-cycle pulses E Modeling an optical attosecond pulse Bibliography