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Intro; Supervisor's Foreword; Abstract; Parts of this thesis have been published in the following journal articles:Chapter 1: S. Zhang, A.A. Baker, S. Komineas, and T. Hesjedal, "Topological computation based on direct magnetic logic communication", Sci. Rep. 5, 1773 (2015). Chapter 2: A.I. Figueroa, S.L. Zhang, A.A. Baker, R. Chalasani, A. Kohn, S.C. Speller, D. Gianolio, C. Pfleiderer, G. van der Laan, and T. Hesjedal, "Strain in epitaxial MnSi films on Si(111) in the thick film limit studied by polarization-dependent extended x; Acknowledgements; Contents; Acronyms; 1 The Story So Far.
1.1 Theoretical Treatments1.1.1 Skyrme Field in the Non-linear Sigma Model; 1.1.2 The Theory of Magnetic Skyrmions; 1.1.3 Magnetism of P213 Helimagnets; 1.2 The Properties of Magnetic Skyrmions; 1.2.1 Interaction with Conduction Electrons; 1.2.2 Interaction with Magnons; 1.3 Characterisation of Magnetic Skyrmions; 1.3.1 Magnetic Neutron Diffraction; 1.3.2 Lorentz Transmission Electron Microscopy; 1.3.3 Magnetic Force Microscopy; 1.4 What Is Missing?; 1.5 Structure of the Thesis; References; 2 Measurement of the Magnetic Long-Range Order; 2.1 Writing Down the Scattering Process.
2.1.1 Scattering from a Single Electron2.1.2 Scattering from a Single Atom; 2.1.3 Scattering from a Periodic Lattice; 2.1.4 Scattering from Helical, Conical, and Skyrmion Order; 2.2 REXS in Reflection Geometry; 2.2.1 Results; 2.3 REXS in Grazing Geometry; References; 3 Measurement of the Skyrmion Lattice Domains; 3.1 Diffraction from the Multidomain Skyrmion Lattice State; 3.2 Imaging of the Multidomain Skyrmion Lattice State; 3.3 Domain Boundary Structure; References; 4 Measurement of the Topological Winding Number; 4.1 REXS Polarisation Dependence; 4.2 Topology Determination Principle.
4.3 Robustness of Topology Determination Principle4.3.1 Numerical Calculations and Robustness of TDP; References; 5 Measurement of the Skyrmion Helicity Angle; 5.1 Representation of the Arbitrary Spin Spiral; 5.2 Writing Down the Circular Dichroism; 5.2.1 Results; 5.3 Measurement of the Skyrmion Helicity Angle; 5.3.1 Characteristic Helix and the Associated Skyrmion; 5.3.2 Numerical Calculations; 5.3.3 Results; References; 6 Dichroism Extinction Rule; Curriculum Vitae.
1.1 Theoretical Treatments1.1.1 Skyrme Field in the Non-linear Sigma Model; 1.1.2 The Theory of Magnetic Skyrmions; 1.1.3 Magnetism of P213 Helimagnets; 1.2 The Properties of Magnetic Skyrmions; 1.2.1 Interaction with Conduction Electrons; 1.2.2 Interaction with Magnons; 1.3 Characterisation of Magnetic Skyrmions; 1.3.1 Magnetic Neutron Diffraction; 1.3.2 Lorentz Transmission Electron Microscopy; 1.3.3 Magnetic Force Microscopy; 1.4 What Is Missing?; 1.5 Structure of the Thesis; References; 2 Measurement of the Magnetic Long-Range Order; 2.1 Writing Down the Scattering Process.
2.1.1 Scattering from a Single Electron2.1.2 Scattering from a Single Atom; 2.1.3 Scattering from a Periodic Lattice; 2.1.4 Scattering from Helical, Conical, and Skyrmion Order; 2.2 REXS in Reflection Geometry; 2.2.1 Results; 2.3 REXS in Grazing Geometry; References; 3 Measurement of the Skyrmion Lattice Domains; 3.1 Diffraction from the Multidomain Skyrmion Lattice State; 3.2 Imaging of the Multidomain Skyrmion Lattice State; 3.3 Domain Boundary Structure; References; 4 Measurement of the Topological Winding Number; 4.1 REXS Polarisation Dependence; 4.2 Topology Determination Principle.
4.3 Robustness of Topology Determination Principle4.3.1 Numerical Calculations and Robustness of TDP; References; 5 Measurement of the Skyrmion Helicity Angle; 5.1 Representation of the Arbitrary Spin Spiral; 5.2 Writing Down the Circular Dichroism; 5.2.1 Results; 5.3 Measurement of the Skyrmion Helicity Angle; 5.3.1 Characteristic Helix and the Associated Skyrmion; 5.3.2 Numerical Calculations; 5.3.3 Results; References; 6 Dichroism Extinction Rule; Curriculum Vitae.