Thesis (proefschrift ter verkrijging van den graad doctor -- Rijksuniversiteit te Leiden, 1933. / Summary in English. Includes bibliographical references.

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The Heusler alloys have been of interest since 1903 when F. Heusler reported that ferromagnetic alloys could be made from non-ferromagnetic constitutents copper-manganese bronze and group B elements such as aluminium and tin.

Thesis advisor: Kevin S. Bedell / The Landau Fermi liquid theory is a very successful theory in condensed matter physics. It provides a phenomenological framework for describing thermodynamics, transport and collective modes of itinerant fermionic systems. In 1957, Silin described the spin waves in polarized Fermi liquids based on Landau Fermi liquid theory, which are related to series of components of the spherical harmonic expansion of the fermi surface. It has been proved by Pomeranchuck that for the Fermi surface to be stable, the Landau parameters should satisfy the relation: $F_l^{s,a}>-(2l+1)$. Whenever the relation is violated, there will exist an instability of the Fermi surface known as a Pomeranchuck instability, such as the Stoner ferromagnetism when $F_0^a→ -1^+$, or phase separation when $F_0^s→ -1^+$. In 1959, Abrikosov and Dzyaloshinskii developed a ferromagnetic Fermi liquid theory(FFLT) of itinerant ferromagnetism based on Landau Fermi liquid theory, whose microscopic foundations were established later by Dzyaloshiskii and Kondratenko. Further studies had been made of this state using a generalized Pomeranchuck instability based on the FFLT of Blagoev, Engelbrecht and Bedell and Bedell and Blagoev. In this thesis, I study a magnetically ordered system with spin orbit magnetism, where the order parameter has a net spin current and no net magnetization in both two dimension and three dimension. Starting from a Fermi liquid theory, similar to that for a weak ferromagnet, I have shown that this excitation emerges from an exotic magnetic Fermi liquid state that is protected by a generalized Pomeranchuck condition. I derive the propagating mode using the Landau kinetic equation, and find that the dispersion of the mode has a $sqrt q$ behavior in leading order in 2D. I also find an instability toward superconductivity induced by this exotic mode, and a further analysis based on the forward scattering sum rule strongly suggests that this superconductivity has triplet pairing symmetry. I perform similar studies in the 3D case, with a slightly different magnetic system and find that the mode leads to a Lifshitz-like instability most likely toward an inhomogeneous magnetic state in one of the phases. I also study the collective modes in itinerant ferromagnetic system, which is related to the $F_0^a$ pomeranchuck instability. Using FFLT, I obtained the well-known magnon (Nambu-Goldstone) mode and a gapped mode that was first found by Bedell and Blagoev. I have identified this mode as the Higgs boson (amplitude mode) of a ferromagnetic metal. This is identified as the Higgs since it can be shown that it corresponds to a fluctuation of the amplitude of the order parameter. I use this model to describe the itinerant-electron ferromagnetic material MnSi. By fitting the model with the existing experimental results, I calculate the dynamical structure function and see well-defined peaks contributed from the magnon and the Higgs. From my estimates of the relative intensity of the Higgs amplitude mode I expect that it can be seen in neutron scattering experiments on MnSi. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Mak Hon-lung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves [105]-107). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgements --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.x / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- The origin of Heisenberg model --- p.1 / Chapter 1.2 --- High temperature superconductivity --- p.3 / Chapter 1.3 --- This project --- p.6 / Chapter Chapter 2. --- Studies of spin wave theory --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- The uniform antiferromagnetic Heisenberg Model --- p.9 / Chapter 2.2.1 --- Linearization --- p.11 / Chapter 2.2.2 --- Quadratic equation --- p.15 / Chapter 2.2.3 --- Quadratic equation with Constraint --- p.20 / Chapter 2.2.4 --- Other results --- p.24 / Chapter 2.3 --- The anisotropic Heisenberg model --- p.29 / Chapter 2.3.1 --- The uniaxial model --- p.29 / Chapter 2.3.2 --- The XY Ferromagnetic model --- p.31 / Chapter Chapter 3. --- Theoretical approach --- p.35 / Chapter 3.1 --- Classical ground state --- p.35 / Chapter 3.2 --- Quantum fluctuation --- p.37 / Chapter 3.2.1 --- Linear combination of operators --- p.42 / Chapter 3.3 --- Calculation of physical quantities --- p.44 / Chapter 3.3.1 --- Zero mode problem --- p.48 / Chapter Chapter 4. --- Results of unfrustrated systems --- p.52 / Chapter 4.1 --- Introduction --- p.52 / Chapter 4.2 --- Uniform system --- p.52 / Chapter 4.3 --- Missing bond case --- p.55 / Chapter 4.4 --- Vacancy case --- p.58 / Chapter 4.5 --- Ferromagnetic impurity case --- p.61 / Chapter 4.6 --- Antiferromagnetic impurity case --- p.65 / Chapter 4.7 --- Abnormal antiferromagnetic bond case --- p.68 / Chapter Chapter 5. --- Ferromagnetic bond case --- p.71 / Chapter 5.1 --- Origin of ferromagnetic bond --- p.71 / Chapter 5.2 --- Numerical results --- p.72 / Chapter 5.2.1 --- The classical results --- p.72 / Chapter 5.2.2 --- Quantum corrections --- p.75 / Chapter 5.3 --- Results of other schemes --- p.76 / Chapter 5.3.1 --- Spin wave approach --- p.76 / Chapter 5.3.2 --- Other approaches --- p.77 / Chapter Chapter 6. --- The transmittance pattern in a necklace like system --- p.80 / Chapter 6.1 --- Introduction --- p.80 / Chapter 6.2 --- The model --- p.81 / Chapter 6.3 --- Ring configuration --- p.82 / Chapter 6.4 --- Chain configuration --- p.86 / Chapter 6.5 --- The transmittance pattern --- p.87 / Chapter 6.5.1 --- Constant and varying flux --- p.89 / Chapter 6.5.2 --- Random flux --- p.91 / Chapter 6.5.3 --- Constant impurity --- p.93 / Chapter 6.5.4 --- Some random effects --- p.96 / Chapter 6.6 --- Summary --- p.98 / Chapter 6.7 --- "Appendix, Derivation of basic equations " --- p.100 / Chapter Chapter 7. --- Conclusion --- p.103 / Bibliography --- p.105