Interaction of magnetism with atomic lattice geometry and nanoscale geometric frustration
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From lodestones to quantum computers, magnetism has been intricately entwined with scientific and technological development of humankind for millennia. A short chronological list of important experiments, theories and effects connected with magnetism that substantially altered the course of human understanding of the physical world: Magnetites, navigation, the concept of fields, electromagnetism and Maxwell's equations, Zeeman effect, Curie's law, special relativity, quantum mechanical spin, cooperative phenomena, phase transitions, frustration, Ising model, quantum statistical mechanics, magnetic memories, high-temperature superconductivity, spintronics and so on. The seemingly uninteresting effect of magnetic anisotropy is probably the only observable effect that requires for its explanation, both quantum mechanics and special relativity, the two towering theories of twentieth century. This effect arises from the interaction between the spin part and the spatial part of an electron's wavefunction, which is due to the relativistic motion of electron around the nucleus. Without such an interaction, magnetism would have remained as a pure academic interest. The macroscopic manifestation of this spin-orbit interaction, magnetic anisotropy, is the central theme of this thesis. In the first chapter, we explore how ionic displacements in a solid and magnetization directions are tied together through spin-orbit coupling. Magnetic ion doped semiconductor Gallium Manganese Arsenide shows rich and intricate magnetic anisotropies, with one of the anisotropy components unexpected from symmetry grounds. This chapter explains how the inclusion of displacements of the impurity ion helps us explain the apparently unexpected observation of uniaxial magnetic anisotropy in the above material. In the second chapter, we utilize this magnetic anisotropy by bringing together two materials, one with very high and another with negligible anisotropy, to introduce magnetic frustration in a nanoscale system. The effect of frustration, where not all the forces or constraints can be simultaneously satisfied, results in rich energetic behavior where the system accesses different sets of energy minima for different strengths of external rotating magnetic field. We propose and computationally demonstrate the functioning of a ternary logic device using the above nanoscale system. Five appendices are included, elaborating on technical details, detailed derivations, explanation of constants and summary of papers whose results were used in the thesis.