This thesis contains discussions of a number of points which arose when the author was studying the "paramagnetic resonance line shape problem". The so-called moment method is discussed, and a new derivation of the moments of the line shape function is given. Single-spin operators are introduced which simplify the calculation of these moments. The Green's function technique, as applied to this problem, and the decoupling approximations associated with the technique, are looked at from the point of view of reliability and complexity. As a test of the reliability of any decoupling, a theorem concerning the moments of a line shape arising from such a decoupling is discussed and proved. The Green's function technique is applied to the case of the one-dimensional Ising model with spin ½, where no decoupling of the hierarchy of Green's function equations is necessary. A method of calculating thermal averages for this case, using difference equations, is given. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis is devoted to a theoretical study of that temperature dependence of the shape of magnetic resonance lines in solids which remain when the direct effect of lattice vibrations can be neglected. This is the case at sufficiently low temperatures. To discuss the shape of resonance lines the "moment method" is used. This procedure was introduced by Van Vleck (1948) and was used also by Pryce and Stevens (1950) and Usui and Kambe (1952). A line shape function which describes the shape of the resonance lines is defined and the first and second moments of this function are calculated in various approximations. In particular, the question to what extent the standard formula of Van Vleck for the second moment is valid is discussed in great detail. The general formulae are applied to the case of a spherical sample of nickel fluosilicate crystal. From the general discussions and from this special case it follows that the temperature dependence of the characteristics of paramagnetic resonance lines becomes noticeable at liquid helium temperatures and that these characteristics are then also dependent on the shape of the sample. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Previous work had shown that near the composition MneoA1₂oC₂o there occurs a highly ordered cubic phase with interesting magnetic properties. A study of the effect of additions of iron and chromium has been carried out with a view to obtaining some information about the structure and magnetic properties. Two alloy groups were studied, first, Mn₆₀(Fe or Cr)ₓA1₂₀-ₓc₂₀ and second Mn₆₀₋ₓ(Fe or Cr)ₓA1₂₀C₂₀. It was found that in the former group the magnetization decreased markedly with either Fe or Cr additions. The results could be represented by assuming the manganese moments were constant and the Fe or Cr atoms had a net moment of -5 Bohr magnetons when replacing an Aluminum atom. The second group yielded no such simple representation because the moment per magnetic atom values varied quite irregularly. The only possible observation was that the average moment was always less than that of manganese in Mո₃A1C. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

No description available.

Quantum materials are solids that have unique electronic, magnetic, or optical properties arising due to quantum mechanical effects. Superconductors, topological insulators, and exotic magnets are examples of quantum materials. This thesis comprises three studies that explore the properties of four superconductors and a breathing pyrochlore magnet. In the first study, we investigate the superconducting properties of Re3B, and Re7B3 and determine the role of Re concentration and crystal inversion symmetry. Our findings reveal conventional superconductivity in both of these superconductors, despite having many ingredients for hosting unconventional superconductivity. The second study investigates the superconducting properties of non-centrosymmetric superconductors TaRuSi and TaReSi, specifically focusing on the role of spin-orbit coupling. By using density functional theory calculations, we determine the magnitude of anti-symmetric spin-orbit coupling and, using a combination of zero field and transverse field muon spin rotation /relaxation, reveal that TaRuSi hosts an unconventional superconducting state with broken time-reversal symmetry. TaReSi, however, hosts a conventional superconducting state. In the third study, we describe the synthesis and physical and magnetic properties of CuAlCr4S8, which is a breathing pyrochlore magnet. Breathing pyrochlores consist of a three-dimensional array of corner-sharing tetrahedra of alternating size formed by magnetic atoms, and their magnetic properties can be tuned by adjusting the breathing ratio. We demonstrate how CuAlCr4S8 allows for the clean realization of breathing pyrochlore physics, due to the absence of any structural transition. Overall, our studies contribute to a deeper understanding of the properties of unconventional superconductors and breathing pyrochlore magnets, revealing new insights into their exotic physics and the underlying mechanisms that govern their behaviors. / Thesis / Candidate in Philosophy / We study superconducting Re3B, Re7B3, TaRuSi, and TaReSi to understand the role of symmetries of the crystal structure and spin-orbital coupling in generating unconventional superconducting properties. We learn that Re3B, Re7B3, and TaReSi display conventional superconducting properties, whereas TaRuSi exhibits unconventional superconducting behavior in the form of time-reversal symmetry-breaking fields and a nodal superconducting gap. A breathing pyrochlore consists of magnetic atoms at the vertices of corner-sharing tetrahedra of alternating sizes. We synthesized a new Cr-based breathing pyrochlore magnet, CuAlCr4S8, and studied its physical and magnetic properties. The ratio of sizes of two tetrahedra in CuAlCr4S8 is 1.0663(8), and it undergoes an antiferromagnetic transition of a purely magnetic nature at 20 K. We conclude that CuAlCr4S8 is an ideal system to study breathing pyrochlore physics due to low anti-site disorder.

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No description available.

This dissertation details studies of three different frustrated magnet families: NaCaNi$_2$F$_7$, Er$_3$Ga$_5$O$_{12}$, and ErMgGaO$_4$, using a variety of techniques, including magnetization, specific heat, neutron scattering and muon spin rotation/relaxation ($\mu$SR). NaCaNi$_2$F$_7$ belongs to the fluoride pyrochlores family. In this thesis, we study the effect of the randomness on the A site on the magnetic property of B site. This chemical disorder randomness was caused by the mixture of two different elements from Group 1 and 2 (Na and Ca). DFT calculation and computation simulations indicates a possible non-centred $F-\mu -F$ muon stopping site. Zero field (ZF) and longitudinal field (LF) $\mu$SR shows that the $Ni^{2+}$ spins undergo spin freezing into a disordered ground state below 4K, with persistent spin dynamics to our lowest temperature 75 mK. We obtained high quality single crystal of Er$_3$Ga$_5$O$_{12}$ by utilizing the optical floating-zone (OFZ) technique. We performed inelastic neutron scattering measurements to determine the crystalline electric field (CEF) Hamiltonian, eigenvalues and eigenvectors, indicating an Ising-like anisotropy ground state which is also consistent with our specific heat experiment with entropy approaching $Rln(2)$. All seven crystalline electric field excitations from the ground state Kramers doublet were identified. In addition, Rietveld refinement of neutron powder diffraction data reveal that Er$_3$Ga$_5$O$_{12}$ orders into the $\Gamma_3$ magnetic structure, with ordered magnetic moment $\mu_{ord} = 5.24(4)~\mu_{B}$, in agreement with $\mu_{Ising}$ = 5.61 $\mu_{B}$ from our deduced CEF Hamiltonian. Our $\mu$SR measurements also reveals the presence of fluctuating local fields on the muon timescale, indicating exotic slow spin dynamics in the ground state. The objective of the work on ErMgGaO$_4$ was to identify a new quantum spin liquid candidate. Single crystals of ErMgGaO$_4$ were obtained through (OFZ) technique as well, and the structure was refined and confirmed by powder X-ray diffraction and Laue diffraction after a repeated refinement of our synthesis process. Susceptibility measurements reveal no evidence of a magnetic transition down to 0.5 K, in agreement with specific heat measurement which exhibit no anomalies which would have been evidence of an ordering transition. ZF-$\mu$SR measurements reveal no sign of coherent long range order or spin freezing down to 25 mK, while LF-$\mu$SR measurements shows persistent spin dynamics at 25 mK. Our observations provides evidence for a quantum spin liquid ground state in this compound. / Thesis / Doctor of Philosophy (PhD)

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Syftet med detta utvecklingsarbete var att utifrån ett nyfikenhets­perspektiv skapa ett arbetsmaterial riktat till förskoleklass och skolår 1 i ämnet magnetism, samt att ta reda på vad begreppet nyfikenhet innebär.Produkten bestod av en högläsningsbok (Magnus Magnet) samt en lärarhandledning med arbetsgång och praktiska övningar. Materialet utvärderades av tre lärare och en lärarstudent. Utvärderingen var mestadels positiv och eleverna tyckte generellt att boken var rolig och underhållande. Till viss del kunde det konstateras att arbetsmaterialet väckte nyfikenhet hos eleverna om fenomenet magnetism. Slutsatsen var att en högläsningsbok samt praktiska övningar om magnetism är en bra metod för att förmedla nyfikenhet och intresse inför naturvetenskapliga fenomen till barn i de första skolåren.