In this thesis Moore and Yeo's proposed mapping of the structural glass to the Ising spin glass in a random field is presented. In contrast to Random First Order Theory and Mode Coupling Theory, this mapping predicts that there should be no glass transition at finite temperature. However, a growing correlation length is predicted from the size of rearranging regions in the supercooled liquid, and from this a growing structural relaxation time is predicted. Also presented is a study of the propensity of binary fluids (i.e. fluids containing particles of two sizes) to phase separate into regions dominated by one type of particle only. Binary fluids like this are commonly used as model glass formers and the study shows that this phase separation behaviour is something that must be taken into account.The mapping relies on the use of replica theory and is therefore very opaque. Here a model is presented that may be mapped directly to a system of spins, and also prevents the process of phase separation from occurring in binary fluids. The system of spins produced in the mapping is then analysed through the use of an effective Hamiltonian, which is in the universality class of the Ising spin glass in a random field. The behaviour of the correlation length depends on the spin-spin coupling J and the strength of the random field h. The variation of these with packing fraction and temperature T is studied for a simple model, and the results extended to the full system. Finally a prediction is made for the critical exponents governing the correlation length and structural relaxation time.

We analyze the replica-symmetry-breaking (RSB) construction in the Sherrington - Kirkpatrick (SK) model and in the p-state Potts glass for p ≤ 4. We present a general scheme for deriving an asymptotic solution with an arbitrary number of discrete hierarchies of broken replica symmetry near the critical temperature for both models, and close to the de Almeida- Thouless instability line in the SK model. We show that in the SK model all solutions with finite many hierarchies are unstable and only the scheme with infinite many hierarchies becomes marginally stable in the spin-glass phase. For the Potts glass, we find, moreover, an one-step RSB solution which co- exists with the infinite RSB solution for p > p∗ ≈ 2.82. The former solution is locally stable but has lower free energy than the latter which is marginally stable and has the highest free energy. 1

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20386号 / 工博第4323号 / 新制||工||1670(附属図書館) / 京都大学大学院工学研究科材料化学専攻 / (主査)教授 田中 勝久, 教授 平尾 一之, 教授 三浦 清貴 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22780号 / 工博第4779号 / 新制||工||1747(附属図書館) / 京都大学大学院工学研究科材料化学専攻 / (主査)教授 田中 勝久, 教授 陰山 洋, 教授 藤田 晃司 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The spin-glass is a peculiar magnetic phase, exhibiting non-trivial dynamics at low temperatures, characterized by an continuously evolving state without long-range order. The behavior requires some degree of disorder to occur, often in the way of impurities or random exchange energy between the spins. However, recent research have found structurally ordered systems exhibiting glassy behaviour. This project aims to further investigate these self-induced spin-glasses. The report provides a short introduction to atomistic spin-dynamics and applies the theory to study self-induced spin-glasses in hexagonal systems with the help of simulations. A variation approach was applied by running simulation using a range of spin-exchange couplings in the Heisenberg Hamiltonian. These systems were then studied by the means of their autocorrelation function and compared to known glassy systems from the Edwards-Andersson model. The resulting behaviour is presented for three different hexagonal structures and glassy behaviour is indicated in stacked hexagonal systems. It is however argued that the autocorrelation function is not sufficient to classify these systems, instead further observables are needed. Nevertheless, the method of studying self-induced spin-glasses by varying couplings in the Heisenberg Hamiltonian is promising. As even with the few spin interactions used in this report we observe the slow relaxation time associated with spin-glasses. Given some extra considerations when choosing the exchange used for the simulation, a self-induced glassy state should be able to be recreated using the method described in this report. / Spinn-glas är en speciell magnetisk fas som uppvisar icke trivial dynamik vid låga temperaturer, en kontinuerlig utveckling samt en avsaknad av ordning på stora skalor. Detta beteende kräver en viss gradav oordning för att uppstå, ofta i form av föroreningar i materialet eller slumpmässiga interaktioner mellan olika spinn. Forskning har dock visat att även strukturellt ordnade system kan uppvisa spinn-glas beteende. Därmed är målet med detta projekt att fortsätta undersöka dessa själv-inducerade spinn-glas. Rapporten ger en kort introduktion till atomistisk spinn-dynamik och applicerar denna teori för att studera själv-inducerade spin-glas i hexagonala system. I projektet simulerades system med varierande spin-interaktioner i Heisenberg Hamiltonianen. Dynamiken undersöktes med hjälp av en korrelationsfunktion som jämfördes mot kända spinn-glas från Edwards-Andersson modellen. Resultat presenteras för tre hexagonala strukturer och spinn-glas-liknande beteende observeras i de tre-dimensionella systemen. Det kan dock argumenteras att korrelationsfunktionen inte är tillräcklig för att klassificera dessa system och att mer kvantitativa mått krävs. Trots detta anses metoden, att variera spinn-interaktioner i Heisenberg Hamiltonianen, vara lovande. Detta eftersom den långa avslappningstiden associerad med spinn-glas påträffades, trots de få interaktioner som användes i denna rapport. Ett själv-inducerat spin-glass borde därmed kunna skapas med de metoder som presenteras i rapporten, givet en mer systematisk metod vid val av interaktionsparametrar för simuleringen.

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This thesis presents experimental results on strongly interacting γ-Fe2O3 magnetic nanoparticles and their collective properties. The main findings are that very dense randomly packed (≈60%) γ-Fe2O3 nanoparticles form a replica of a spin glass. The magnetic properties of the nanoparticle system are in most regards the same as those of an atomic spin glass. The system is therefore proposed as a model superspin glass. In superspin glasses the interacting building blocks that form the collective state are single domain nanoparticles, superspins with a magnetic moment of about 10000 μB, which can be compared to the atomic magnetic moment in spin glasses of approximately 1 μB.  It was found that the relaxation time of the individual nanoparticles impacts the collective properties and governs the superspin dimensionality. Several dense compacts, each prepared with nanoparticles of a specific size, with diameters 6, 8, 9 and 11.5 nm, were studied. All the studied compacts were found to form a superspin glass state. Non-interacting reference samples, consisting of the same particles but coated with a silica shell, were synthesized to determine the single particle magnetic properties.  It was also found that the effects of the nanoparticle size distribution, which lead to a variation of the magnetic properties, can be mitigated by having strong enough interparticle interactions. The majority of the work was carried out using SQUID magnetometry.

The structural chemistry and magnetic properties of compounds isostructural with La₁₈Li₈Rh₅O₃₉ have been studied. In this cubic structure (space group Pm^{^_}<sub style='position: relative; left: -.5em;'>3</sub>n), [111] chains of alternating RhO₆ octahedra (2a, 8e sites) and LiO₆ trigonal prisms (16i site) occupy channels within a La-O framework. In order to study the consequences of both reducing the dimensions of the channels and introducing paramagnetic cations into both the framework and the polyhedral chains, compositions in the series Nd₁₈Li₈Rh_5-xFe_xO₃₉ (1 &le; x &le; 4) have been synthesised and characterised by magnetometry, neutron diffraction and Mössbauer spectroscopy. Iron preferentially occupies the 2a site as low-spin Fe(IV) and the larger 8e site as high-spin Fe(III). Compositions having x > 1 show spin-glass-like behaviour below ~5 K. The behaviour of this series of compositions has been compared with that of the known series La₁₈Li₈Rh_5-xFe_xO₃₉. In order to facilitate this comparison, the structure of La₁₈Li₈Fe₅O₃₉ has been fully characterised by both neutron diffraction and EXAFS. The use of both techniques has revealed differences between the mean and local environments of iron. In order to explore and extend the range and combinations of elements that can be accommodated in this structure, the Ti-containing compounds Ln₁₈Li₈M₄TiO₃₉ (Ln=La,Nd,Pr,Sm; M=Rh,Fe,Co) have been synthesised. Nd₁₈Li₈Fe₄TiO₃₉ was selected for a detailed study by magnetometry, neutron diffraction, Mössbauer spectroscopy and XANES. Cations were found to be stabilised in unusual oxidation states and disordered over three sites of the Nd₁₈Li₈Fe₄TiO₃₉ polyhedral chains. The 8e site is occupied by high-spin Fe³⁺, Ti³⁺ and Li⁺ in a ratio of 76:20:4; the 2a site by low-spin Fe⁴⁺ and Ti⁴⁺ in a ratio of 79:21 and the trigonal-prismatic 16i site by Li⁺ and Fe³⁺ in a ratio of 98:2. Nd₁₈Li₈Fe₄TiO₃₉ undergoes a transition to a spin-glass state at 4.25(5) K, whereas La₁₈Li₈Fe₄TiO₃₉ revealed a different type of magnetic transition at ~8 K. The nature of this transition is not yet clear. Monophasic samples could not be prepared in the Nd/Rh system and cation vacancies were found in Nd/Co. No pure samples of Sm-containing compositions could be prepared, while the only Pr composition which was obtained pure, according to X-ray diffraction, Pr₁₈Li₈Co₄TiO ₃₉ shows the similar magnetic properties to Pr₁₈Li₈Co₃TiO₃₉. The compositions Ln₁₈Li₈M₃ M'O₃₉ (Ln=La,Nd,Pr,Sm; M,M'=Fe,Co,Ti) with 25% of the 8e sites vacant have been investigated. The Co-containing compositions Nd₁₈Li₈Co₃FeO_39-y, Nd₁₈Li₈CoFe₃O_39-y and Nd₁₈Li₈Co₃TiO_39-y were characterised by neutron diffraction. Cation vacancies on the 8e sites were found to coexist with anion vacancies around the 2a sites. The remaining octahedral sites are occupied by a disordered arrangement of transition-metal cations. The trigonal-prismatic sites are fully occupied by Li except in the case of Nd₁₈Li₈CoFe₃O_39-y where some Fe is present, as confirmed by Mössbauer spectral data. Antiferromagnetic interactions are present on the Nd sublattice in each composition, but a spin glass forms below 5 K when a high concentration of spins is also present on the octahedral sites. The magnetic character of the Ln cations plays an important role in determining the properties of these compounds. Long-range magnetic order of the transition-metal cations was not observed in any compositions. Although this might be partly attributable to the cation disorder in the polyhedral chains, the apparent antiferromagnetic behaviour of Nd-containing compositions in which the transition metals have a low magnetic moment, e.g. Nd₁₈Li₈Co₃TiO_39-y, and the marked contrast between certain La and Nd compositions in which the transition metal content is the same, e.g. Nd₁₈Li₈Fe₄TiO₃₉ and La₁₈Li₈Fe₄TiO₃₉, suggests that the Ln sublattice is fully involved in determining the magnetic behaviour.

Na primeira parte deste trabalho propomos uma aproximacão de campo médio dinâmico para analisar modelos de Ising com elementos e aleatoriedade definidos por distribuicões de probabilidades discretas. Analisamos o modelo com campo aleatório (S = 1/2), com interações aleatórias (S = 1/2), com diluição de sítios (S = 1/2) e com anisotropia aleatória (S = 1), obtendo  os respectivos diagramas de fases.   Na segunda parte analisamos modelos de vidros de spin (S= 3/2) com anisotropia de campo cristalino. Estudamos o modelo de van Hemmen, e o modelo clássico à la Sherrington e Kirkpatrick dentro do esquema de réplicas simétricas, obtendo os  diagramas de fases correspondentes. / In the first part of this work we propose a dynamical mean field approximation to analyse Ising models with elements of randomnss, defined by discret probability functions. We have analysed the random field model (S = 1/2); the random bond model (S = 1/2); the site diluted model (S = 3/2) and the random crystal field model (S = 1), obtaining the respective phase diagrams.   In the second part we have analysed spinglass models (S = 3/2) in the presence of a crystal field. We have studied the van Hemmen and the classic spin glass model à la Sherrington and Kirkpatrick, using replica symmetric scheme, to obtain the corresponding phase diagrams.