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\begin_layout Chapter
Introduction
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name "chap:introduction"

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\begin_layout Standard
Magnetism is a field encompassing profound fundamental questions and cutting-edg
e technological applications.
 In the absence of a reliable universal description of the bulk behaviour
 of atoms in crystalline solids, empirical research into magnetic materials
 continues to be of great importance.
 Furthermore, the limits on our understanding inevitably mean that future
 technological developments may well arise at least partly serendipitously,
 lending further weight to the case for a wealth and diversity of experimentatio
n.
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\begin_layout Standard
This thesis concentrates on a selection of magnetic materials with unusual
 properties, ranging from the strangely weak magnetism in a pair of osmium
 compounds, to the quasi--low-dimensional magnetism in molecular magnetic
 systems, where the magnetic interactions in three-dimensional crystals
 are significantly stronger in two-dimensional planes than they are between
 those planes.
 Molecular magnetism in particular offers a rich playground for both fundamental
 physicists and aspiring technologists: based on the complex chemistry of
 carbon, molecular materials can be created with an increasing degree of
 control, iterating towards bespoke design of magnets to test specific theories,
 or to dovetail precisely into desired applications.
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The unifying theme of this thesis is the study of these novel materials
 using muon-spin relaxation, or 
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muSR 
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.
 Muons are short-lived exotic particles rather like heavy, positively-charged
 electrons, and their use as probes in magnetic systems provides unique
 insight into the physics of many materials.
 Muons can be created fully spin-polarised, and embedding them within a
 material allows its local properties to be studied by following how the
 muon-spin relaxes during its brief existence.
 One of the chief difficulties with 
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 is that where exactly the muon will choose to embed is 
\emph on
a priori
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 unknown, making quantitative interpretation of some of the results impossible.
 However, work in this thesis seeks to partially circumvent this restriction
 by making reasonable assumptions about where a muon is 
\emph on
likely
\emph default
 to sit, and consequently making probabilistic estimates of magnetic moments
 or structures.
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Thesis structure
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reference "chap:musr"

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:
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 The 
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 technique is described, providing background together with a brief overview
 of theoretical and experimental considerations.
 Aspects relevant to this thesis are emphasised.
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Dipole-field simulations for locating muon sites are explained, along with
 the mathematical tools underpinning them (Ewald summation, magnetic propagation
 vectors).
 A novel Bayesian method allowing muons to be used to extract bounds on
 magnetic properties is introduced.
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: 
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A pair of unusual osmate compounds are investigated, with 
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 results being used to ascertain the magnitude of probable low magnetic
 moments in both.
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Introductory material is provided for the following two chapters, introducing
 two-dimensional magnetism and the molecular compounds which we will use
 as model systems to probe it.
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Magnetism in a family of copper-based molecular compounds is explored with
 
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, with a combination of 
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 oscillations and Bayesian dipole field simulations being used to extract
 the moments on the copper ions.
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: 
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A short review of related two-dimensional molecular magnets investigated
 with 
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 is provided.
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