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\begin_layout Chapter*
Quantum magnetism probed with muon-spin relaxation
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Andrew J.
 Steele
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Christ Church, Oxford
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Trinity term 2011
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Abstract of thesis submitted for the degree of Doctor of Philosophy
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This thesis presents the results of muon-spin relaxation (
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muSR 
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) studies into magnetic materials, and demonstrates how these results can
 be exploited to quantify the materials' low moments and reduced dimensionality.
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Dipole-field simulations, traditionally used to estimate likely muon sites
 within a crystal structure, are described.
 A novel Bayesian approach is introduced which allows bounds to be extracted
 on magnetic moment sizes and magnetic structures---previously very difficult
 using 
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muSR 
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---based on reasonable assumptions about positions in which muons are likely
 to stop.
 The simulations are introduced along with relevant theory, and 
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mmcalc 
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, a platform-independent program which I have developed for performing the
 calculations is described.
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The magnetic ground states of the isostructural double perovskites Ba
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2
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NaOsO
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6
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 and Ba
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2
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LiOsO
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6
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 are investigated with 
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muSR 
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.
 In Ba
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2
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NaOsO
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6
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 long-range magnetic order is detected via the onset of a spontaneous muon-spin
 precession signal below 
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, while in Ba
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2
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LiOsO
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 a static but spatially-disordered internal field is found below 
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SI{8}{
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.
 Bayesian analysis is used to show that the magnetic ground state in Ba
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NaOsO
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 is most likely to be low-moment (
\begin_inset Formula $\approx0.2\mu_{\mathrm{B}}$
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) ferromagnetism and not canted antiferromagnetism.
 Ba
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2
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LiOsO
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 is antiferromagnetic and a spin-flop transition is found at 
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SI{5.5}{
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tesla}
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.
 A reduced osmium moment is common to both compounds, probably arising from
 a combination of spin--orbit coupling and frustration.
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Results are also presented from 
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muSR
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 investigations concerning magnetic ordering in several families of layered,
 quasi--two-dimensional molecular antiferromagnets based on transition metal
 ions such as 
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 Cu
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2+
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 bridged with organic ligands such as pyrazine.
 
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muSR
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 allows us to identify ordering temperatures and study the critical behaviour
 close to 
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, which is difficult using conventional probes.
 Combining this with measurements of in-plane magnetic exchange 
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 and predictions from quantum Monte Carlo simulations allows assessment
 of the degree of isolation of the 2D layers through estimates of the effective
 inter-layer exchange coupling and in-layer correlation lengths at 
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.
 Likely metal-ion moment sizes and muon stopping sites in these materials
 are identified, based on probabilistic analysis of dipole-fields and of
 muon--fluorine dipole--dipole coupling in fluorinated materials.
 
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