| Summary: | <p>This thesis describes the application of various techniques to the study of magnetic phenomena in condensed matter systems with a particular focus given to a.c. magnetic susceptibility. This is accomplished by briefly discussing the basic theory of condensed matter magnetism before describing measurement techniques employed in this thesis. I discuss magnetometry in detail, contrasting d.c. susceptibility with a.c. susceptibility in the context of the applicability of the latter to the study of slow magnetic dynamics. In order to understand the a.c. response of materials containing slow magnetic dynamics I take a theoretical approach and show how the commonly used models for describing such behaviour arise from the more overarching linear response theory. I then show common treatments of a.c. susceptibility data before reviewing the a.c. response of various classes of material while discussing the origin of the associated magnetic sluggishness.</p> <p>Subsequently, I show studies of two different classes of material showing magnetic sluggishness. In the first study of single-molecule magnets two families are examined: the simpler Co<sup>3+</sup><sub>2</sub>Ln<sup>3+</sup> family (Ln = Gd, Ho, Tb and Er) and the more complex Ni<sup>2+</sup><sub>4</sub>Ln<sup>3+</sup><sub>4</sub> family (Ln = Gd, Ho, Dy, and Tb). By beginning with the Co<sub>2</sub>Ln family in which only the central Ln<sup>3+</sup> ion possesses a magnetic moment I use a.c. susceptibility to show the Tb and Er analogues to display field-induced slow magnetic relaxation consistent with single-molecule magnet behaviour while the Gd and Ho analogues do not. Combining these results with d.c. magnetic measurements in the context of the structure of these compounds allows the origin of this behaviour to be shown to be associated with the relevant Ln<sup>3+</sup> ions. This sets out the process utilised for elucidating the magnetic behaviour of the more complex Ni<sup>2+</sup><sub>4</sub>Ln<sup>3+</sup><sub>4</sub> family in which both transition metal ions and lanthanide ions possess a magnetic moment. As such, the possible magnetic exchanges between ions are evaluated using d.c. techniques and I propose the Dy and Tb analogues to form Ni–Ln dimers (ferromagnetic and antiferromagnetic respectively). Using a.c. susceptibility I demonstrate Ni<sub>4</sub>Dy<sub>4</sub> and Ni<sub>4</sub>Tb<sub>4</sub> to display field-induced slow magnetic relaxation of single-molecule magnet origin only in Ni<sub>4</sub>Dy<sub>4</sub>.</p> <p>The second study I present focuses on the low temperature magnetism associated with the superconducting family Li<sub>1-x</sub>Fe<sub>x</sub>(OH)Fe<sub>1-y</sub>Se which is comprised of alternating two-dimensional layers of Fe<sub>1-y</sub>Se and Li<sub>1-x</sub>Fe<sub>x</sub>(OH). The Fe<sup>2+</sup> ions of the hydroxide layer possess a magnetic moment and by considering a random distribution of these ions in such a layer I suggest the low temperature magnetic state to likely be disordered and spin glass-like. Taking advantage of samples provided by synthetic chemists of superconducting and nonsuperconducting members of this family I show that d.c. magnetometry and heat capacity measurements support a spin glass-like state. A.c. susceptibility and $\mu$SR measurements demonstrate that the magnetic state of Li<sub>1-x</sub>Fe<sub>x</sub>(OH)Fe<sub>1-y</sub>Se contains slow relaxation of a spin glass type.</p>
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