Complex lanthanide oxide systems are known to host novel phases of matter, while also providing functionality for practical applications. In this dissertation, the structural, magnetic and magnetocaloric properties of three families of lanthanide oxides have been studied with the dual aims of investigating the magnetic behaviour and identifying promising magnetic refrigerants for cooling to temperatures currently accessible using non-renewable liquid He.

The thesis presents a two-part study of the magnetic and magnetocaloric properties of the geometrically frustrated lanthanide garnets, where the magnetic $Ln3+$ form corner-sharing triangles. First, the family of garnets $Ln3A2X3$O$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$, $Ln$ = Gd, Tb, Dy, Ho, $A$ = Ga, Sc, In, Te, $X$ = Ga, Al, Li are investigated. Changes to the single-ion anisotropy of the magnetic ion as well as variations in the chemical pressure radically alters the nature of magnetic ordering, the degree of frustration and the magnetocaloric performance. In the second part, the garnets $Ln3A$Ga$4$O$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$, $Ln$ = Gd, Tb, Dy, Ho, $A$ = Cr, Mn, are studied. Introducing additional spins significantly reduces the frustration in the garnet lattice. Low temperature powder neutron diffraction of Ho$3$MnGa$4$O$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$ reveals concomitant ordering of Ho$\mathrm{<mrow\; data-mjx-texclass="ORD">3+</mrow>}$ and Mn$\mathrm{<mrow\; data-mjx-texclass="ORD">3+</mrow>}$ moments below the ordering temperature, $TN$ = 5.8 K. The magnetocaloric performance of $Ln$_3CrGa$4$O$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$, $Ln$ = Gd, Dy, Ho, greatly surpasses that of the parent $Ln3$Ga$5$O$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$ at $T$ = 2 K.

The final results chapters in the thesis describe the magnetism and magnetocaloric effect in the lanthanide orthoborates, $Ln$BO$3$ , $Ln$ = Eu, Gd, Tb, Dy, Ho, Er, Yb and the lanthanide metaborates, $Ln$(BO$2$)$3$, $Ln$ = Pr, Nd, Gd, Tb. The magnetic $Ln3+$ form slightly distorted edge-sharing triangular layers in $Ln$BO$3$. Unique magnetic features are observed, including short-range ordering and spin reorientation transitions depending on the single-ion anisotropy of the $Ln3+$. The $Ln$BO$3$ are also efficient magnetocalorics in the liquid helium temperature range. The lanthanide metaborates contain one-dimensional chains of magnetic lanthanide ions. Bulk magnetic measurements show features consistent with low-dimensional magnetism, such as magnetisation plateaux at one-third of the saturation magnetisation for Nd(BO$2$)$3$ and Tb(BO$2$)$3$ in a field of 14 T.

This thesis provides insight into the fundamental magnetic properties of complex lanthanide oxide systems and also demonstrates strategies for identifying new magnetocaloric materials: both through chemical control of the structure of well-known magnetocalorics and by studying materials that have not been explored previously. The results pave the way for further in-depth investigations and finding new magnetic coolants based on complex lanthanide oxide systems.