There has been significant interest in BiFeO₃ over the past decade. This interest has focused on the magnetic and electrical properties, which in the long term may prove useful in device applications. This thesis focuses on the synthesis, electrical characterisation, and structural origin of the electrical properties of rare earth doped bismuth ferrite. Two systems have been studied: BiFeO₃ doped with lanthanum and neodymium (Bi₁₋ₓREₓFeO₃ RE= La, Nd). Specific examples have been highlighted focusing on a detailed structural analysis of a lanthanum doped bismuth ferrite, Bi₀.₅La₀.₅FeO₃, and a neodymium analogue, Bi₀.₇Nd₀.₃FeO₃. Both adopt an orthorhombic GdFeO₃-type structure (space group: Pnma) with G-type antiferromagnetism. Structural variations were investigated by Rietveld refinement of temperature dependent powder neutron diffraction using a combination of both conventional “bond angle/bond length” and symmetry-mode analysis. The latter was particularly useful as it allowed the effects of A-site displacements and octahedral tilts/distortions to be considered separately. This in-depth structural analysis was complemented with ac-immittance spectroscopy using the multi-formulism approach of combined impedance and modulus data to correlate structural changes with the bulk electrical properties. This approach was essential due to the complex nature of the electrical response with contributions from different electroactive regions. The structural variations occur due to a changing balance between magnetic properties and other bonding contributions in the respective systems. This results in changes in the magnitude of the octahedral tilts, and A-site displacements giving rise to phenomena such as negative thermal expansion and invariant lattice parameters i.e., the invar effect. More specifically, analysis of Bi₀.₅La₀.₅FeO₃ highlights a structural link between changes in the relative dielectric permittivity and changes in the FeO₆ octahedral tilt magnitudes, accompanied by a structural distortion of the octahedra with corresponding A-site displacement along the c-axis; this behaviour is unusual due to an increasing in-phase tilt mode with increasing temperature. The anomalous orthorhombic distortion is driven by magnetostriction at the onset of antiferromagnetic ordering resulting in an Invar effect along the magnetic c-axis and anisotropic displacement of the A-site Bi³⁺ and La³⁺ along the a-axis. This contrasts with the neodymium analogue Bi₀.₇Nd₀.₃FeO₃ in which a combination of increasing A-site displacements in the ac-plane and decrease in both in-phase and anti-phase tilts combine with superexchange giving rise to negative thermal expansion at low temperature. The A-site displacements correlate with the orthorhombic strain. By carefully changing the synthesis conditions, a significant change in bulk conductivity was observed for a number for Bi₁₋ₓLaₓFeO₃ compositions. A series of Bi₀.₆La0.₄FeO₃ samples are discussed, where changes in the second step of the synthesis result in significantly different bulk conductivities. This behaviour is also observed in other compositions e.g. Bi₀.₇₅La₀.₂₅FeO₃. Changes in the electrical behaviour as a function of temperature are discussed in terms of phase composition and concentration gradients of defects. Activation energies associated with the conduction process(es) in Bi₁₋ₓLaₓFeO₃ samples, regardless of composition, fall within one of two broad regimes, circa. 0.5 eV or 1.0 eV, associated with polaron hopping or migration of charge via oxygen vacancies, respectively. The use of symmetry-mode analysis, in combination with conventional crystallographic analysis and electrical analysis using multi-formulism approach, presents a new paradigm for investigation of structure-property relationships in rare earth doped BiFeO₃.

That certain iron and nickel alloys exhibit an anomalously low thermal expansion of a wide temperature range has been observed since late 1800s, and this effect is known as the Invar effect. Since then, many theories have been proposed to explain the phenomenon. While it is generally agreed that the effect is related to magnetism, a full explanation of the effect has yet to be found. One recent theory connected the effect to spin-flips in the iron atoms' magnetic moment and that the probability for a spin-flip to occur depends on the atom's local chemical environment. The aim of this thesis is to perform a theoreticalinvestigation into the magneticenergy landscapes for atomic magnetic moments in different local chemical environments in disordered Fe64Ni36 alloys, and the change in pressure upon populating different parts of the magnetic energy landscape. Constrained calculations are performed to obtain the energy landscapes for both iron and nickel atoms in ferromagnetic Fe64Ni64. The calculated nickel atoms all show one global minimum between 0.64 to 0.72μB. The calculated iron atoms all exhibit two local minima: one where the magnetic moment's direction is the same as the ferromagnetic background's direction and has a size between 2 to 3μB, one where the magnetic moment is flipped and has a reversed direction in regards to the ferromagnetic background with a size between -2.5 to -1.9μB. A weak trend is seen for the energy difference between the two local minima: for iron-atoms with iron-rich local environments the energy difference is smaller than for iron-atoms with nickel-rich local environments. The energy landscapes for a moment rotated with respect to the background show that it is energetically favored to rotate the moment from the spin-up local minimum to the spin-flipped local minimum, rather than shrink in size and then increase in size in the opposite direction. This indicates that the negative local minimum might not be a local minimum, but further calculations are needed to determine if the spin-flipped state is a local minimum or just a saddle point in the complete size-and angle magnetic energy landscape. It is observed that the pressure varies little for different magnetic moment sizes for a nickel atom, but shows a larger variation for different magnetic moment sizes for an iron atom. The pressure difference between the magnetic local minima is about 6-9 kbar, and from thermodynamical simulations a small, nonlinear, decline in pressure with increased temperature is observed.

Ca2RuO4 is a structurally-driven Mott insulator with a metal-insulator (MI) transition at TMI = 357K, followed by a well-separated antiferromagnetic order at TN = 110 K. Slightly substituting Ru with a 3d transition metal ion M effectively shifts TMI and induces exotic magnetic behavior below TN. Moreover, M doping for Ru produces negative thermal expansion in Ca2Ru1-xMxO4 (M = Cr, Mn, Fe or Cu); the lattice volume expands on cooling with a total volume expansion ratio reaching as high as 1%. The onset of the negative thermal expansion closely tracks TMI and TN, sharply contrasting classic negative thermal expansion that shows no relevance to electronic properties. In addition, the observed negative thermal expansion occurs near room temperature and extends over a wide temperature interval. These findings underscores new physics driven by a complex interplay between orbital, spin and lattice degrees of freedom. These materials constitute a new class of Negative Thermal Expansion (NTE) materials with novel electronic and magnetic functions.