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Bismuth iron oxide (BFO) crystals have potential for applications ranging from next-generation, magnetoelectricity-based electronics to photocatalysts for the breakdown of toxic chemicals. Hydrothermal synthesis (HTS) has been shown to be an attractive solution growth method for producing well-defined, phase-pure BFO crystals. Until now, research in this field has focused on understanding the relationships between external experimental parameters in HTS and resultant crystalline phases of BFO, neglecting the role of the solution chemistry in crystal phase determination. Two spectator cations, Na+ and K+, commonly used in HTS of BFOs were investigated for their potential roles in determining the phase outcome of the final products in relation to a recently discovered, time-dependent transformation of an intermediate phase that was found to strongly influence the final phase outcome. Synthesis of BFOs was performed using wet chemistry techniques and reaction in a high-pressure, low-temperature environment. Characterization was performed using powder X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray spectroscopy. Phase-pure BiFeO3 was confirmed to form in the presence of K+ only when the intermediate underwent transformation while phase-pure Bi2Fe4O9 could be formed in the presence of Na+ regardless of the status of the intermediate. A new synthetic method was developed to elucidate whether the cations affected the transformation of the intermediate, and whether this potential transformation was the cause of the phase control. It was found that the intermediate was not crystallographically affected by the cations and the presence of the cations themselves only during heat treatment determined the final phase of the product. Finally, a thought experiment was conducted that suggests a stabilization role for spectator anions and a formation mechanism for Bi2Fe4O9. The effects of cations on crystal morphology were inconclusive. The methods developed for these investigations and subsequent results lay the groundwork for a better understanding of the role of other ions in the HTS of BFOs.

In this dissertation, a first-principle-based approach is developed to study magnetoelectric effect in multiferoic materials. Such approach has a significant predictive power and might serve as a guide to new experimental works. As we will discuss in the course of this work, it also gives an important insight to the underlying physics behind the experimentally observed phenomena. We start by applying our method to investigate properties of a generic multiferroic material. We observe how magnetic susceptibility of such materials evolves with temperature and compare this evolution with the characteristic behavior of magnetic susceptibility for pure magnetic systems. Then we focus our attention to particular multiferroic - BiFeO3 - and reproduce its magnetic states with all of their essential features. Those magnetic states include (i) antiferromagnetic state, (ii) state with weak ferromagnetism resulting from canting of magnetic moments, and (iii) cycloidal magnetic structure. All of those magnetic states were also studied under external electric and magnetic fields. Under such electric fields magnetic order parameters of the systems undergo interesting transformations and sometimes take unexpected path. Finally, we study the material under strain and explore possibilities of favoring one magnetic state over another and even "creating" states that can be stable only under the strain.