Ir L3 edge Resonant Inelastic X-ray Scattering (RIXS) and La2 Resonant X-ray Emission Spectroscopy (RXES) have been used to investigate A2IrO3 (A= Na or Li) and CuIr2S4. First principle calculations show that the low-energy dd-excitations in the RIXS spectra of A2IrO3 originate from a split jeff=3/2 to jeff=1/2 excitation. A magnetic excitation is observed in Na2IrO3, whose dispersion is consistent with the theoretical prediction including a bond-dependent Kitaev interaction between jeff=1/2 magnetic moments. In CuIr2S4, RXES measurements reveal that the unoccupied Ir t2g level shift upward in energy as a result of the metal-insulator transition, confirming density functional theory calculations. In the x-ray irradiation induced phase of CuIr2S4, a mid-infrared peak emerges in the RIXS spectrum around 0.4 eV, suggesting that both the crystal structure and the electronic structure are modified due to x-ray irradiation. The size of the magnetic moments in Fe based superconductors has been investigated using Fe Kb X-ray Emission Spectroscopy (XES). Local magnetic moments are found in Fe pnictides and chalcogenides, independent of temperature or carrier concentration. This result supports the notion of local moments coexisting with metallic bands. Our investigation of Ca{1-x}RExFe2As2 (RE=La, Pr, and Nd) shows results consistent with a spin-state transition. We argue that the gradual change of the spin-state over a wide temperature range reveals the importance of multiorbital physics, and in particular the competition between the crystal field split Fe 3d orbitals and the Hund's rule coupling.

Ir L3 edge Resonant Inelastic X-ray Scattering (RIXS) and La2 Resonant X-ray Emission Spectroscopy (RXES) have been used to investigate A2IrO3 (A= Na or Li) and CuIr2S4. First principle calculations show that the low-energy dd-excitations in the RIXS spectra of A2IrO3 originate from a split jeff=3/2 to jeff=1/2 excitation. A magnetic excitation is observed in Na2IrO3, whose dispersion is consistent with the theoretical prediction including a bond-dependent Kitaev interaction between jeff=1/2 magnetic moments. In CuIr2S4, RXES measurements reveal that the unoccupied Ir t2g level shift upward in energy as a result of the metal-insulator transition, confirming density functional theory calculations. In the x-ray irradiation induced phase of CuIr2S4, a mid-infrared peak emerges in the RIXS spectrum around 0.4 eV, suggesting that both the crystal structure and the electronic structure are modified due to x-ray irradiation. The size of the magnetic moments in Fe based superconductors has been investigated using Fe Kb X-ray Emission Spectroscopy (XES). Local magnetic moments are found in Fe pnictides and chalcogenides, independent of temperature or carrier concentration. This result supports the notion of local moments coexisting with metallic bands. Our investigation of Ca{1-x}RExFe2As2 (RE=La, Pr, and Nd) shows results consistent with a spin-state transition. We argue that the gradual change of the spin-state over a wide temperature range reveals the importance of multiorbital physics, and in particular the competition between the crystal field split Fe 3d orbitals and the Hund's rule coupling.

Thesis advisor: Vidya Madhavan / Spin-orbit coupling (SOC) is the interaction of an electron's intrinsic angular momentum (spin) with its orbital momentum. The strength of this interaction is proportional to Z<super>4</super> where Z is the atomic number, so generally it is stronger in atoms with higher atomic number, such as bismuth (Z=83) and iridium (Z=77). In materials composed of such heavy elements, the prominent SOC can be sufficient to modify the band structure of the system and lead to distinct phase of matter. In recent years, SOC has been demonstrated to play a critical role in determining the unusual properties of a variety of compounds. SOC associated materials with exotic electronic states have also provided a fertile platform for studying emergent phenomena as well as new physics. As a consequence, the research on these interesting materials with any insight into understanding the microscopic origin of their unique properties and complex phases is of great importance. In this context, we implement scanning tunneling microscopy (STM) and spectroscopy (STS) to explore the surface states (SS) of the two major categories of SOC involved materials, Bi-based topological insulators (TI) and Ir-based transition metal oxides (TMO). As a powerful tool in surface science which has achieved great success in wide variety of material fields, STM/STS is ideal to study the local density of states of the subject material with nanometer length scales and is able to offer detailed information about the surface electronic structure. In the first part of this thesis, we report on the electronic band structures of three-dimensional TIs Bi₂Te₃ and Bi₂Se₃. Topological insulators are distinct quantum states of matter that have been intensely studied nowadays. Although they behave like ordinary insulators in showing fully gapped bulk bands, they host a topologically protected surface state consisting of two-dimensional massless Dirac fermions which exhibits metallic behavior. Indeed, this unique gapless surface state is a manifestation of the non-trivial topology of the bulk bands, which is recognized to own its existence to the strong SOC. In chapter 3, we utilize quasiparticle interference (QPI) approach to track the Dirac surface states on Bi₂Te₃ up to ~800 meV above the Dirac point. We discover a novel interference pattern at high energies, which probably originates from the impurity-induced spin-orbit scattering in this system that has not been experimentally detected to date. In chapter 4, we discuss the topological SS evolution in (Bi_1-xIn_x)₂Se₃ series, by applying Landau quantization approach to extract the band dispersions on the surface for samples with different indium content. We propose that a topological phase transition may occur in this system when x reaches around 5%, with the experimental signature indicating a possible formation of gapped Dirac cone for the surface state at this doping. In the second part of this thesis, we focus on investigating the electronic structure of the bilayer strontium iridate Sr₃Ir₂O₇. The correlated iridate compounds belong to another domain of SOC materials, where the electronic interaction is involved as well. Specifically, the unexpected Mott insulating state in 5<italic>d</italic>-TMO Sr₂IrO₄ and Sr₃Ir₂O₇ has been suggested originate from the cooperative interplay between the electronic correlations with the comparable SOC, and the latter is even considered as the driving force for the extraordinary ground state in these materials. In chapter 6, we carried out a comprehensive examination of the electronic phase transition from insulating to metallic in Sr₃Ir₂O₇ induced by chemical doping. We observe the subatomic feature close to the insulator-to-metal transition in response with doping different carriers, and provide detailed studies about the local effect of dopants at particular sites on the electronic properties of the system. Additionally, the basic experimental techniques are briefly described in chapter 1, and some background information of the subject materials are reviewed in chapter 2 and chapter 5, respectively. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Michael J. Graf / This thesis is concerned with experimentally determining the magnetic and electronic states in a unique class of transition metal oxides known as the pyrochlore iridates, A₂Ir₂O₇ (A = Y or Rare earth). The extended nature of the 5d Ir orbitals in the iridates places these materials in a regime of intermediate electron correlation and large spin-orbit interaction such that this system may host several novel or topological states of matter which may be perturbed by incorporating different A-species. Additionally, the pyrochlore structure is geometrically frustrated and has been long been studied as a potential host of a number of exotic magnetic phenomenon. However, even after years of intense theoretical and experimental interest many fundamental questions still remain about the nature of the magnetic ground sates in this series which are of vital importance in understanding the roles of various interactions and potential of such novel phenomenon. The primary aim of this thesis is therefore to determine how magnetic order develops on the Ir sublattice in this series, particularly how it is perturbed through variation of the crystalline structure, magnetism of the A-site ions, and presence of mobile charges. This thesis is the first comprehensive experimental study of these effects which has utilized several complementary experimental probes of both bulk and local magnetism in a number of compounds. The techniques presented in this work include magnetotransport, bulk magnetization, elastic neutron scattering, and muon spin relaxation (µSR) measurements. All of the three compounds studied in this work (A = Y, Yb, and Nd) are shown to definitively exhibit long-range magnetic order on the Ir sublattice, which has previously only been inferred based on studies of other compounds. The compounds Y₂Ir₂O₇ and Yb₂Ir₂O₇ are correlated insulators at low temperature and are found to have identical configuration of the Ir moments, despite the presence of the large localized Yb³⁺. Numerical investigations presented here have provided the first conclusive evidence that this order is of the `all-in/all-out' type, consistent with recent resonant x-ray studies; additionally, we have shown that this order exists for all insulating compounds regardless of structural parameters or properties of the A-ion. On the other hand, Nd₂Ir₂O₇ is weakly metallic with Kondo-like behavior at low temperature, with long-range order only on the Ir site, in disagreement with previous results from neutron scattering. Measurements of the field dependent magnetization and Hall effect reveal a large anomalous Hall component, suggesting that the Nd<super>3+</super> may exhibit a spin-ice state with very short correlation length, while the Ir sublattice is likely in the `all-in/all-out' state. From this, it is determined that Nd₂Ir₂O₇ lies at an important cross-over point in the series in which correlation energy and conduction bandwidth yield chiral order with features akin to both the metallic unordered Pr₂Ir₂O₇ and those of the magnetically ordered insulators. These results are discussed with regard to recent theoretical models exploring the role of electron correlation, frustration and various exchange interactions in these materials. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Stephen Wilson / The magnetic interaction in materials generally can be categorized into two extremes: localized and itinerant. This work will focus on the electronic and magnetic properties of two prototypical magnetic compounds, which fall into the opposite extremes, i:e:, the spin-orbit coupled Mott insulator Sr₂IrO₄ (Sr214) described by the localized Heisenberg model and the itinerant helical (nearly-ferromagnetic) metal MnSi pictured with band or Stoner magnetism. The single layered cuprate analogue Sr₂IrO₄ has attracted considerable attentions in recent years, due to its unusual electronic and magnetic properties and the potential to access superconducting states. The exotic jeff = 1/2 ground state for the Ir⁴⁺ (5d⁵) ions results from the delicate balance of competing/cooperating energy scales, such as the stronger spin-orbit coupling (SOC) in 5d materials as compared to 3d transition metal oxides (TMOs), crystal electric field (CEF) splitting and electron-electron correlations. Superconducting states are theoretically predicted to be achievable if sufficient carriers are introduced into this spin-orbit assisted compound, which later triggers tremendous experimental works toward the realization of superconductivity. Here in this work a combined study of various probes, such as transport, magnetization, X-ray and neutron scattering measurements, focusing on the electronic and magnetic properties, is presented in the perturbed spin-orbit coupled Mott (SOM) state. Specifically in electron doped (Sr₁₋ₓLaₓ)₂IrO₄, a detailed mapping of magnetism with respect to electron doping is presented, demonstrating the gradual transition from long range magnetic order in parent state, to intermediate short range order, and eventually into the incommensurate (IC) spin density wave (SDW) state with increasing electron doping. Our picture supports the conjecture that the quenched Mott phases in electron-doped Sr₂IrO₄ and hole doped La₂CuO₄ share common competing electronic phases. On the other hand, the prototypical itinerant metal MnSi is examined by inelastic neutron scattering (INS). Our experimental data directly demonstrate the collapse of linear spin wave theory for localized Heisenberg magnets in the large energy limit, although the low energy dispersion is still described by the ferromagnetic spin wave theory. Most importantly, our observations display the chimney-like dispersion spectrum up to the energy scale of at least 240 meV, which is more than one order of magnitude larger than the Heisenberg interaction energy scale. For the first time, solid characterizations of Stoner excitations in itinerant helimagnet (nearly ferromagnetic) have been demonstrated up to an exceedingly large energy scale. Our intriguing results will greatly promote further understanding and exploration of Stoner excitations in itinerant magnets. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Thesis advisor: Stephen Wilson / The work performed within this thesis is divided into two parts, each focusing primarily on the study of magnetic phase behavior using neutron scattering techniques. In first part, I present transport, magnetization, and neutron scattering studies of materials within the iridium oxide-based Ruddelsden-Popper series [Srn+1IrnO3n+1] compounds Sr3Ir2O7 (n=2) and Sr2IrO4 (n=1). This includes a comprehensive study of the doped bilayer system Sr3(Ir1-xRux )2O7. In second part, I present my studies of the effect of uniaxial pressure on magnetic and structural phase behavior of the iron-based high temperature superconductor Ba(Fe1-xCox)2As2. Iridium-based 5d transition metal oxides host rather unusual electronic/magnetic ground states due to strong interplay between electronic correlation, lattice structure and spin-orbit effects. Out of the many oxides containing iridium, the Ruddelsden-Popper series [Srn+1IrnO3n+1] oxides are some of the most interesting systems to study both from the point of view of physics as well as from potential applications. My work is focused on two members of this series Sr3Ir2O7 (n=2) and Sr2IrO4 (n=1). In particular, our combined transport, magnetization and neutron scattering studies of Sr3Ir2O7 (n=2) showed that this system exhibits a complex coupling between charge transport and magnetism. The spin magnetic moments form a G-type antiferromagnetic structure with moments oriented along the c-axis, with an ordered moment of 0.35±0.06 µB/Ir. I also performed experiments doping holes in this bilayer Sr3(Ir1-xRux)2O7 system in order to study the role of electronic correlation in these materials. Our results show that the ruthenium-doped holes remain localized within the Jeff=1/2 Mott insulating background of Sr3Ir2O7, suggestive of `Mott blocking' and the presence of strong electronic correlation in these materials. Antiferromagnetic order however survives deep into the metallic regime with the same ordering q-vector, suggesting an intricate interplay between residual AF correlations in the Jeff=1/2 state and metallic nanoscale hole regions. Our results lead us to propose an electronic/magnetic phase diagram for Sr3(Ir1-xRux)2O7 system showing how the system moves from Jeff=1/2 antiferromagnetic Mott insulator (Sr3Ir2O7) to paramagnetic Fermi liquid metal (Sr3Ru2O7). On the other hand, our neutron scattering measurements on Sr2IrO4 (n=1), a prototypical Jeff=1/2 Mott insulator, showed that the spins arranged antiferromagnetically in ab-plane with an ordered moment comparable to that of Sr3Ir2O7. The second part of my work is comprised of a neutron scattering-based study of the Ba(Fe1-xCox)2As2 system, a bilayer family of iron-based high temperature superconductors. Undoped, this system exhibits either simultaneous or nearly simultaneous magnetic and structural phase transitions from a high temperature paramagnetic tetragonal phase to low temperature orthorhombic antiferromagnetic phase. With the gradual suppression of these two temperatures, the superconducting phase appears with the highest TC obtained just beyond their complete suppression. It has been proposed that these coupled magnetostructural transitions are secondary manifestations which arise as a consequence of electronic nematic ordering that occurs at a temperature higher than either of them. My work is mainly focused on probing the spin behaviors coupling to this electronic nematic phase. I devised a small device to apply uniaxial pressure along an in-plane high symmetry axis and studied the magnetic and structural behavior in series of Ba(Fe1-xCox)2As2 compounds via neutron scattering in presence of uniaxial pressure. There is an upward thermal shift in the onset of structural and magnetic transition temperature caused by this uniaxial pressure which is surprisingly insensitive to cobalt concentration in the absolute scale. Furthermore, on the first order side of the phase diagram (below the tricritical point), the structural and magnetic transitions are decoupled with magnetic transition following structural distortion. This study suggests the importance of both spin-lattice and orbital-lattice interactions in these families of compounds. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

L'étude de l'état isolant de Mott est un des domaines très actif de la recherche en matière condensée car les fortes corrélations qui en sont à l'origine donnent naissance à des états de la matière très variés et avec des applications potentielles. Sr₂IrO₄ est un isolant de Mott exotique car induit par un fort couplage spin-orbite. Il permet d'étudier l'impact des corrélations électroniques sur les propriétés de basses énergies sous un angle nouveau. L'objet de cette thèse est l'étude expérimentale des propriétés électroniques de ces composés iridates par des mesures d'ARPES permettant des observations directes de la structure électronique dans l'espace réciproque et de RMN et μSR, qui donnent une vision locale dans l'espace réel. Nous nous sommes en particulier intéressés à la transition isolant métal pouvant survenir en dopant ce composé. Une façon originale de doper Sr₂IrO₄ que nous avons étudiée en détails est de substituer l'iridium par du rhodium. Les deux sont isovalents, mais le rhodium capture un électron conduisant à un dopage effectif en trous. Grâce à l’ARPES, nous avons mis en évidence les différentes bandes de la structure électronique. Nous avons étudié attentivement le caractère orbital de ces bandes et mis en évidence des anisotropies résiduelles en certains points de l’espace réciproque, survivant malgré la présence du fort couplage spin-orbite. Ceci, ainsi que des effets de repliement de la structure électronique, donnent lieu à des variations brutales d'intensité, qui doivent être prises en compte pour analyser correctement les spectres. Lors du dopage avec le Rh, la phase métallique obtenue reste très incohérente, avec une absence de pic de quasiparticule et un pseudogap uniforme sur l'ensemble de la surface de Fermi. Le gap de Mott ne semble pas se fermer. Le pseudogap peut révéler une brisure de symétrie mais aussi l’effet du désordre introduit par le Rh et nous discuterons son origine, en lien avec la physique d’autres systèmes corrélés. Nous montrons que pour de faibles taux de substitution Ir/Rh, l’ajout de porteurs trous contrôle le comportement du système alors qu’à des taux de substitutions plus élevés, le nombre de porteurs est stable mais le désordre augmente et contrôle à son tour la physique. Nous nous sommes aussi intéressés aux propriétés électroniques et magnétiques sondées par la RMN de l'oxygène 17 sur poudre et poudre orientée et par μSR. La RMN permet de différencier les deux sites d'oxygène de Sr₂IrO₄ nous permettant de déterminer certains paramètres nucléaires préalables à l'étude fine des propriétés électroniques. Dans le composé pur, nous avons étudié la transition magnétique et observé ce qui semble être le développement d'un moment sur l'oxygène apical. Dans les composés dopés, nous ne voyons pas de désordre structural important malgré des taux de dopage allant jusqu'à 15% de rhodium. Les propriétés magnétiques présentent néanmoins des signes d’inhomogénéité, plus marqués dans le cas du dopage lanthane. Les fluctuations dans le composé métallique montrant une prédominance des corrélations antiferromagnétiques. De son côté, la μSR a permis de construire le diagramme de phases de la transition antiferromagnétique et de mettre en évidence l'inhomogénéité de la transition magnétique dans les échantillons faiblement dopés. À basse température, nous confirmons que la phase magnétique évolue, peut-être avec l’apparition d’un moment sur l’oxygène, et cet effet est même renforcé dans les composés faiblement dopés. Au-dessus de la température de transition antiferromagnétique, nous n'avons pas trouvé de signature d'une transition vers une phase de boucles de courant observée par d'autres techniques. Cette étude permet d’attribuer à Sr₂IrO₄ dopé rhodium le caractère assez rare de matériau 2D fortement corrélé à désordre contrôlé. De manière plus générale, cet exemple devrait permettre de mieux comprendre les effets éventuels de désordre associés à d’autre façons de doper les iridates. / The study of the insulating Mott state is a very active field of research in condensed matter because of the strong correlations usually at play which can lead to a large variety of states of matter, with potential applications. Sr₂IrO₄ is an exotic Mott insulator because it is induced by a strong spin-orbit coupling. It allows studying the impact of electronic correlations on the low energy properties from a new viewpoint. The subject of this thesis is the experimental study of the electronic properties of these iridate compounds by ARPES measurements allowing direct observations of the electronic structure in reciprocal space and NMR and μSR, which give a local view in real space. We have in particular studied the metal to insulator transition which can occur in this compound upon doping. An original way to dope Sr₂IrO₄ that we have investigated in details is to substitute iridium by rhodium. Both are isovalent but the rhodium captures an electron leading to an effective hole doping. Thanks to ARPES we have identified the different bands in the electronic structure. We have studied in details the orbital character of these bands and pointed out residual anisotropies at some points in the reciprocal space, which survive despite the strong spin-orbit coupling. This, as well as the folding effects of the electronic structure, give rise to sudden variations in intensity, which must be taken into account in order to correctly analyze the spectra. Upon doping with Rh, the obtained metallic phase remains very incoherent, with no quasiparticle peak and a uniform pseudogap over the full Fermi surface. The Mott gap does not seem to be closing. The pseudogap can reveal symmetry breaking but also the effect of the disorder introduced by the Rh and we will discuss its origin, in relation to the physics of other correlated systems. We show that for low Ir/Rh substitution rates, the addition of hole carriers controls the behavior of the system while at higher substitution rates, the number of carriers is stable but the disorder increases and in turn controls physics.We were also interested in the electronic and magnetic properties probed by 17 oxygen NMR on powder and oriented powder samples and by μSR. NMR makes it possible to differentiate the two oxygen sites in Sr₂IrO₄ allowing determining some nuclear parameters necessary to the fine study of the electronic properties. In the pure compound, we have studied the magnetic transition and observed what appears to be the development of a moment on the apical oxygen. In the doped compounds, we do not see any significant structural disorder despite doping levels up to 15% rhodium. However, the magnetic properties nevertheless show signs of inhomogeneity, which are more pronounced in the case of lanthanum doping. The fluctuations in the correlated metal compound show a predominance of antiferromagnetic correlations. From our μSR investigation, we could construct the magnetic phase diagram which highlights the inhomogeneity of the magnetic transition in the low-doped samples. At low temperature, we confirm that the magnetic phase evolves, perhaps with the appearance of a moment on the oxygen, and this effect is even enhanced in the lightly doped compounds. Above the antiferromagnetic transition temperature, we did not find signatures of the current loop phase observed by other techniques. This study makes it possible to attribute to Sr₂IrO₄ doped with rhodium the rather rare character of strongly correlated 2D material with controlled disorder. More generally, this example should provide a better understanding of the potential effects of disorder associated with other ways to dope iridates.

A Walker-type multianvil high-pressure facility is capable of high-pressure syntheses and measurements beyond 10 GPa and has been utilized in my research to synthesize the 4d Ruthenium and Rhodium and the 5d Iridium oxides with the perovskite-related structures. Under high-pressure and high-temperature conditions, these families of oxides can be enlarged to a great extent so that enables us not only to address the long-standing problem about ferromagnetism in the perovskite ruthenates but also explore new phenomena associated with the structural and electronic properties in the iridates and rhodates. In the perovskite ruthenates ARuO₃ (A= Ca, Sr, and Ba), a systematic study of the variations of the ferromagnetic transition temperature T[subscript c] and the critical isothermal magnetization as a function of the average A-site cation size and the size variance as well as external high pressures reveals explicitly the crucial role of the local lattice strain and disorder on T[subscript c] and the nature of the localized-electron ferromagnetism. However, such a steric effect is dominated by the electronic effect in another perovskite ruthenate PbRuO₃, which is a paramagnetic metal down to 1.8 K and undergoes a first-order structural transition to a low-temperature Imma phase at Tt [almost equal to] 90 K. Bandwidth broadening due to orbital hybridization between Pb-6s and Ru-4d plays an important role in suppressing the ferromagnetism in the Sr1-zPbzRuO₃ system. The high-pressure sequence of the 9R-BaIrO₃ was explored and three more polytypes, i.e. 5H, 6H and 3C, were identified under 10 GPa. With increasing fraction of the corner- to face-sharing IrO₆/₂ octahedra, the ground states of BaIrO₃ evolve from a ferromagnetic insulator with T[subscript c] [almost equal to] 180 K in the 9R phase to a ferromagnetic metal with T[subscript c] [almost equal to] 50 K in the 5H phase, and finally to an exchange-enhanced paramagnetic metal near a quantum critical point in the 6H phase. In addition to the perovskite SrRhO₃, a new 6H polytype was synthesized for the first time under high pressure and a pressure-temperature phase diagram was given for the 6H-perovskite transformation. Restoration of the Curie-Weiss behavior in the high-temperature magnetic susceptibility [chi](T) of the perovskite SrRhO₃ resolves the puzzle about unusual dependence of [chi]⁻¹ [symbol] T² reported earlier and highlights the importance of spin-orbit coupling in the 4d and 5d transition-metal oxides. / text

This thesis focuses on the interplay of the spin-orbit coupling, the electronic correlations and the bandwidth energy scales, along with the lattice distortions seen in perovskite iridates. In particular, we study the magnetic phases in these materials and the insulator to metal transition that occurs as the dimensionality of the system is changed. Motivated by the novel magnetic phases seen in the Sr2IrO4 system, we study the band structures of three materials in the Sr(n+1)Ir(n)O(3n+1) Ruddlesden-Popper series by use of a tight-binding model. From the effect of spin-orbit coupling, we see that the relevant bands near the Fermi energy are indeed made of effective J=1/2 states. This spin-orbit separation of the bands creates effectively smaller bandwidth which can then be split via magnetic ordering driven by electronic correlations. By the use of a self-consistent mean-field theory, we derive the ordering for each of the three materials studied and show that the nature of the magnetic ordering is highly dependent on the lattice structure. The ordering in the bilayer Sr3Ir2O7, which has been a topic of debate in recent experimental studies, is understood within the current approach to be a collinear antiferromagnetic order, in agreement with the latest results. Given that the iridate systems have large spin-orbit coupling, and that the topic of topological insulators has become a very popular subject of research, we discuss the proximity of the perovskite iridates to topological insulators. Since the SrIrO3 material displays a semimetal structure with nodal dispersion near the Fermi level, we looked at an extra term in the Hamiltonian that could lift the nodal lines and turn the system into an insulator. Further studies of the parity eigenvalues of the bands at each time reversal invariant momentum point confirms that for a range of this extra term, a topological phase can be achieved. A discussion on material realization of such a phase is also given where we suggest that a Sr2IrRhO6 superstructure might be a good candidate to achieve this state.

This thesis focuses on the interplay of the spin-orbit coupling, the electronic correlations and the bandwidth energy scales, along with the lattice distortions seen in perovskite iridates. In particular, we study the magnetic phases in these materials and the insulator to metal transition that occurs as the dimensionality of the system is changed. Motivated by the novel magnetic phases seen in the Sr2IrO4 system, we study the band structures of three materials in the Sr(n+1)Ir(n)O(3n+1) Ruddlesden-Popper series by use of a tight-binding model. From the effect of spin-orbit coupling, we see that the relevant bands near the Fermi energy are indeed made of effective J=1/2 states. This spin-orbit separation of the bands creates effectively smaller bandwidth which can then be split via magnetic ordering driven by electronic correlations. By the use of a self-consistent mean-field theory, we derive the ordering for each of the three materials studied and show that the nature of the magnetic ordering is highly dependent on the lattice structure. The ordering in the bilayer Sr3Ir2O7, which has been a topic of debate in recent experimental studies, is understood within the current approach to be a collinear antiferromagnetic order, in agreement with the latest results. Given that the iridate systems have large spin-orbit coupling, and that the topic of topological insulators has become a very popular subject of research, we discuss the proximity of the perovskite iridates to topological insulators. Since the SrIrO3 material displays a semimetal structure with nodal dispersion near the Fermi level, we looked at an extra term in the Hamiltonian that could lift the nodal lines and turn the system into an insulator. Further studies of the parity eigenvalues of the bands at each time reversal invariant momentum point confirms that for a range of this extra term, a topological phase can be achieved. A discussion on material realization of such a phase is also given where we suggest that a Sr2IrRhO6 superstructure might be a good candidate to achieve this state.