Thesis advisor: Fazel Tafti / The search for an ideal quantum spin-liquid (QSL) material which can host a QSL ground state as well as exotic excitations has been one of the leading research topics in condensed matter physics over the past few decades. Out of all the proposals to realize the physics of a QSL, the Kitaev model is the most promising proposal with a QSL ground state. The Kitaev Hamiltonian is exactly solvable via fractionalization of its spin degrees of freedom into Majorana excitations, and it can be engineered in real materials. Among all the proposed Kitaev candidates, α-Li2IrO3, Na2IrO3, Li2RhO3, and α-RuCl3 are the most promising candidates. During my Ph.D. research I explored new physics related to Kitaev materials via modification of the symmetry and structural properties of these known Kitaev candidates. First, I studied how modification of the inter-layer chemistry can alter the thermodynamic properties of Kitaev candidate α-Li2IrO3 via an enhancement of the spin-orbit coupling (SOC) effect. The light, octahedrally-coordinated inter-layer Li atoms are replaced with heavier, linearly-coordinated Ag atoms to synthesize Ag3LiIr2O6. In addition to these structural modifications to the parent compound α-Li2IrO3, having heavier elements between the honeycomb layers in the Ag compound increased the effect of SOC in the honeycomb layers and led to a decrease in the long-range ordering temperature in Ag3LiIr2O6 compared to its parent compound. Second, I studied the effect of local crystal distortion in the presence of a weak SOC effect to explore a new spin-orbital state different from the Jeff=1/2 state. Based on theoretical predictions, the ground states of Kitaev materials can be tuned to other exotic spin-orbital states such as an Ising spin-1/2 state. To provide the proper conditions for a competition between the trigonal crystal distortion and the SOC effect, I modified the crystal environment around the magnetic elements in the parent compound Li2RhO3 via a topo-chemical method and synthesized Ag3LiRh2O6. An increase in the strength of trigonal distortion in Ag3LiRh2O6, in the presence of weak SOC, led to a transition from the Jeff=1/2 ground state (Kitaev limit) in the parent compound to an Ising spin-1/2 ground state (Ising limit) in the product. This change in spin-orbital state resulted in a dramatic change in magnetic behavior. Whereas Li2RhO3 shows a spin-freezing transition at 6 K, Ag3LiRh2O6 reveals a robust long-range antiferromagnetic transition at 94 K. This is the first realization of a change of ground state between the Kitaev and Ising limits in the same structural family. Lastly, I studied how the crystal symmetry can be an important factor in the physics of Kitaev materials. Honeycomb layered materials can be crystallized in space groups C2/m, C2/c, and P6_322. However, the crystal symmetry of most Kitaev candidates is described by the C2/m space group. We successfully synthesized a polymorph of a 3d Kitaev candidate, hexagonal Na2Co2TeO6 (P6_322 space group) in space group C2/m. The change in crystal symmetry of this cobalt tellurate replaced three anti-ferromagnetic (AFM) orders at 27, 15, 7 K in the hexagonal polymorph by a single AFM peak at 9.6 K in the monoclinic Na2Co2TeO6. / Thesis (PhD) — Boston College, 2023. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

In the context of the search and tuning for novel magnetic materials, transition metal compounds exhibit remarkable features where the spin-orbit interaction is crucial. The collective interactions between various effects, like spins and charges, create different classes of unique magnetic systems. For heavy transition-metal compounds, the strength of spin-orbital coupling is enhanced. The jeff. = 1/2 Mott insulating state emerges from the combination of the spin-orbit interaction and the electronic correlations. The quantum-chemistry methods are employed in this thesis to investigate single- and two-site magnetic interactions of the selected transition-metal compounds. We also provide different estimations for the single- and two-site magnetic interactions based on the level of calculation accuracy. In this thesis, we apply ab initio quantum-chemistry methods to explore the electronic and magnetic properties of several d/f compounds. The thesis structure is as follows: In Chapter 1, the introduction of the thesis provides a short discussion of the electronic correlations and magnetism in transition metal compounds. In Chapter 2, the fundamentals of the quantum chemistry wavefunction-based approach are covered. This chapter gives an overview of the applied methods in this thesis. In Chapter 3, we discuss the quantum chemistry approach to investigate the material candidates to host Kitaev physics. The technique to obtain the strength of two-site magnetic couplings, including the Kitaev coupling, is discussed in-depth. In Chapter 4, we apply the technique, which is described in Chapter 3, to investigate the two-site magnetic interactions in the H3LiIr2O6, and Cu2IrO2 compounds as Kitaev candidates. The two-site magnetic couplings are reported in these compounds. In Chapter 5, we use quantum chemistry methods to investigate the on-site electronic and magnetic properties in the KCeO2 compound where 4f1 Ce3+ ions form a triangular two-dimensional lattice with sites of effective spin-1/2. Similar ytterbiumbased delafossites had been investigated as candidates for quantum spin liquid ground states. The absence of ordinary magnetic order is characteristic of quantum spinliquid states where quantum entanglements and fractionalized excitations are enriched. In Chapter 6, the magnetic properties of Co 3d8 ions doped in the Li3N crystalline solid are discussed. The results of the quantum chemistry investigation are been set side by side along with the experiment’s results. The Co ion in such a rare environment gives rise to single-site magnetism of an easy-plane anisotropy.:Table of Contents . . . . . . . . . . . . . . . . . . . . . . iv List of Figures . . . . . . . . . . . . . . . . . . . . . . . . .vi Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i Acknowledgements . . . . . . . . . . . . . . . . . . . . . .iii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.1 Electronic correlations and magnetism in transition metal compounds ...........1 1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Quantum chemistry methodology . . . . . . . . . . . . . . . . .6 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Many-electron Hartree-Fock approximation . . . . . . . . . . . . . . . 9 2.3 Multi-configurational self-consistent field and multi-reference configuration methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Spin-orbit interaction and g-factors calculation . . . . . . . . . . . . . 15 2.5 Embedded cluster approach . . . . . . . . . . . . . . . . . . . . . . . 18 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 Quantum chemistry investigation of Kitaev material candidates . . . . . . . . . . .21 3.1 Introduction to the Kitaev model . . . . . . . . . . . . . . . . . . . . 23 3.2 Kitaev materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Two-site quantum chemistry calculations . . . . . . . . . . . . . . . . 36 3.4 Effective Model of Two Spin-1/2 . . . . . . . . . . . . . . . . . . . . . 38 3.5 Non-canonical correspondence between two-site QC results and the effective Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.6 Pseudospin coordinate system and canonical correspondence between two-site QC results and the effective Hamiltonian . . . . . . . . . . . 51 3.7 Signs of the g-tensor in the Kitaev limit . . . . . . . . . . . . . . . . 53 3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4 Kitaev material candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2 Details of QC calculations . . . . . . . . . . . . . . . . . . . . . . . . 64 4.3 QC investigation of H3LiIr2O6 . . . . . . . . . . . . . . . . . . . . . . 66 4.4 QC investigation of Cu2IrO3 . . . . . . . . . . . . . . . . . . . . . . . 75 4.5 Impact of local symmetries on the obtained sets of magnetic couplings ......... 82 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5 Ce ions in two-dimensional triangular spin-1/2 lattices . . . . . . . . . . . . . . . . . . . . 89 5.1 Spin-1/2 frustrated triangular lattice . . . . . . . . . . . . . . . . . . 90 5.2 Correlated 4f -compounds as frustrated triangular lattices . . . . . . 94 5.3 Crystal structure of KCeO2 . . . . . . . . . . . . . . . . . . . . . . . 95 5.4 QC results for the electronic structure of Ce3+ ions in KCeO2 . . . . 100 5.5 The competition of SOC and crystal field splittings in KCeO2 . . . . 102 5.6 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6 Co-ion substitutes with linear coordination in Li3N . . . . . . . . . . . . . . . . . . . . . . 109 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.2 Crystal structure of Li2(Li(1−x)Cox)N and spectroscopic measurements .......112 6.3 QC computational details . . . . . . . . . . . . . . . . . . . . . . . . 115 6.4 Ab initio QC investigation of the Co+ 3d8 electronic structure doped into Li3N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135