Academic literature on the topic 'Pyrochlore iridates'

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 Nd3+ 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

In this thesis we focus on two problems. First we propose a numerical method for generating optimized Wannier functions with desired properties. Second we perform the state of the art density functional plus dynamical mean-field calculations in pyrochlore iridates, to investigate the physics induced by the cooperation of spin-orbit coupling and electron correlation. We begin with the introduction for maximally localized Wannier functions and other related extensions. Then we describe the current research in the field of spin-orbit coupling and its interplay with correlation effects, followed by a brief introduction of the `hot' materials of iridates. Before the end of the introduction, we discuss the numerical methods employed in our work, including the density functional theory; dynamical mean-field theory and its combination with the exact diagonalization impurity solver. Then we propose our approach for constructing an optimized set of Wannier functions, which is a generalization of the functionality of the classic maximal localization method put forward by Marzari and Vanderbilt. Our work is motivated by the requirement of the effective description of the local subspace of the Hamiltonian by the beyond density functional theory methods. In extensions of density functional theory such as dynamical mean-field theory, one may want highly accurate description of particular local orbitals, including correct centers and symmetries; while the basis for the remaining degrees of freedom is unimportant. Therefore, we develop the selectively localized Wannier function approach which allows for a greater localization in the selected subset of Wannier functions and at the same time allows us to fix the centers and ensure the point symmetries. Applications in real materials are presented to demonstrate the power of our approach. Next we move to the investigation of pyrochlore iridates, focussing on the metal-insulator transition and material dependence in these compounds. We perform combined density functional plus dynamical mean-field calculations in Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$, Eu$_2$Ir$_2$O$_7$, with spin-orbit coupling included and both single-site and cluster approximations appiled. A broad range of Weyl metal is predicted as the intervening phase in the metal-insulator transition. By comparing to experiments, we find that the single-site approximation fails to predict the gap values and substantial difference between the Y and Eu-compound, demonstrating the inadequacy of this approximation and indicating the key role played by the intersite effects. Finally, we provide a more accurate description of the vicinity of the metal-insulator and topological transitions implied by density functional plus cluster dynamical mean-field calculations of pyrochlore iridates. We find definitive evidence of the Weyl semimetal phase, the electronic structure of which can be approximately described as ``Weyl rings" with an extremely flat dispersion of one of the Weyl bands. This Weyl semimetal phase is further investigated by the $k\cdot p$ analysis fitting to the numerical results. We find that this unusual structure leads to interesting behavior in the optical conductivity including a Hall effect in the interband component, and to an enhanced susceptibility.

In the search for novel magnetic materials, systems with strong spin-orbit coupling are a focus. 5d Ir-oxides and 4d Ru-halide, in particular, are associated in this context with a flurry of new theoretical concepts, models, and predictions, and more recently to various exotic topological states. In this thesis, we use computational quantum-chemistry methods to determine nearest-neighbor (NN) magnetic interactions in such systems. We also explore different routes to tune NN exchange couplings and provide guidelines for material design. In the first chapter, an introduction to concepts of electron correlations, spin-orbit coupling and magnetic interactions is provided. Many-body quantum chemistry methods used to determine electronic and magnetic properties of the transition metal systems in this work are outlined in the second chapter. In chapter 3, we determine multiplet-structure, magnetic g factors as well as NN magnetic interaction for the edge-shared 4d5 honeycomb lattice-based system, i.e., α-RuCl3. We find that the the magnetic anisotropy shows up in the form of bond-dependent Kitaev couplings, which defines the largest superexchange energy scale in this system. Magnetic couplings obtained by mapping the ab initio data onto an effective spin Hamiltonian are then used in the the subsequent exact diagonalization calculation to retrieve the magnetic phase diagram as a function of second and third NN coupling. Further, in chapter 4, we investigate the effects of uniform pressure and strain on the magnetic interactions in honeycomb and related lattice-based systems. We find that the Heisenberg and Kitaev terms are affected differently: for strain, in particular, the Heisenberg component decreases more rapidly than the Kitaev counterpart. This suggests a scenario where strain can stabilize a spin liquid state in such materials. In chapter 5, we discuss another factor that allows to modify magnetic couplings, i.e., the electrostatics between layered stackings with different metallic species. We examine magnetic interactions between Ir moments in H3LiIr2O6, a recently proposed Kitaev spin liquid candidate, and clarify the effect of interlayer electrostatics on the anisotropic Kitaev exchange . We show that the precise position of H+ cations between magnetically active [LiIr2O6]3− honeycomb-like layers has a strong impact on the magnitude of Kitaev interactions. In the last chapter, we examine Ir-oxides on the pyrochlore lattice. In these corner-sharing systems the NN anisotropic exchange occurs in the form of antisymmetric exchange, also known as Dzyaloshinskii-Moriya (DM) coupling. Our calculations predict that a highly unusual regime can be realized in such systems due to the vanishing NN Heisenberg interaction, making the antisymmetric DM exchange to be the dominant interaction in the oxides where the Ir-O-Ir links show bond-angles less than 125◦. We also confirm the accuracy of the employed quantum-chemistry methods by reproducing experimental data for Sm2Ir2O7.:Table of contents 1 Introduction 1 1.1 Electronic correlations 2 1.2 Crystal fields and d-level splitting 5 1.3 Spin-orbit Coupling 8 1.4 Magnetic interactions 10 1.5 Conclusions 13 2 Quantum Chemistry Methods 15 2.1 Introduction 15 2.2 Motivation for using quantum chemical approach 17 2.3 The Hartree-Fock approach 19 2.4 Multiconfigurational approach 22 2.5 Multireference configuration interaction 26 2.5.1 Recent developments towards performing FCI 27 2.6 Embedded cluster approach 28 2.7 Conclusions 30 3 Anisotropic spin interactions in α-RuCl3 31 3.1 Introduction 31 3.2 Spin-orbit ground state and excitations 33 3.2.1 Structural details .34 3.2.2 Computational details 37 3.2.3 Results and Discussions 40 3.3 Intersite exchange interactions for j=1/2 moments 44 3.3.1 Kitaev-Heisenberg model and symmetric anisotropies 45 3.3.2 Computational details 49 3.3.3 Results and Discussion 53 3.4 Conclusions 61 x Table of contents 4 Strain and pressure tuned magnetic interactions in Kitaev materials 63 4.1 Introduction 64 4.2 Qualitative analysis: Kitaev-Heisenberg model 65 4.3 Quantitative analysis: ab initio results 66 4.3.1 Computational approach 69 4.3.2 Results and discussion 70 4.4 Experimental results for pressurized α-RuCl3 74 4.4.1 Pressure induced dimerization 75 4.4.2 Ab initio calculations 76 4.5 Conclusions 78 5 Impact of inter-layer species on in-plane magnetism in H3LiIr2O6 79 5.1 Introduction 79 5.2 Structural details 81 5.3 Computational approach 82 5.4 Results and discussion 85 5.4.1 Magnetic couplings 85 5.4.2 Phase diagram and longer-range interactions 86 5.4.3 Position of H cations and effect on in-plane interactions 88 5.4.4 Angle dependence, the Kitaev limit 91 5.5 Conclusions 92 6 Anisotropic spin interactions in pyrochlore iridates 95 6.1 Introduction 95 6.2 Structural details 97 6.3 Computational details 98 6.3.1 Embedded cluster and basis sets 98 6.3.2 Quantum chemistry calculations 99 6.3.3 Effective spin model Hamiltonian 99 6.4 Results and Discussion 101 6.4.1 Magnetic couplings 101 6.4.2 Spin Dynamics 103 6.4.3 Magnetic ground state 105 6.5 Conclusions 109 Summary 111

We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.

Spins often prefer to anti-align with their neighbors in antiferromagnetic correlation. Materials with triangle lattices exhibit energetic degeneracy among the possible rearrangements of anti-aligned spins, which is denoted geometric frustration that is associated with strongly depressed transitions to magnetic order. Honeycomb iridates and ruthenates, pyrochlore systems, and double-perovskite iridates all feature triangular lattices as primary building blocks of their structures. Another frustration mechanism evolves from the Kitaev’s exact solution of a spin-liquid model on a honeycomb lattice with strong spin-orbit interactions. The protracted search for a Kitaev spin liquid has recently focused on the honeycomb itidates Na₂IrO₃ and Li₂IrO₃. A newer kind of quantum liquid has been identified in the magnetic insulator Ba₄Ir₃O₁₀, where Ir₃O₁₂ trimers form an unfrustrated square lattice.