Spin and orbital contributions to magnetically ordered moments in 5d layered perovskite Sr2IrO4

The Jeff = 1/2 Antiferromagnet Sr2 IrO4 : A Golden Avenue toward New Physics and Functions

Iridates have been providing a fertile ground for studying emergent phases of matter that arise from the delicate interplay of various fundamental interactions with approximate energy scale. Among these highly focused quantum materials, the perovskite Sr₂ IrO₄ , which belongs to the Ruddlesden-Popper series, stands out and has been intensively addressed in the last decade, since it hosts a novel J_eff = 1/2 state that is a profound manifestation of strong spin-orbit coupling. Moreover, the J_eff = 1/2 state represents a rare example of iridates that is better understood both theoretically and experimentally. Here, Sr₂ IrO₄ is taken as an example to review the recent advances of the J_eff = 1/2 state in two aspects: materials fundamentals and functionality potentials. In the fundamentals part, the basic issues for the layered canted antiferromagnetic order of the J_eff = 1/2 magnetic moments in Sr₂ IrO₄ are illustrated, and then the progress of the antiferromagnetic order modulation through diverse routes is highlighted. Subsequently, for the functionality potentials, fascinating properties such as atomic-scale giant magnetoresistance, anisotropic magnetoresistance, and nonvolatile memory, are addressed. To conclude, prospective remarks and an outlook are given.

Interfacial charge-transfer Mott state in iridate-nickelate superlattices

We investigate [Formula: see text]/[Formula: see text] superlattices in which we observe a full electron transfer at the interface from Ir to Ni, triggering a massive structural and electronic reconstruction. Through experimental characterization and first-principles calculations, we determine that a large crystal field splitting from the distorted interfacial [Formula: see text] octahedra surprisingly dominates over the spin-orbit coupling and together with the Hund's coupling results in the high-spin (S = 1) configurations on both the Ir and Ni sites. This demonstrates the power of interfacial charge transfer in coupling lattice, charge, orbital, and spin degrees of freedom, opening fresh avenues of investigation of quantum states in oxide superlattices.

Spectral functions of Sr2IrO4: theory versus experiment

The spin-orbit Mott insulator Sr₂IrO₄ has attracted a lot of interest in recent years from theory and experiment due to its close connection to isostructural high-temperature copper oxide superconductors. Despite not being superconductive, its spectral features closely resemble those of the cuprates, including Fermi surface and pseudogap properties. In this article, we review and extend recent work in the theoretical description of the spectral function of pure and electron-doped Sr₂IrO₄ based on a cluster extension of dynamical mean-field theory ('oriented-cluster DMFT') and compare it to available angle-resolved photoemission data. Current theories provide surprisingly good agreement for pure and electron-doped Sr₂IrO₄, both in the paramagnetic and antiferromagnetic phases. Most notably, one obtains simple explanations for the experimentally observed steep feature around the M point and the pseudo-gap-like spectral feature in electron-doped Sr₂IrO₄.

Pseudo-Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators

The consequences of the Jahn-Teller (JT) orbital-lattice coupling for magnetism of pseudospin J_{eff}=1/2 and J_{eff}=0 compounds are addressed. In the former case, represented by Sr_{2}IrO_{4}, this coupling generates, through the so-called pseudo-JT effect, orthorhombic deformations of a crystal concomitant with magnetic ordering. The orthorhombicity axis is tied to the magnetization and rotates with it under magnetic field. The theory resolves a number of puzzles in Sr_{2}IrO_{4} such as the origin of in-plane magnetic anisotropy and magnon gaps, metamagnetic transition, etc. In J_{eff}=0 systems, the pseudo-JT effect leads to spin-nematic transition well above magnetic ordering, which may explain the origin of "orbital order" in Ca_{2}RuO_{4}.

Noncollinear Magnetic Structure and Multipolar Order in Eu_{2}Ir_{2}O_{7}

The magnetic properties of the pyrochlore iridate material Eu_{2}Ir_{2}O_{7} (5d^{5}) have been studied based on first principles calculations, where the crystal field splitting Δ, spin-orbit coupling (SOC) λ, and Coulomb interaction U within Ir 5d orbitals all play significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction U, where a stable antiferromagnetic ground state with all-in-all-out (AIAO) spin structure has been found. In addition, another antiferromagnetic state with energy close to AIAO has also been found to be stable. The calculated nonlinear magnetization of the two stable states both have the d-wave pattern but with a π/4 phase difference, which can perfectly explain the experimentally observed nonlinear magnetization pattern. Compared with the results of the nondistorted structure, it turns out that the trigonal lattice distortion is crucial for stabilizing the AIAO state in Eu_{2}Ir_{2}O_{7}. Furthermore, besides large dipolar moments, we also find considerable octupolar moments in the magnetic states.

Coulomb correlations in 4d and 5d oxides from first principles-or how spin-orbit materials choose their effective orbital degeneracies

The interplay of spin-orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin-orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr₂IrO₄) and its 4d metallic counterpart, strontium rhodate (Sr₂RhO₄). While a Mott-insulating state is obtained for Sr₂IrO₄ in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr₂RhO₄ show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin-orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin-orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d¹ perovskites.

Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates

Combining density functional theory (DFT) and embedded dynamical mean-field theory (DMFT) methods, we study the metal-insulator transition in R_{2}Ir_{2}O_{7} (R=Y, Eu, Sm, Nd, Pr, and Bi) and the topological nature of the insulating compounds. Accurate free energies evaluated using the charge self-consistent DFT+DMFT method reveal that the metal-insulator transition occurs for an A-cation radius between that of Nd and Pr, in agreement with experiments. The all-in-all-out magnetic phase, which is stable in the Nd compound but not the Pr one, gives rise to a small Ir^{4+} magnetic moment of ≈0.4  μ_{B} and opens a sizable correlated gap. We demonstrate that within this state-of-the-art theoretical method, the insulating bulk pyrochlore iridates are topologically trivial.

Ultrafast dynamics of localized magnetic moments in the unconventional Mott insulator Sr2IrO4

We report a time-resolved study of the ultrafast dynamics of the magnetic moments formed by the [Formula: see text] states in Sr2IrO4 by directly probing the localized iridium 5d magnetic state through resonant x-ray diffraction. Using optical pump-hard x-ray probe measurements, two relaxation time scales were determined: a fast fluence-independent relaxation is found to take place on a time scale of 1.5 ps, followed by a slower relaxation on a time scale of 500 ps-1.5 ns.

Iridates from the molecular side

New exotic phenomena have recently been discovered in oxides of paramagnetic Ir⁴⁺ ions, widely known as ‘iridates'. Their remarkable properties originate from concerted effects of the crystal field, magnetic interactions and strong spin-orbit coupling, characteristic of 5d metal ions. Despite numerous experimental reports, the electronic structure of these materials is still challenging to elucidate, and not attainable in the isolated, but chemically inaccessible, [IrO₆]^8– species (the simplest molecular analogue of the elementary {IrO₆}⁸⁻ fragment present in all iridates). Here, we introduce an alternative approach to circumvent this problem by substituting the oxide ions in [IrO₆]⁸⁻ by isoelectronic fluorides to form the fluorido-iridate: [IrF₆]²⁻. This molecular species has the same electronic ground state as the {IrO₆}⁸⁻ fragment, and thus emerges as an ideal model for iridates. These results may open perspectives for using fluorido-iridates as building-blocks for electronic and magnetic quantum materials synthesized by soft chemistry routes.

Iridates are known to exhibit a range of exotic electronic and magnetic behaviours but it is difficult to prepare isolated [IrO₆]⁸⁻ species via soft chemical routes. Here, the authors isolate the isoelectronic [IrF₆]²⁻ complex, and assess it as a model and for iridate analogues.

Orbital reconstruction in nonpolar tetravalent transition-metal oxide layers

A promising route to tailoring the electronic properties of quantum materials and devices rests on the idea of orbital engineering in multilayered oxide heterostructures. Here we show that the interplay of interlayer charge imbalance and ligand distortions provides a knob for tuning the sequence of electronic levels even in intrinsically stacked oxides. We resolve in this regard the d-level structure of layered Sr₂IrO₄ by electron spin resonance. While canonical ligand-field theory predicts g_||-factors less than 2 for positive tetragonal distortions as present in Sr₂IrO₄, the experiment indicates g_|| is greater than 2. This implies that the iridium d levels are inverted with respect to their normal ordering. State-of-the-art electronic-structure calculations confirm the level switching in Sr₂IrO₄, whereas we find them in Ba₂IrO₄ to be instead normally ordered. Given the nonpolar character of the metal-oxygen layers, our findings highlight the tetravalent transition-metal 214 oxides as ideal platforms to explore d-orbital reconstruction in the context of oxide electronics.

The iridate compounds display interesting physical properties, including quasi-two-dimensional behaviour similar to cuprates. Bogdanov et al. explore the d-level structure of Sr₂IrO₄ using electron spin resonance measurements and detailed calculations and find it is inverted compared to its normal ordering

J(eff)=1/2 Mott-insulating state in Rh and Ir fluorides

Discovery of new transition metal compounds with large spin orbit coupling coexisting with strong electron-electron correlation among the d electrons is essential for understanding the physics that emerges from the interplay of these two effects. In this study, we predict a novel class of J_{eff}=1/2 Mott insulators in a family of fluoride compounds that are previously synthesized, but not characterized extensively. First principles calculations in the level of all electron density functional theory+dynamical mean field theory indicate that these compounds have large Mott gaps and some of them exhibit unprecedented proximity to the ideal, SU(2) symmetric J_{eff}=1/2 limit.