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arXiv:2207.04795 · Physical review. B./Physical review. B

Quasimolecular electronic structure of the spin-liquid candidate Ba 3 InIr 2 O 9

Alessandro Revelli, M. Moretti Sala, G. Monaco, M. Magnaterra, Jan Attig, L. Peterlini, T. Dey, Alexander A. Tsirlin, P. Gegenwart, T. Fröhlich, M. Braden, Christoph P. Grams, J. Hemberger, P. Becker, Paul H. M. van Loosdrecht, Daniel I. Khomskii, Jeroen van den Brink, Maria Hermanns, M. Grüninger

Published Oct 4, 2022• 14 citations
arXivHTMLPDF

Abstract

The mixed-valent iridate ${\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}$ has been discussed as a promising candidate for quantum spin-liquid behavior. The compound exhibits ${\mathrm{Ir}}^{4.5+}$ ions in face-sharing ${\mathrm{IrO}}_{6}$ octahedra forming ${\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$ dimers with three ${t}_{2g}$ holes per dimer. Our results establish ${\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}$ as a cluster Mott insulator. Strong intradimer hopping delocalizes the three ${t}_{2g}$ holes in quasimolecular dimer states while interdimer charge fluctuations are suppressed by Coulomb repulsion. The magnetism of ${\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}$ emerges from spin-orbit entangled quasimolecular moments with yet unexplored interactions, opening up a new route to unconventional magnetic properties of $5d$ compounds. Using single-crystal x-ray diffraction we find the monoclinic space group $C2/c$ already at room temperature. Dielectric spectroscopy shows insulating behavior. Resonant inelastic x-ray scattering reveals a rich excitation spectrum below 1.5 eV with a sinusoidal dynamical structure factor that unambiguously demonstrates the quasimolecular character of the electronic states. Below 0.3 eV, we observe a series of excitations. According to exact diagonalization calculations, such low-energy excitations reflect the proximity of ${\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}$ to a hopping-induced phase transition based on the condensation of a quasimolecular spin-orbit exciton. The dimer ground state roughly hosts two holes in a bonding $j=\frac{1}{2}$ orbital and the third hole in a bonding $j=\frac{3}{2}$ orbital.

DOI
10.1103/physrevb.106.155107

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The mixed-valent iridate Ba3InIr2O9{\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}Ba3​InIr2​O9​ has been discussed as a promising candidate for quantum spin-liquid behavior. The compound exhibits Ir4.5+{\mathrm{Ir}}^{4.5+}Ir4.5+ ions in face-sharing IrO6{\mathrm{IrO}}_{6}IrO6​ octahedra forming Ir2O9{\mathrm{Ir}}_{2}{\mathrm{O}}_{9}Ir2​O9​ dimers with three t2g{t}_{2g}t2g​ holes per dimer. Our results establish Ba3InIr2O9{\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}Ba3​InIr2​O9​ as a cluster Mott insulator. Strong intradimer hopping delocalizes the three t2g{t}_{2g}t2g​ holes in quasimolecular dimer states while interdimer charge fluctuations are suppressed by Coulomb repulsion. The magnetism of Ba3InIr2O9{\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}Ba3​InIr2​O9​ emerges from spin-orbit entangled quasimolecular moments with yet unexplored interactions, opening up a new route to unconventional magnetic properties of 5d5d5d compounds. Using single-crystal x-ray diffraction we find the monoclinic space group C2/cC2/cC2/c already at room temperature. Dielectric spectroscopy shows insulating behavior. Resonant inelastic x-ray scattering reveals a rich excitation spectrum below 1.5 eV with a sinusoidal dynamical structure factor that unambiguously demonstrates the quasimolecular character of the electronic states. Below 0.3 eV, we observe a series of excitations. According to exact diagonalization calculations, such low-energy excitations reflect the proximity of Ba3InIr2O9{\mathrm{Ba}}_{3}{\mathrm{InIr}}_{2}{\mathrm{O}}_{9}Ba3​InIr2​O9​ to a hopping-induced phase transition based on the condensation of a quasimolecular spin-orbit exciton. The dimer ground state roughly hosts two holes in a bonding j=12j=\frac{1}{2}j=21​ orbital and the third hole in a bonding j=32j=\frac{3}{2}j=23​ orbital.
The trimer compound Ba4{}_{4}4​NbIr3{}_{3}3​O12{}_{12}12​ is found to be a spin-orbit-entangled cluster Mott insulator, with two holes per trimer occupying quasimolecular orbitals. The authors employ here resonant inelastic x-ray scattering (RIXS) and exact diagonalization. The quasimolecular nature yields a characteristic interference pattern in the RIXS intensity, reflecting the character of the wavefunction. Despite a large hopping, strong spin-orbit coupling is decisive for the electronic states. This promises nontrivial magnetic moments in trimers with an odd number of holes.
In the recent years, interest in TM oxides with 5d valence electrons has grown immensely due to the realization of novel spin-orbit coupled ground states. In these compounds, e.g., iridates and osmates, the intriguing situation arises where the spin-orbit and electron-electron interactions meet on the same energy scale. This has created a new window of interest in these compounds since the interplay of crystal field effects, local multiplet physics, spin-orbit couplings, and intersite hopping can offer novel types of correlated ground states and excitations. In 5d5 iridates, a spin-orbit entangled j = 1/2 Mott insulating state has been realized recently. A remarkable feature of such a ground state is that it gives rise to anisotropic magnetic interactions. The 2D honeycomb-lattice 213 iridium oxides, A2IrO3 (A=Li,Na), have been put forward to host highly anisotropic bond-dependent spin-spin interactions that resemble the Kitaev spin model, which supports various types of topological phases relevant in quantum computing. The 2D square-lattice 214 iridates Sr2IrO4 and Ba2IrO4 are, on the other hand, appealing because of their perceived structural and magnetic simi- larity to La2CuO4, the mother compound of the cuprate high-Tc superconductors. This has promoted the latter iridium oxide compounds as novel platforms for the search of high-Tc superconductivity. To put such considerations on a firm footing, it is essential to quantify the different coupling strengths and energy scales, as they for instance appear in effective Hamiltonian descriptions of these correlated systems. Moreover, it is important to correctly describe their effects. In this thesis, the electronic structure and magnetic properties of 5d5 (mainly 214 and 213) iridates are studied using wave-function-based quantum chemistry methods. These methods are fully ab initio and are capable of accurately treating the electron-electron interactions without using any ad hoc parameters. The spin-orbit entangled j = 1/2 ground state in 214, 213 and other lower symmetry Sr3CuIrO6 and Na4Ir3O8 iridates is first analyzed in detail, by studying the local electronic structure of the 5d5 Ir4+ ion. We establish that the longer-range crystal anisotropy, i.e., low-symmetry fields related to ionic sites beyond the nearest neighbor oxygen cage, strongly influence the energies of Ir d levels. The ground state in all the compounds studied is j = 1/2 like with admixture from j ≃ 3/2 states ranging from 1 – 15 %. Further, the average j ≃ 1/2 → j ≃ 3/2 excitation energy we find is around 0.6 eV. The NN magnetic exchange interactions we computed for 214 iridates are predominantly isotropic Heisenberg-like with J ~ 60 meV, 3 – 4 times smaller than found in isostructural copper oxides. However, the anisotropic interactions are an order of magnitude larger than those in cuprates. Our estimates are in excellent agreement with those extracted from experiments, e.g., resonant inelastic x-ray scattering measurements. For the 213 honeycomb-lattice Na2IrO3 our calculations show that the relevant spin Hamiltonian contains further anisotropic terms beyond the Kitaev-Heisenberg model. Nevertheless, we predict that the largest energy scale is the Kitaev interaction, 10 to 20 meV, while the Heisenberg superexchange and off-diagonal symmetric anisotropic couplings are significantly weaker. In the sister compound Li2IrO3, we find that the structural inequivalence between the two types of Ir-Ir links has a striking influence on the effective spin Hamiltonian, leading in particular to two very different NN superexchange pathways, one weakly AF (~ 1 meV) and another strongly FM (−19 meV). The latter gives rise to rigid spin-1 triplets on a triangular lattice.
The quantum nature of electrons emerges in various exotic ways when they are put together with quantum many-body interactions. In Mott insulating systems with strong electron correlation, frustration and strong quantum fluctuations promote localized electron spins to form nontrivial quantum paramagnetic phases such as quantum spin liquid and valence bond solid preventing the development of conventional magnetic orders. In this thesis, we study such exotic quantum phases in various different frustrated quantum magnets. First, encouraged by the spin liquid phenomenology observed in Ba3XSb2O9 (X=Cu, Ni), we investigate Z2 spin liquids on a three dimensional triangular lattice by employing the Schwinger boson mean-field theory with projective symmetry group analysis. It is found that a nematic spin liquid is energetically favorable on this lattice structure rather than symmetric spin liquids. Next, we study various valence bond solid phases that can appear in kagome lattice antiferromagnets by generalizing the recently proposed phenomenological Z2 gauge theory for the topological Z2 spin liquid state found in the nearest-neighbor kagome lattice Heisenberg model. This work provides a bridge between the topological spin liquid and valence bond solid phases previously proposed for kagome lattice antiferromagnets via vison condensation in the gauge theory. Then, we consider optical conductivity in Mott insulators as an experimental probe to detect quantum paramagnetic phases like valence bond solid. Applying this idea to deformed kagome lattice antiferromagnet Rb2Cu3SnF12 with a 12-site valence bond solid state, we estimate the size of optical conductivity in this quantum magnet. After this, another quantum paramagnet BiCu2PO6 is carefully investigated to clarify its puzzling ground state nature and quasiparticle excitations. Utilizing recent high resolution neutron scattering data, we construct a microscopic spin model and also an effective theory for the low energy spin excitations in the compound. We find significant influences of magnetic anisotropies on the ground state and quasiparticle dynamics. Lastly, we investigate emergent quantum phases in the thin film geometries of the pyrochlore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases, as well as the novel quantum states that may arise only in a thin film setting, are studied via a theoretical model that allows layer-dependent magnetic structures.
Strong spin-orbital-coupling magnetic systems with the honeycomb structure can provide bond-directional interactions which may result in Kitaev quantum spin liquids and exotic anyonic excitations. However, one of the key ingredients in real materials---disorders---has been much less studied in Kitaev systems. Here we synthesized a trigonal ${\mathrm{SrIr}}_{2}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}$ with $\ensuremath{\delta}\ensuremath{\approx}0.25$, which consists of two-dimensional honeycomb Ir planes with edge-sharing IrO6{\mathrm{IrO}}_{6}IrO6​ octahedra. First-principles computation and experimental measurements suggest that the electronic system is gapped, and there should be no magnetic moment as the Ir5+{\mathrm{Ir}}^{5+}Ir5+ ion has no unpaired electrons. However, significant magnetism has been observed in the material, and it can be attributed to disorders that are most likely from oxygen vacancies. No magnetic order is found down to 0.05 K, and the low-temperature magnetic properties exhibit power-law behaviors in magnetic susceptibility and zero-field specific heat, and a single-parameter scaling of the specific heat under magnetic fields. These results provide strong evidence for the existence of the random singlet phase in ${\mathrm{SrIr}}_{2}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}$, which offers a different member to the family of spin-orbital entangled iridates and Kitaev materials.
We study a spin-orbital model for 4d14{d}^{1}4d1 or 5d15{d}^{1}5d1 Mott insulators in ordered double perovskites with strong spin-orbit coupling. This model is conveniently written in terms of pseudospin and pseudo-orbital operators representing multipoles of the effective j=32j=\frac{3}{2}j=23​ angular momentum. Similarities between this model and the effective theories of Kitaev materials motivate the proposal of a chiral spin-orbital liquid with Majorana fermion excitations. The thermodynamic and spectroscopic properties of this quantum spin liquid are characterized using parton mean-field theory. The heat capacity, spin-lattice relaxation rate, and dynamic structure factor for inelastic neutron scattering are calculated and compared with the experimental data for the spin liquid candidate Ba2YMoO6{\mathrm{Ba}}_{2}{\mathrm{YMoO}}_{6}Ba2​YMoO6​. Moreover, based on a symmetry analysis, we discuss the operators involved in resonant inelastic x-ray scattering (RIXS) amplitudes for double-perovskite compounds. In general, the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.