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The 5d^{1} ordered double perovskites present an exotic playground for studying novel multipolar physics due to large spin-orbit coupling. We present Re L_{3} edge resonant inelastic x-ray scattering (RIXS) results that reveal the presence of the dynamic Jahn-Teller effect in the A_{2}MgReO_{6} (A=Ca, Sr, Ba) family of 5d^{1} double perovskites. The spin-orbit excitations in these materials show a strongly asymmetric line shape and exhibit substantial temperature dependence, indicating that they are dressed with lattice vibrations. Our experimental results are explained quantitatively through a RIXS calculation based on a spin-orbit-lattice entangled electronic ground state with the dynamic Jahn-Teller effect taken into consideration. We find that the spin-orbit-lattice entangled state is robust against magnetic and structural phase transitions as well as against significant static Jahn-Teller distortions. Our results illustrate the importance of including vibronic coupling for a complete description of the ground state physics of 5d^{1} double perovskites.

The valence electronic structure of magnetic centers is one of the factors that determines the characteristics of a magnet. This may refer to orbital degeneracy, as for j eff  = 1/2 Kitaev magnets, or near-degeneracy, e.g., involving the third and fourth shells in cuprate superconductors. Here we explore the inner structure of magnetic moments in group-5 lacunar spinels, fascinating materials featuring multisite magnetic units in the form of tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful landscape, much richer than the single-electron, single-configuration description applied so far to all group-5 GaM 4 X 8 chalcogenides, and clarifies the basic multiorbital correlations on M 4 tetrahedral clusters: while for V strong correlations yield a wave-function that can be well described in terms of four V 4+ V 3+ V 3+ V 3+ resonant valence structures, for Nb and Ta a picture of dressed molecular-orbital j eff  = 3/2 entities is more appropriate. These internal degrees of freedom likely shape vibronic couplings, phase transitions, and the magneto-electric properties in each of these systems., (© 2023. Springer Nature Limited.)

The lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo 4 13+ tetrahedron has been postulated as single-configuration a 1 2  e 4  t 2 5 , where a 1 , e, and t 2 are symmetry-adapted linear combinations of single-site Mo t 2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a 1 2  e 4  t 2 5 configuration. While spin-orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin-orbit operator and the g factors deviate from figures describing nominal t 5 j eff  = 1/2 moments. As such, our data documents the dressing of a spin-orbit j eff  = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitions observed at low temperatures in these materials., (© 2023. The Author(s).)

Spin-orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f 1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d 1 transition-metal compounds. The latter effect has been studied since the 1960s on t 2g 1 octahedral ML 6 units in both molecular complexes and extended solid-state lattices. Here we analyze the J eff = 3/2 quartet ground state of larger cubane-like M 4 L 4 entities in lacunar spinels, composed of transition-metal ( M ) tetrahedra caged by chalcogenide ligands ( L ). These represent a unique platform where spin-orbit coupling acts on molecular-like, delocalized t 2 orbitals. Using quantum chemical methods, we pin down the interplay of spin-orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t 2 1 . We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa 4 Se 8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.

We report the results of the experimental and theoretical study of the magnetic anisotropy of single crystals of the Co-doped lithium nitride Li 2 (Li 1- x Co x )N with x = 0.005, 0.01, and 0.02. It was shown recently that doping of the Li 3 N crystalline matrix with 3d transition metal (TM) ions yields superior magnetic properties comparable with the strongly anisotropic single-molecule magnetism of rare-earth complexes. Our combined electron spin resonance (ESR) and THz spectroscopic investigations of Li 2 (Li 1- x Co x )N in a very broad frequency range up to 1.7 THz and in magnetic fields up to 16 T enable an accurate determination of the energies of the spin levels of the ground state multiplet S ̂ = 1 of the paramagnetic Co(I) ion. In particular, we find a very large zero field splitting (ZFS) of almost 1 THz (∼4 meV or 33 cm -1 ) between the ground-state singlet and the first excited doublet state. On the computational side, ab initio many-body quantum chemistry calculations reveal a ZFS gap consistent with the experimental value. Such a large ZFS energy yields a very strong single-ion magnetic anisotropy of easy-plane type resembling that of rare-earth ions. Its microscopic origin is the unusual linear coordination of the Co(I) ions in Li 2 (Li 1- x Co x )N with two nitrogen ligands. Our calculations also evidence a strong 3d-4s hybridization of the electronic shells resulting in significant electron spin density at the 59 Co nuclei, which may be responsible for the experimentally observed extraordinary large hyperfine structure of the ESR signals. Altogether, our experimental spectroscopic and computational results enable comprehensive insights into the remarkable properties of the Li 2 [Li 1- x (TM) x ]N magnets on the microscopic level.

Novel functionalities may be achieved in oxide electronics by appropriate stacking of planar oxide layers of different metallic species, MO p and M'O q . The simplest mechanism allowing the tailoring of the electronic states and physical properties of such heterostructures is of electrostatic nature-charge imbalance between the M and M' cations. Here we clarify the effect of interlayer electrostatics on the anisotropic Kitaev exchange in H 3 LiIr 2 O 6 , a recently proposed realization of the Kitaev spin liquid. By quantum chemical calculations, we show that the precise position of H + cations between magnetically active [LiIr 2 O 6 ] 3- honeycomb-like layers has a strong impact on the magnitude of Kitaev interactions. In particular, it is found that stacking with straight interlayer O-H-O links is detrimental to in-plane Kitaev exchange since coordination by a single H-ion of the O ligand implies an axial Coulomb potential at the O site and unfavorable polarization of the O 2p orbitals mediating the Ir-Ir interactions. Our results therefore provide valuable guidelines for the rational design of Kitaev quantum magnets, indicating unprecedented Kitaev interactions of ≈40 meV if the linear interlayer linkage is removed.

Very recently a quantum liquid was reported to form in H_{3}LiIr_{2}O_{6}, an iridate proposed to be a close realization of the Kitaev honeycomb model. To test this assertion we perform detailed quantum chemistry calculations to determine the magnetic interactions between Ir moments. We find that weakly bond dependent ferromagnetic Kitaev exchange dominates over other couplings, but still is substantially lower than in Na_{2}IrO_{3}. This reduction is caused by the peculiar position of the interlayer species: removing hydrogen cations next to a Ir_{2}O_{2} plaquette increases the Kitaev exchange by more than a factor of 3 on the corresponding Ir─Ir link. Consequently, any lack of hydrogen order will have a drastic effect on the magnetic interactions and strongly promote spin disordering.

A method for the selective synthesis of sulfide clusterfullerenes Dy 2 S@C 2 n is developed. Addition of methane to the reactive atmosphere reduces the formation of empty fullerenes in the arc-discharge synthesis, whereas the use of Dy 2 S 3 as a source of metal and sulfur affords sulfide clusterfullerenes as the main fullerene products along with smaller amounts of carbide clusterfullerenes. Two isomers of Dy 2 S@C 82 with C s (6) and C 3v (8) cage symmetry, Dy 2 S@C 72 - C s (10528), and a carbide clusterfullerene Dy 2 C 2 @C 82 - C s (6) were isolated. The molecular structure of both Dy 2 S@C 82 isomers was elucidated by single-crystal X-ray diffraction. SQUID magnetometry demonstrates that all of these clusterfullerenes exhibit hysteresis of magnetization, with Dy 2 S@C 82 - C 3v (8) being the strongest single molecule magnet in the series. DC- and AC-susceptibility measurements were used to determine magnetization relaxation times in the temperature range from 1.6 K to 70 K. Unprecedented magnetization relaxation dynamics with three consequent Orbach processes and energy barriers of 10.5, 48, and 1232 K are determined for Dy 2 S@C 82 - C 3v (8). Dy 2 S@C 82 - C s (6) exhibits faster relaxation of magnetization with two barriers of 15.2 and 523 K. Ab initio calculations were used to interpret experimental data and compare the Dy-sulfide clusterfullerenes to other Dy-clusterfullerenes. The smallest and largest barriers are ascribed to the exchange/dipolar barrier and relaxation via crystal-field states, respectively, whereas an intermediate energy barrier of 48 K in Dy 2 S@C 82 - C 3v (8) is assigned to the local phonon mode, corresponding to the librational motion of the Dy 2 S cluster inside the carbon cage.

A remarkably large magnetic anisotropy energy of 305 K is computed by quantum chemistry methods for divalent Fe 2+ d 6 substitutes at Li-ion sites with D 6h point-group symmetry within the solid-state matrix of Li 3 N. This is similar to values calculated by the same approach and confirmed experimentally for linearly coordinated monovalent Fe 1+ d 7 species, among the largest so far in the research area of single-molecule magnets. Our ab initio results therefore mark a new exciting exploration path in the search for superior single-molecule magnets, rooted in the configuration of d 6 transition-metal ions with linear or quasilinear nearest-neighbor coordination. This d 6 axial anisotropy may be kept robust even for symmetries lower than D 6h , provided the ligand and farther-neighbor environment is engineered such that the splitting remains large enough.

In existing theoretical approaches to core-level excitations of transition-metal ions in solids relaxation and polarization effects due to the inner core hole are often ignored or described phenomenologically. Here we set up an ab initio computational scheme that explicitly accounts for such physics in the calculation of x-ray absorption and resonant inelastic x-ray scattering spectra. Good agreement is found with experimental transition-metal L-edge data for the strongly correlated d 9 cuprate Li 2 CuO 2 , for which we determine the absolute scattering intensities. The newly developed methodology opens the way for the investigation of even more complex d n electronic structures of group VI B to VIII B correlated oxide compounds.

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d 5 honeycomb halide α-RuCl 3 . From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general.

Due to the combination of a substantial spin-orbit coupling and correlation effects, iridium oxides hold a prominent place in the search for novel quantum states of matter, including, e.g., Kitaev spin liquids and topological Weyl states. We establish the promise of the very recently synthesized hyper-honeycomb iridate β-Li2IrO3 in this regard. A detailed theoretical analysis reveals the presence of large ferromagnetic first-neighbor Kitaev interactions, while a second-neighbor antiferromagnetic Heisenberg exchange drives the ground state from ferro to zigzag order via a three-dimensional Kitaev spin liquid and an incommensurate phase. Experiment puts the system in the latter regime but the Kitaev spin liquid is very close and reachable by a slight modification of the ratio between the second- and first-neighbor couplings, for instance via strain.

Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.

With large spin-orbit coupling, the electron configuration in d-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In 5d(5) iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li2RhO3, a 4d(5) honeycomb oxide. For pristine crystals without Rh-Li site inversion, we predict a dimerized ground state as in the isostructural 5d(5) iridate Li2IrO3, with triplet spin dimers effectively placed on a frustrated triangular lattice. With Rh-Li anti-site disorder, we explain the observed spin-glass phase as a superposition of different, nearly degenerate symmetry-broken configurations.

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 electronic structure of the low-dimensional 4d(5) oxides Sr2RhO4 and Ca3CoRhO6 is herein investigated by embedded-cluster quantum chemistry calculations. A negative tetragonal-like t2g splitting is computed in Sr2RhO4 and a negative trigonal-like splitting is predicted for Ca3CoRhO6, in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longer-range crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t2g(5)-t2g(4)eg(1) couplings via spin-orbit interactions produce in Sr2RhO4 ⟨Z⟩ = ⟨Σ(i)l(i)·s(i)⟩ ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d(5) spin-orbit-driven oxides such as Sr2IrO4. On the other hand, in Ca3CoRhO6, the ⟨Z⟩ values are lower because of larger t2g-eg splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the ⟨Z⟩ values that we predict here, the importance of many-body t2g-eg couplings mediated by spin-orbit interactions, and the role of low-symmetry fields associated with the extended surroundings.

By many-body quantum-chemical calculations, we investigate the role of two structural effects--local ligand distortions and the anisotropic Cd-ion coordination--on the magnetic state of Cd(2)Os(2)O(7), a spin S = 3/2 pyrochlore. We find that these effects strongly compete, rendering the magnetic interactions and ordering crucially dependent on these geometrical features. Without trigonal distortions, a large easy-plane magnetic anisotropy develops. Their presence, however, reverses the sign of the zero-field splitting and causes a large easy-axis anisotropy (D ≃ -6.8 meV), which in conjunction with the antiferromagnetic exchange interaction (J ≃ 6.4 meV) stabilizes an all-in-all-out magnetic order. The competition uncovered here is a generic feature of pyrochlore magnets.

It has long been argued that the minimal model to describe the low-energy physics of the high T(c) superconducting cuprates must include copper states of other symmetries besides the canonical [see text] one, in particular the [see text] orbital. Experimental and theoretical estimates of the energy splitting of these states vary widely. With a novel ab initio quantum chemical computational scheme we determine these energies for a range of copper-oxides and -oxychlorides, determine trends with the apical Cu-ligand distances and find excellent agreement with recent Resonant Inelastic X-ray Scattering measurements, available for La(2)CuO(4), Sr(2)CuO(2)Cl(2), and CaCuO(2).