Using the tools of group theory we have mapped out the symmetry consequences of structural distortions in hybrid layered perovskites. These distortions include octahedral tilting and cation ordering within the inorganic layers as well as orientational ordering of organic cations in the organic layers. This analysis is coupled with synthesis and crystal structure determination of a wide variety Ruddlesden-Popper phases. The combined analysis shows that certain modes of octahedral tilting are strongly favored in large part because they lead to favorable hydrogen bonding interactions between the halide ions of the inorganic layers and the ammonium-type protons of the organic cations that sit between the layers. This information is used to guide our search for new lead-free ferroelectrics and multiferroics among this large class of compounds.

The A-site ordered quadruple perovskites AA’₃B₄O₁₂ can accommodate transition metal cations at the square-planar A’ site. When the B site is occupied by non-magnetic cations, the complex magnetic interactions between the spins at the orthogonally-oriented A’-sites can result in a wide variety of non-trivial magnetic orders. For example, A’-site Cu²⁺ (S = 1/2) spins can align either ferromagnetically (FM) in CaCu₃Sn₄O₁₂ or CaCu₃Ge₄O₁₂ (T_C = 10 and 13 K respectively), or antiferromagnetically (AFM) in CaCu₃Ti₄O₁₂ (T_N = 25 K) as a result of competition between direct exchange and superexchange interactions. A’-site Mn³⁺ (S = 2) in YMn₃Al₄O₁₂ yields a G-type AFM structure (T_N = 37 K) and Mn²⁺ (S = 5/2) spins in LaMn₃V₄O₁₂ break the symmetry to form a helix-type AFM structure (T_N = 44 K).

We recently revisited the material CaFe₃Ti₄O₁₂ with S = 2 (Fe²⁺) centers at the A’-sites for which initial studies did not find any long range magnetic order down to 4.2 K. This absence of magnetic ordering was notably unconventional. We discovered that the Fe²⁺ (S = 2) spins in CaFe₃Ti₄O₁₂ order in a complex triple-k AFM ground state at T_N = 2.8 K. In contrast to most magnetic insulating oxides, the Heisenberg superexchange between first- and second-neighbour spins are minimised by strong easy-axis anisotropy. Further-neighbour interactions yield the resulting spin ground state. On application of magnetic field, a canted FM spin structure is induced. This magnetic ordering is contrastingly different from those previously reported for A’-site magnetic quadruple perovskite materials. Furthermore, our results show that exotic long-range magnetically ordered ground states can emerge in large-spin systems when the symmetric exchange is quenched.

Charge ordering is prone to occur in crystalline materials with mixed-valence ions. It is often accompanied by a structural phase transition between a low-symmetry phase and a more symmetric high-temperature parent crystal structure. Such a structural transition may be absent if the mixed-valence ions are already located in inequivalent crystallographic sites in the parent structure. In this work, we investigate the representative case of the homometallic Co ludwigite (Co²⁺)₂(Co³⁺)O₂BO₃ (Pbam space group) with four distinct Co crystallographic sites surrounded by oxygen octahedra [Co(1)-Co(4)]. X-ray Absorption Near-Edge Spectroscopy provide experimental support for a Co²⁺/Co³⁺ mixed-valence scenario at all temperatures. X-ray and neutron diffraction confirm that the oxygen octahedron surrounding the Co(4) site is much smaller than those associated with the Co(1)-Co(3) sites at low temperatures, consistent with a localization of the Co³⁺ ions at the Co(4) site. The size differentiation of the Co(4)O₆ and Co(2)O₆ octahedra is continuously reduced upon warming above ~ 370 K, revealing a gradual charge redistribution along the Co(4)-Co(2)-Co(4) (424) ladder. In addition, small anomalies in specific Co-O bond lengths in the Co(3)-Co(1)-Co(3) (313) ladder are observed at 470 K and 495 K, respectively, matching the temperatures where sharp transitions were previously revealed by calorimetry and resistivity measurements. These bond length anomalies occur without an accompanying space group change within our sensitivity. An increasing structural disorder, clearly beyond a conventional thermal effect, is noted above ~ 370 K, manifested by an anomalous increment of some XRD Debye-Waller factors and broadened vibrational modes observed by Raman scattering. The local Co-O distance distribution, revealed by Co K-edge Extended X-Ray Absorption Fine Structure (EXAFS) data and analyzed with an evolutionary algorithm method, is similar to that inferred from the XRD crystal structure below ~ 370 K. At higher temperatures, the local Co-O distance distribution remains similar to that found at low temperatures, indicating that the size differentiation between smaller Co³⁺ ions and larger Co²⁺ions is maintained despite the growing oxidation-state disorder within the 424 ladder upon warming. This study provides insight into the physics of ludwigites and other related complex oxides at high temperatures.

Acknowledgments: This work was supported by CNPq Grants 134752/2016-3 and 308607/2018-0,
FAPESP Grant 2018/20142-8, and CAPES, Brazil.

Transition metal oxides are a platform for a plethora of exotic electronic phases where multiple degrees of freedom of correlated d-electrons, together with an underlying lattice topology, are at play. The ground states of these systems are governed by a subtle balance of relevant electronic parameters such as Coulomb repulsion, bandwidth, and crystal fields. 4d ruthenium compounds have been playing a significant role in providing novel electronic states such as unconventional superconductivity, metal-insulator transition and quantum magnetism.

Besides metallic or Mott insulating ground states, some ruthenium compounds exhibit a nonmagnetic ground state, which is accompanied by the formation of molecular orbitals generated by direct hopping between spatially extended 4d orbitals. A prominent example is the honeycomb ruthenate Li₂RuO₃, which undergoes dimerization of Ru atoms below ~ 550 K and forms a "molecular orbital crystal", where the 4d electrons are accommodated into the bonding and antibonding molecular orbitals localized on the dimers.

In heavy-transition-metal compounds such as ruthenates, another key ingredient for their exotic electronic states is spin-orbit coupling (SOC) which produces spin-orbit entangled J_eff pseudospins. Probably the most striking impact on magnetism is realised in Ru⁴⁺ ruthenates with a d⁴ configuration. While SOC produces a nominally non-magnetic J_­eff = 0 singlet, “excitonic” magnetism can arise via the interaction between excited states, and spin-orbit excitons may condense into an exotic long-range magnetic order. Up to date, excitonic magnetism has been only established in a layered perovskite Ca₂RuO₄ and remains unexplored in other ruthenates.

The competition between electronic phases including molecular orbital crystal and spin-orbit magnetism is expected to be more pronounced in ruthenates with a frustrated lattice, such as pyrochlore ruthenates A₂Ru₂O₇ (A: trivalent cation). The pyrochlore ruthenates have been regarded as S = 1 Mott insulators due to the presence of a trigonal distortion which may lift the degeneracy of the t_2g orbitals and thus competes with SOC. While most of them order magnetically at low temperatures, Tl₂Ru₂O₇ exhibits a metal to non-magnetic insulator transition at ~ 120 K. The origin of the nonmagnetic ground state has been attributed to the formation of a Haldane gap in the one-dimensional zigzag chains of Ru atoms on top of the pyrochlore lattice. The distinct behaviour of Tl₂Ru₂O₇ may be related to the covalency of Tl-O bonds, which has been discussed as playing a key role in the metal-insulator transition. The covalent character of A-O bonds thus may be an important parameter for the ground state of pyrochlore oxides. On the other hand, the role of spin-orbit coupling has not been fully investigated in pyrochlore ruthenates.

In an attempt to explore the novel phase competition in pyrochlore ruthenates, we discovered a new compound In₂Ru₂O₇ using high pressure synthesis. At high temperatures above ~ 450 K, In₂Ru₂O₇ crystallizes in a cubic pyrochlore structure, but adopts a weakly distorted tetragonal structure at room temperature as elucidated with single crystal x-ray and powder neutron diffraction. From the spectroscopic measurements, In₂Ru₂O₇ was found to host a spin-orbit-entangled J_eff = 0 -like state at room temperature, despite presenting the largest trigonal distortion among the family of pyrochlore ruthenates. The spin-orbit entangled singlet state is expected to display excitonic magnetism. Strikingly, through successive structural transitions likely associated with the covalent In-O bonds, the singlet state collapses and In₂Ru₂O₇ forms a non-magnetic state below ~ 220 K as evidenced by muon spin rotation. The non-magnetic ground state was found to originate from a molecular orbital formation in the semi-isolated Ru₂O trimer molecules decorating the pyrochlore lattice. Such molecular orbital formation, which involves not only the Ru⁴⁺ ions but the O^2- anions as well, has not been reported in other pyrochlore oxides.

In this talk we discuss the subtle competition between spin-orbit coupling and molecular orbital crystal formation in pyrochlore ruthenate In₂Ru₂O₇. We present the structural details of the Ru₂O trimer formation and its impact on the magnetism and electronic structure of In₂Ru₂O₇. We argue that the unique molecular orbital formation involving an oxygen atom, distinct from dimers with direct overlap of d-orbitals commonly found in other transition metal oxides, is assisted by the distortion of the In-O network. Our result demonstrates that bond covalency of constituent ions can be an additional key parameter in understanding phase competitions in complex transition-metal oxides.

The scheelites are a family of compounds with chemical formula ABO₄, and a characteristic crystal structure consisting of AO₈ dodecahedra and BO₄ tetrahedra. This structure is flexible and can accommodate a large variety of cations with a range of atomic radii and valence combinations. Scheelite-type oxides, such as CaWO₄, BiVO₄ and NaLa(MoO₄)₂ have been extensively studied due to their diverse range of physical and electronic properties [1]. In particular, Bi³⁺ containing molybdates have been found to be efficient photocatalysts due to the strong repulsive force of the 6s² lone pair of Bi³⁺, resulting in distortion of the BO₄ tetrahedra and alteration of the band gap [2, 3].

In 1974 Bi₃FeMo₂O₁₂ (BFMO) was reported as the first scheelite-type compound containing trivalent cations on the tetrahedral sites [4]. Interestingly, two different polymorphs of BFMO can be isolated by varying the synthesis conditions [5]. The tetragonal scheelite-type polymorph, described by space group I4₁/a with a = 5.32106(13) Å and c = 11.656(4) Å, can be prepared by a sol-gel route from aqueous solution of the constituent ionic species and has a disordered arrangement of the Fe and Mo cations. When heated above 500 °C, a 2:1 ordering of the Mo and Fe cations occurs, which lowers the symmetry to monoclinic (C2/c). The corresponding superstructure has a tripling of the a axis (a = 16.9110 (3) Å, b = 11.6489(2) Å, c= 5.25630(9) Å, β = 107.1395(11)°). The two structures are illustrated in Fig. 1.

In the present study, both polymorphs of BFMO were synthesized and their structure and magnetic properties characterized using a combination of powder diffraction, microscopy and magnetometry techniques. In situ neutron powder diffraction (NPD) measurements of the structural evolution of disordered tetragonal BFMO with increasing temperature showed that no amorphization takes place prior to the formation of the ordered monoclinic phase. The lack of a structural break-down, despite the substantial cation movement required in such a transformation, suggests that a certain degree of local cation order exists in the “disordered” tetragonal phase, facilitating the direct conversion to the fully ordered monoclinic structure. Instead of the expected amorphization and recrystallization, the conversion takes place via a 1^st order phase transition, with the tetragonal polymorph exhibiting negative thermal expansion prior to its conversion into the monoclinic structure. Zero-field-cooled/field-cooled and field-dependent magnetization curves of the monoclinic structure revealed the existence of a magnetic transition below 15 K. The long-range nature of the low-temperature magnetic structure in the monoclinic polymorph was verified by high-resolution NPD data, which revealed the emergence of an incommensurate magnetic structure. There is no evidence for long-range magnetic order in the tetragonal polymorph. This is, to the best of our knowledge, the first study of the phase transition mechanism and magnetic properties of this complex system and represents a milestone in the structural understanding and targeted design of Bi³⁺ containing molybdates as efficient photocatalysts.

[1] Brazdil, J. F. (2015). Catalysis Science & Technology 5, 3452-3458.

[2] Feng, Y., Yan, X., Liu, C., Hong, Y., Zhu, L., Zhou, M. & Shi, W. (2015). Appl Surf Sci 353, 87-94.

[3] Tokunaga, S., Kato, H. & Kudo, A. (2001). Chem Mater 13, 4624-4628.

[4] Sleight, A. W. & Jeitschko, W. (1974). Materials Research Bulletin 9, 951-954.

[5] Jeitschko, W., Sleight, A. W., Mcclellan, W. R. & Weiher, J. F. (1976). Acta Crystallogr B 32, 1163-1170.

A detailed account of the local atomic structure and disorder at 5 K across the phase diagram of the high-temperature superconductor K_xFe_2-ySe_2-zS_z (0≤z≤2) is obtained from neutron total scattering and associated atomic pair distribution function (PDF) approaches [1]. Various model-independent and model-dependent aspects of the analysis reveal a high level of structural complexity on the nanometer length scale. Evidence is found for considerable disorder in the c-axis stacking of the FeSe S slabs without observable signs of turbostratic character of the disorder. In contrast to the related FeCh (Ch = S, Se)-type superconductors, substantial Fe-vacancies are present in K_xFe_2-ySe_2-zS_z, deemed detrimental for superconductivity when ordered. Our study suggests that the distribution of vacancies significantly modifies the iron-chalcogen bond-length distribution, in agreement with observed evolution of the PDF signal. A crossover-like transition is observed at a composition of z≈1, from a correlated disorder state at the selenium end to a more vacancy-ordered (VO) state closer to the sulfur end of the phase diagram. The S-content-dependent measures of the local structure are found to exhibit distinct behavior on either side of this crossover, correlating well with the evolution of the superconducting state to that of a magnetic semiconductor toward the z≈2 end. The behavior reinforces the idea of the intimate relationship of correlated Fe-vacancy order in the local structure and the emergent electronic properties.

[1] P. Mangelis et al., (2019) Physical Review B 100, 094108.

Work at Brookhaven National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DOE-BES) under Contract No. DE-SC0012704. Alexandros Lappas acknowledges support by the U.S. Office of Naval Research Global, NICOP Grant Award No. N62909-17-1-2126. This research used resources at the Spallation Neutron Source, a U.S. Department of Energy Office of Science User Facility operated by the Oak Ridge National Laboratory.