Spin-Cluster Glassy and Long-Range Ordered Magnetic States in Honeycomb-Layered Compositionally Complex Oxides Na3-xLixT2SbO6 (T = Cu1/3Ni1/3Co1/3)

The concept of high-entropy oxides has triggered extensive research of this novel class of materials because their numerous functional properties are usually not mere linear combinations of those of the components. Here, we introduce the new series of compositionally complex honeycomb-layered magnets Na3-xLixT2SbO6 (T = Cu1/3Ni1/3Co1/3). An unusual feature of the system is its nonmonotonous dependences of the monoclinic lattice parameters b and β on x. Rietveld refinement of the crystal structures of the Na and Li end members reveals apparent Sb-T site inversion in the former and considerable Li-Cu site inversion in the latter. The materials are characterized by measurements of specific heat Cp, magnetization M, and ac and dc magnetic susceptibility χ. Na3T2SbO6 exhibits sharp long-range antiferromagnetic order (TN = 10.2 K) preceded by noticeable correlation effects at elevated temperatures. The magnetic phase diagram of Na3T2SbO6 is established. Introduction of Li, just at x = 0.8, destroys AFM order, resulting in spin-cluster glass behavior attributed to Li/Cu inversion, with TG growing with x to 10.4 K at x = 3.

Successive short- and long-range magnetic ordering in rosiaite-type CoGeTeO6 prepared by ion-exchange reaction

The missing member of the rosiaite family, CoGeTeO₆, was synthesized by mild ion-exchange reactions and characterized by magnetization M and specific heat C_p measurements. It exhibits a successive short- and long-range magnetic ordering at T_short-range ≈ 45 K and T_N = 15 K, respectively. Based on these measurements, the magnetic H-T phase diagram was established, showing two antiferromagnetic phases separated by a spin-flop transition. The reason why the pronounced short-range correlation occurs at a temperature nearly three times higher than T_N was found by evaluating the Co-O⋯O-Co exchange interactions using energy-mapping analysis. Although CoGeTeO₆ has a layered structure, its magnetic structure consists of three-dimensional antiferromagnetic lattices made up of rhombic boxes of Co²⁺ ions. The experimental data obtained at high temperatures agree well with the computational results by treating the Co²⁺ ions of CoGeTeO₆ as S = 3/2 ions, but the heat capacity and magnetization data were obtained at low temperatures by treating the Co²⁺ ion as a J_eff = 1/2 ion.

Recent Progress on Honeycomb Layered Oxides as a Durable Cathode Material for Sodium-Ion Batteries

Sodium-ion batteries (SIBs) are becoming promising candidates for energy storage devices due to the low cost, abundant reserves, and excellent electrochemical performance. As the most important unit, layered cathodes attract much attention, where honeycomb-layered-oxides (HLOs) manifest outstanding structural stability, high redox potential, and long-life electrochemistry. Here, recent progress on HLOs as well as Na₃ Ni₂ SbO₆ and Na₃ Ni₂ BiO₆ as two representative materials are introduced, and the crystal and electronic structure, electrochemical performance, and modification strategies are summarized. The advanced high nickel HLOs are highlighted toward development of state-of-the-art sodium-ion batteries. This review would deepen the understanding of superstructure in layered oxides, as well as structure-property relationship, and inspire more interest in high output voltage, long lifespan sodium-ion batteries.

Evidence of Long-Range and Short-Range Magnetic Ordering in the Honeycomb Na3Mn2SbO6 Oxide

We present a comprehensive study of the synthesis, structure, and magnetic properties of the honeycomb oxide Na₃Mn₂SbO₆ supported by neutron diffraction, heat capacity, and magnetization measurements. The refinements of the neutron diffraction patterns (150, 50, and 45 K) using the Rietveld method confirm the monoclinic (S. G. C2/m) structure. Temperature-dependent magnetic susceptibilities measured at varying fields along with the heat capacity measurements demonstrate the coexistence of long-range ordering (∼42 K) and short-range ordering (∼65 K). The field-dependent isothermal magnetization measurements at 5 K indicate a spin-flop transition around 5 T. Rietveld refinements of the low-temperature (below 45 K) neutron diffraction data further confirm the long-range magnetic ordering. In addition, the temperature variation of the lattice parameters obtained from the neutron powder diffraction analysis exhibited a distinct anomaly near the antiferromagnetic transition temperature. The appearance of the concomitant broadened backgrounds in the neutron powder diffraction data collected at 80, 50, and 45 K supports the short-range ordering. The resultant magnetic structure consists of spins that are aligned antiparallel with the nearest neighbors and also with the spins of the adjacent honeycomb layers. The occurrence of a fully ordered magnetic ground state (Neel antiferromagnetic (AFM)) in Na₃Mn₂SbO₆ consolidates the significance of fabricating new honeycomb oxides.

Excitations in the Ordered and Paramagnetic States of Honeycomb Magnet Na_{2}Co_{2}TeO_{6}

Na_{2}Co_{2}TeO_{6} is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging effective link in the ordered state. The presence of at least six nonoverlapping spin-wave branches is at odds with all models proposed to date. Above the ordering temperature, persisting dynamic correlations can be described by equal-time magnetic structure factors of a hexagonal cluster, which reveal the leading instabilities. Our result sets definitive constraints on theoretical models for Na_{2}Co_{2}TeO_{6} and provides new insight for the materialization of the Kitaev model.

Cationic vacancies as defects in honeycomb lattices with modular symmetries

Layered materials tend to exhibit intriguing crystalline symmetries and topological characteristics based on their two dimensional (2D) geometries and defects. We consider the diffusion dynamics of positively charged ions (cations) localized in honeycomb lattices within layered materials when an external electric field, non-trivial topologies, curvatures and cationic vacancies are present. The unit (primitive) cell of the honeycomb lattice is characterized by two generators, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_1, J_2 \in \mathrm{SL}_2({\mathbb {Z}})$$\end{document}J1,J2∈SL2(Z) of modular symmetries in the special linear group with integer entries, corresponding to discrete re-scaling and rotations respectively. Moreover, applying a 2D conformal metric in an idealized model, we can consistently treat cationic vacancies as topological defects in an emergent manifold. The framework can be utilized to elucidate the molecular dynamics of the cations in exemplar honeycomb layered frameworks and the role of quantum geometry and topological defects not only in the diffusion process such as prediction of conductance peaks during cationic (de-)intercalation process, but also pseudo-spin and pseudo-magnetic field degrees of freedom on the cationic honeycomb lattice responsible for bilayers.

Absence of long-range magnetic order in lithium-containing honeycombs in the Li-Cr-Sb(Te)-O phases

Li₃((LiCr)(Te/Sb))O₆compounds where Cr atoms along with Li and Te or Sb are part of a honeycomb and are studied using magnetic susceptibility, specific heat, x-ray photoelectron spectroscopy and neutron diffraction. The oxides stoichiometries as determined from the neutron diffraction studies are Li_4.47Cr_0.53TeO₆and Li_3.88Cr_1.12SbO₆with a stable oxidation state of +3 for Cr. Both the compounds crystallize in space groupC2/mwith intermixing of cations at the 4gsites leaving the 2asites preferentially for Te or Sb. Again, the Li⁺ions alone predominantly occur in the interlayer sites. Both the compounds show a broad anomaly in specific heat at 8 K, which is robust against 8 T. A corresponding anomaly is absent in the magnetic susceptibility but recovers from its derivative, dχ(T)/dT. We ascertain the magnetic anomaly temperatures (T_a) of Li_4.47Cr_0.53TeO₆and Li_3.88Cr_1.12SbO₆as 5.9 K and 6.7 K respectively from specific heat. Although the physical properties indicated a low temperature anomaly, neutron diffraction data did not reveal a magnetic signal or a structural anomaly down to 1.5 K. This rules out a conventional long-range ordered magnetic ground state in either compounds. Combining the results from specific heat, neutron diffraction and electron paramagnetic resonance, we put forth a scenario of depleted honeycomb lattice of Cr³⁺with predominant short-range magnetic correlations as the magnetic ground states of the title compounds.

Honeycomb layered oxides: structure, energy storage, transport, topology and relevant insights

The advent of nanotechnology has hurtled the discovery and development of nanostructured materials with stellar chemical and physical functionalities in a bid to address issues in energy, environment, telecommunications and healthcare. In this quest, a class of two-dimensional layered materials consisting of alkali or coinage metal atoms sandwiched between slabs exclusively made of transition metal and chalcogen (or pnictogen) atoms arranged in a honeycomb fashion have emerged as materials exhibiting fascinatingly rich crystal chemistry, high-voltage electrochemistry, fast cation diffusion besides playing host to varied exotic electromagnetic and topological phenomena. Currently, with a niche application in energy storage as high-voltage materials, this class of honeycomb layered oxides serves as ideal pedagogical exemplars of the innumerable capabilities of nanomaterials drawing immense interest in multiple fields ranging from materials science, solid-state chemistry, electrochemistry and condensed matter physics. In this review, we delineate the relevant chemistry and physics of honeycomb layered oxides, and discuss their functionalities for tunable electrochemistry, superfast ionic conduction, electromagnetism and topology. Moreover, we elucidate the unexplored albeit vastly promising crystal chemistry space whilst outlining effective ways to identify regions within this compositional space, particularly where interesting electromagnetic and topological properties could be lurking within the aforementioned alkali and coinage-metal honeycomb layered oxide structures. We conclude by pointing towards possible future research directions, particularly the prospective realisation of Kitaev-Heisenberg-Dzyaloshinskii-Moriya interactions with single crystals and Floquet theory in closely-related honeycomb layered oxide materials.

Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, and also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. For example, they result in the famous Jahn-Teller effect, leading to a plethora of consequences for static and dynamic properties, including nontrivial quantum effects. In the present review, we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarizing the basic phenomena and their descriptions, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to the directional character of orbitals, with the concomitant appearance of some instabilities that lead in particular to the formation of dimers, trimers, and similar clusters in a material. The properties of such cluster systems, which are largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field that has acquired special significance relatively recently is the role of the relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in detail in the second part of the review. In discussing all of these questions, special attention is paid to novel quantum effects.

Competing antiferromagnetic-ferromagnetic states in a d7 Kitaev honeycomb magnet

The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li3Co2SbO6, built of high-spin d 7 (Co2+) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/ m , below T N   =   11 K at μ 0 H   =   0 T . The magnetic entropy recovered between T   =   2 and 50 K is estimated to be 0.6 R ln2 , in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C 2/ m under an applied magnetic field of μ 0 H   ≈   0.7 T at T   =   2   K . Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li3Co2SbO6, and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. This material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.

Kitaev Spin Liquid in 3d Transition Metal Compounds

We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co^{2+} ions, the low-energy pseudospin-1/2 Hamiltonian is dominated by bond-dependent Ising couplings that constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Δ, resulting in spin liquid ground state. Considering Na_{3}Co_{2}SbO_{6} as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Δ by ∼20  meV, e.g., via strain or pressure control. We argue that, due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.

Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism

The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar interactions can be yielded by the synergy of spin-orbit coupling and electron correlations for specific electron configuration and lattice geometry, which is known as the Jackeli-Khaliullin mechanism. Based on this mechanism, there has been a fierce race for the materialization of the Kitaev spin liquid over the last decade, but the candidates have been still limited mostly to 4d- and 5d-electron compounds including cations with the low-spind5electron configuration, such as Ir4+and Ru3+. Here we discuss recent efforts to extend the material perspective beyond the Jackeli-Khaliullin mechanism, by carefully reexamining the two requisites, formation of thejeff= 1/2 doublet and quantum interference between the exchange processes, for not onlyd- but alsof-electron systems. We present three examples: the systems including Co2+and Ni3+with the high-spind7electron configuration, Pr4+with thef1-electron configuration, and polar asymmetry in the lattice structure. In particular, the latter two are intriguing since they may realize the antiferromagnetic Kitaev interactions, in contrast to the ferromagnetic ones in the existing candidates. This partial overview would stimulate further material exploration of the Kitaev spin liquids and its topological properties due to fractional excitations.