Zig-zag magnetic ordering in honeycomb-layered Na3Co2SbO6

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.

Antiferromagnetic Kitaev interaction inJeff1/2 cobalt honeycomb materials Na3Co2SbO6and Na2Co2TeO6

Finding new materials with antiferromagnetic (AFM) Kitaev interaction is an urgent issue for quantum magnetism research. We conclude that Na₃Co₂SbO₆and Na₂Co₂TeO₆are new honeycomb cobalt-based systems with AFM Kitaev interaction by carrying out inelastic neutron scattering experiments and subsequent analysis. The spin-orbit excitons observed at 20-28 meV in both compounds strongly support the idea that Co²⁺ions of both compounds have a spin-orbital entangledJ_eff= 1/2 state. Furthermore, we found that a generalized Kitaev-Heisenberg Hamiltonian can describe the spin-wave excitations of both compounds with additional 3rd nearest-neighbor interaction. Our best-fit parameters show significant AFM Kitaev terms and off-diagonal symmetric anisotropy terms of a similar magnitude in both compounds. We also found a strong magnon-damping effect at the higher energy part of the spin waves, entirely consistent with observations in other Kitaev magnets. Our work suggests Na₃Co₂SbO₆and Na₂Co₂TeO₆as rare examples of the AFM Kitaev magnets based on the systematic studies of the spin waves and analysis.

Spin-orbital entangled state and realization of Kitaev physics in 3dcobalt compounds: a progress report

The realization of Kitaev's honeycomb magnetic model in real materials has become one of the most pursued topics in condensed matter physics and materials science. If found, it is expected to host exotic quantum phases of matter and offers potential realizations of fault-tolerant quantum computations. Over the past years, much effort has been made on 4d- or 5d-heavy transition metal compounds because of their intrinsic strong spin-orbit coupling. But more recently, there have been growing shreds of evidence that the Kitaev model could also be realized in 3d-transition metal systems with much weaker spin-orbit coupling. This review intends to serve as a guide to this fast-developing field focusing on systems withd⁷transition metal occupation. It overviews the current theoretical and experimental progress on realizing the Kitaev model in those systems. We examine the recent experimental observations of candidate materials with Co²⁺ions: e.g., CoPS₃, Na₃Co₂SbO₆, and Na₂Co₂TeO₆, followed by a brief review of theoretical backgrounds. We conclude this article by comparing experimental observations with density functional theory calculations. We stress the importance of inter-t_2ghopping channels and Hund's coupling in the realization of Kitaev interactions in Co-based compounds, which has been overlooked in previous studies. This review suggests future directions in the search for Kitaev physics in 3dcobalt compounds and beyond.

Magnetic structure, excitations and short-range order in honeycomb Na2Ni2TeO6

Na₂Ni₂TeO₆has a layered hexagonal structure with a honeycomb lattice constituted by Ni²⁺and a chiral charge distribution of Na⁺that resides between the Ni layers. In the present work, the antiferromagnetic (AFM) transition temperature of Na₂Ni₂TeO₆is confirmed atT_N≈ 27 K, and further, it is found to be robust up to 8 T magnetic field and 1.2 GPa external pressure; and, without any frequency-dependence. Slight deviations from nominal Na-content (up to 5%) does not seem to influence the magnetic transition temperature,T_N. Isothermal magnetization curves remain almost linear up to 13 T. Our analysis of neutron diffraction data shows that the magnetic structure of Na₂Ni₂TeO₆is faithfully described by a model consisting of two phases described by the commensurate wave vectorsk→c,0.500and0.500.5, with an additional short-range order component incorporated in to the latter phase. Consequently, a zig-zag long-range ordered magnetic phase of Ni²⁺results in the compound, mixed with a short-range ordered phase, which is supported by our specific heat data. Theoretical computations based on density functional theory predict predominantly in-plane magnetic exchange interactions that conform to aJ₁-J₂-J₃model with a strongJ₃term. The computationally predicted parameters lead to a reliable estimate forT_Nand the experimentally observed zig-zag magnetic structure. A spin wave excitation in Na₂Ni₂TeO₆atE≈ 5 meV atT= 5 K is mapped out through inelastic neutron scattering experiments, which is reproduced by linear spin wave theory calculations using theJvalues from our computations. Our specific heat data and inelastic neutron scattering data strongly indicate the presence of short-range spin correlations, atT>T_N, stemming from incipient AFM clusters.

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.

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.

Synthesis, structure and magnetic properties of honeycomb-layered Li3Co2SbO6 with new data on its sodium precursor, Na3Co2SbO6

Crystallographic and magnetic properties of new layered honeycomb-lattice Li₃Co₂SbO₆ antimonate were studied and compared with its sodium precursor Na₃Co₂SbO₆.