Ni2Mo3O8: Complex antiferromagnetic order on a honeycomb lattice

Synthesis and Magnetic, Optical, and Electrocatalytic Properties of High-Entropy Mixed-Metal Tungsten and Molybdenum Oxides

High-entropy oxides (HEOs) are of interest for their unique physical and chemical properties. Significant lattice distortions, strain, and tolerance for high-vacancy concentrations set HEOs apart from single-metal or mixed-metal oxides. Herein, we synthesized and characterized the structures and compositions, along with the optical, magnetic, and electrocatalytic properties, of two families of high-entropy mixed-metal tungsten and molybdenum oxides, AWO₄ and B₂Mo₃O₈, where A and B are 3d transition metals. The HEOs A⁶WO₄ (A = Mn, Fe, Co, Ni, Cu, and Zn) and B₂⁵Mo₃O₈ (B = Mn, Fe, Co, Ni, and Zn), as well as all accessible single-metal AWO₄ and B₂Mo₃O₈ parent compounds, were synthesized using high-temperature solid-state methods. X-ray photoelectron spectroscopy analysis of the surfaces revealed that the HEOs largely had the metal oxidation states expected from the bulk chemical formulas, but in some cases they were different than in the parent compounds. A⁶WO₄ exhibited antiferromagnetic (AFM) ordering with a Néel temperature of 30 K, which is less than the average of its AFM parent compounds, and had a narrow band gap of 0.24 eV, which is much lower than all of its parent compounds. B₂⁵Mo₃O₈ was paramagnetic, despite the existence of AFM and ferromagnetic ordering in several of its parent compounds and had no observable band gap, which is analogous to its parent compounds. Both A⁶WO₄ and B₂⁵Mo₃O₈ exhibited superior catalytic activity relative to the parent compounds for the oxygen evolution reaction, the oxidation half reaction of overall water splitting, under alkaline conditions, based on the overpotential required to reach the benchmark surface area normalized current density. Consistent with literature predictions of OER durability for ternary tungsten and molybdenum oxides, A⁶WO₄ and B₂⁵Mo₃O₈ also exhibited stable performance without significant dissolution during 10 h stability experiments at a constant current.

Diffusive excitonic bands from frustrated triangular sublattice in a singlet-ground-state system

Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni₂Mo₃O₈, where Ni²⁺ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.

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.

Density-wave-ordered phases of Rydberg atoms on a honeycomb lattice

Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the (2+1)-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.

PyCrystalField: software for calculation, analysis and fitting of crystal electric field Hamiltonians

PyCrystalField is a Python software package for calculating single-ion crystal electric field (CEF) Hamiltonians. This software can calculate a CEF Hamiltonian ab initio from a point charge model for any transition or rare earth ion in either the J basis or the LS basis, perform symmetry analysis to identify nonzero CEF parameters, calculate the energy spectrum and observables such as neutron spectrum and magnetization, and fit CEF Hamiltonians to any experimental data. The theory, implementation and examples of its use are discussed.

Discovery and Single Crystal Growth of High Entropy Pyrochlores

A family of high entropy oxides with the formula Mg₂Ta₃Ln₃O₁₄ (Ln = La, Pr, Nd, Sm, Eu, Gd) has been discovered and synthesized. Single crystals, 5 mm OD × 2.5 cm, for Ln = Nd have been grown using the laser optical floating zone technique. Crystal orientations are confirmed by Laue diffraction, and structure solutions were obtained via single crystal X-ray diffraction. The structure is found to be a partially disordered pyrochlore, space group Fd-3m, fractional chemical formula (Mg_0.25Nd_0.75)₂(Mg_0.25Ta_0.75)₂O₇. Magnetization measurements indicate ordinary paramagnetic behavior in all compounds down to T = 2 K, except in the Eu variant which possesses Van Vleck paramagnetism. Specific heat measurements for Ln = Nd shows no phase transitions between T = 300 and 2 K. We demonstrate the ability to prepare magnetically disordered materials by substitution of Mg with Ni, Mn, and Co, demonstrating the flexibility of this family in accommodating defects. The stabilization of these compounds could be due to the entropy gain associated with defects, showcasing a "materials by design" approach by using disorder to stabilize novel magnetic and optical materials. Our work also demonstrates the feasibility of preparing high entropy oxides in single crystalline form.

Magnetic and electric properties of single crystal MnI2

Multiferroic materials endowed with both dielectric and magnetic orders, are ideal candidates for a wide range of applications. In this work, we reported two phase transitions of MnI2at 3.45 K and 4 K by systemically measuring the magnetic-field and temperature-dependent magnetization of the MnI2thin flakes. Furthermore, we observed similar temperature and field-dependent behaviours for the magnetic susceptibility of MnI2and electronic capacitance of the Ag/MnI2/Ag devices below 3.5 K. Considering the related theory work, we discussed the relationship between the antiferromagnetic and ferroelectric orders in MnI2. Our work reveals the in-plane magnetic and electric properties of MnI2materials, which might be helpful for the further investigation and application of MnI2multiferroics in the future.

Coupling Magnetic Single-Crystal Co2 Mo3 O8 with Ultrathin Nitrogen-Rich Carbon Layer for Oxygen Evolution Reaction

Transition-metal oxides as electrocatalysts for the oxygen evolution reaction (OER) provide a promising route to face the energy and environmental crisis issues. Although palmeirite oxide A₂ Mo₃ O₈ as OER catalyst has been explored, the correlation between its active sites (tetrahedral or octahedral) and OER performance has been elusive. Now, magnetic Co₂ Mo₃ O₈ @NC-800 composed of highly crystallized Co₂ Mo₃ O₈ nanosheets and ultrathin N-rich carbon layer is shown to be an efficient OER catalyst. The catalyst exhibits favorable performance with an overpotential of 331 mV@10 mA cm^-2 and 422 mV@40 mA cm^-2 , and a full water-splitting electrolyzer with it as anode catalyst shows a cell voltage of 1.67 V@10 mA cm^-2 in alkaline. Combined HAADFSTEM, magnetic, and computational results show that factors influencing the OER performance can be attributed to the tetrahedral Co sites (high spin, t₂ ³ e⁴ ), which improve the OER kinetics of rate-determining step to form *OOH.

Nonpolar-to-Polar Trimerization Transitions in the S = 1 Kagomé Magnet Na2Ti3Cl8

Kagomé lattice magnets have emerged as a versatile platform on which to discover and explore the underlying physics of quantum-spin liquids and related states of matter, although experimental examples of ideal kagomé lattices remain rare. Here we report that Na₂Ti₃Cl₈ is an ideal realization of an insulating S = 1 kagomé magnet. This material undergoes a discrete two-step trimerization upon cooling, transforming from a centrosymmetric, paramagnetic high-temperature (HT) R3m phase to noncentrosymmetric, polar, and trimerized intermediate- (IT) and low-temperature (LT) R3m phases via two successive first-order phase transitions. Symmetry mode decomposition analysis shows that trimerization requires activation of the proper polar order parameter Γ₂^- and that this mode becomes active at the HT → IT phase transition. The magnitude of this order parameter approximately doubles at the IT → LT transition, with possible activation of a second polar mode, corresponding to Na₂ and Ti₃Cl₈ displacing layers toward each other, at the IT → LT transition. Specific heat measurements reveal comparable changes in entropy between the LT → IT transition, 18.6(1.0) J (mol of f.u.)^-1 K^-1, and the IT → LT transition, 16.8(1.0) J (mol of f.u.)^-1 K^-1, demonstrating loss of the magnetic degrees of freedom and constraining possible models for the magnetic and electronic structures of the IT and LT phases. Thus, Na₂Ti₃Cl₈ demonstrates a novel mechanism to obtain polar structures driven by geometrically frustrated lattices and metal-metal bonding and highlights the rich physics arising from kagomé lattice materials.

Ni2Mo3O8: Complex antiferromagnetic order on a honeycomb lattice

Theoretical studies have predicted the existence of topological magnons in honeycomb compounds with stripy or zigzag antiferromagnetic (AFM) order. Here we report the discovery of AFM order in the layered and noncentrosymmetric honeycomb nickelate Ni2Mo3O8 through a combination of magnetization, specific heat, x-ray and neutron diffraction, and electron paramagnetic resonance measurements. The AFM order is complex, with a mixture of stripy and zigzag character on an integer spin noncentrosymmetric honeycomb lattice (P63 mc). Further, each of the two sublattices of the bipartite honeycomb lattice is comprised of a different crystal field environment, i.e., octahedral and tetrahedral Ni2+, respectively, enabling independent substitution on each. Replacement of Ni by Mg on the octahedral site suppresses the long-range magnetic order and results in a weakly ferromagnetic state. Conversely, substitution of Fe for Ni enhances the strength of the AFM exchange and increases the ordering temperature. Thus, Ni2Mo3O8 provides a platform on which to explore the rich physics of S = 1 on the honeycomb lattice in the presence of competing magnetic interactions with a noncentrosymmetric, formally piezopolar, crystal structure.