Stellated cuboctahedron of FeIII.

The solvothermal reaction of FeCl2 ⋅ 4H2O and H4TBC[4] in a basic dmf/EtOH solution affords an [FeIII 18] Keplerate conforming to a stellated cuboctahedron. Magnetic and heat capacity measurements reveal spin frustration effects arising from the high symmetry. A crossover between inverse and direct magnetocaloric effects is observed at ~10 K for applied-field changes lower than 3 T.

Triindenotriphenylenes: Spin-Frustrated Triskelion Triradicals with Excellent Ambient Stability.

A triskelion-shaped triradical triindeno[1,2-a:1',2'-g : 1'',2''-m]triphenylen-7-yl (1) and its internally fused derivative (2) obtained by oxidative cyclization were prepared in a straightforward synthetic sequence. Both compounds were confirmed to be triradicals and to possess intramolecular antiferromagnetic exchange interactions between spins, displaying a spin-frustrated doublet ground state with doublet-quartet energy gaps of -0.14 kcal/mol for 1 and -0.06 kcal/mol for 2. Despite their open-shell character, they were sufficiently stable to be handled under ambient conditions on a timescale of days. Both compounds could be reversibly reduced to mono-, di-, and trianions and oxidized to 1+ and 22+, with strong NIR absorptions (1800 to over 3200 nm) observed for all open-shell ions.

Quantum scaling of the spin lattice relaxation rate in the checkerboardJ-Qmodel.

Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboardJ-Qmodel by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergentO(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance,1/T1, exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature,1/T1rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas1/T1drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponentφ ≈ 0.3, consistent with the scaling ansatzϕ=νzwithν ≈ 0.3 andz = 1. Near the quantum phase transition, the temperature dependent1/T1shows a broad crossover regime where a universal scaling1/T1∼Tηwithη ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.

Robust Spin Liquidity in 2D Metal-Organic Framework Cu3 (HHTP)2 with S=1 /2 Kagome Lattice.

On one hand electron or hole doping of quantum spin liquid (QSL) may unlock high-temperature superconductivity and on the other hand it can disrupt the spin liquidity, giving rise to a magnetically ordered ground state. Recently, a 2D MOF, Cu3 (HHTP)2 (HHTP - 2,3,6,7,10,11-hexahydroxytriphenylene), containing Cu(II) S= 1 / 2 ${{ 1/2 }}$ frustrated spins in the Kagome lattice is emerging as a promising QSL candidate. Herein, we present an elegant in situ redox-chemistry strategy of anchoring Cu3 (HHTP)2 crystallites onto diamagnetic reduced graphene oxide (rGO) sheets, resulting in the formation of electron-doped Cu3 (HHTP)2 -rGO composite which exhibited a characteristic semiconducting behavior (5 K to 300 K) with high electrical conductivity of 70 S ⋅ m-1 and a carrier density of ~1.1×1018  cm-3 at 300 K. Remarkably, no magnetic transition in the Cu3 (HHTP)2 -rGO composite was observed down to 1.5 K endorsing the robust spin liquidity of the 2D MOF Cu3 (HHTP)2 . Specific heat capacity measurements led to the estimation of the residual entropy values of 28 % and 34 % of the theoretically expected value for the pristine Cu3 (HHTP)2 and Cu3 (HHTP)2 -rGO composite, establishing the presence of strong quantum fluctuations down to 1.5 K (two times smaller than the value of the exchange interaction J).

Spin Frustration in Organic Radicals.

Spin frustration, which results from geometric frustration and a systematical inability to satisfy all antiferromagnetic (AF) interactions between unpaired spins simultaneously, is under the spotlight for its importance in physics and materials science. Spin frustration is treated as the structural basis of quantum spin liquids (QSLs). Featuring flexible chemical structures, organic radical species exhibit great potential in building spin-frustrated molecules and lattices. So far, the reported examples of spin-frustrated organic radical compounds include triradicals, tetrathiafulvalene (TTF) radicals and derivatives, [Pd(dmit)2 ] compounds (dmit=1,3-dithiol-2-thione-4,5-dithiolate), nitronyl nitroxides, fullerenes, polycyclic aromatic hydrocarbons (PAHs), and other heterocyclic compounds where the spin frustration is generated intra- or intermolecularly. In this Minireview, we provide a brief summary of the reported radical compounds that possess spin frustration. The related data, including magnetic exchange coupling parameters, spin models, frustration parameters, and crystal lattices, are summarized and discussed.

Odd and Even Numbered Ferric Wheels.

The structurally related odd and even numbered wheels [FeIII 11 ZnII 4 (tea)10 (teaH)1 (OMe)Cl8 ] (1) and [FeIII 12 ZnII 4 (tea)12 Cl8 ] (2) can be synthesized under ambient conditions by reacting FeIII and ZnII salts with triethanolamine (teaH3 ), the change in nuclearity being dictated by the solvents employed. An antiferromagnetic exchange between nearest neighbors, J = -10.0 cm-1 for 1 and J = -12.0 cm-1 for 2, leads to a frustrated S = 1/2 ground state in the former and an S = 0 ground state in the latter.

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration.

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C96 H24 Ar6 )2 (Ar=2,6-dimethylphenyl) (12 ) was transformed to a triply negatively charged species 12 3.- , which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 12 3.- features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp2 carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 12 3.- , which indicates graphene upon reduction doping may behave as a quantum spin liquid.

Two-dimensional quantum universality in the spin-1/2 triangular-lattice quantum antiferromagnet Na2BaCo(PO4)2.

An interplay of geometrical frustration and strong quantum fluctuations in a spin-1/2 triangular-lattice antiferromagnet (TAF) can lead to exotic quantum states. Here, we report the neutron-scattering, magnetization, specific heat, and magnetocaloric studies of the recently discovered spin-1/2 TAF Na2BaCo(PO4)2, which can be described by a spin-1/2 easy axis XXZ model. The zero-field neutron diffraction experiment reveals an incommensurate antiferromagnetic ground state with a significantly reduced ordered moment of about 0.54(2) µB/Co. Different magnetic phase diagrams with magnetic fields in the ab plane and along the easy c-axis were extracted based on the magnetic susceptibility, specific heat, and elastic neutron-scattering results. In addition, two-dimensional (2D) spin dispersion in the triangular plane was observed in the high-field polarized state, and microscopic exchange parameters of the spin Hamiltonian have been determined through the linear spin wave theory. Consistently, quantum critical behaviors with the universality class of d = 2 and νz = 1 were established in the vicinity of the saturation field, where a Bose-Einstein condensation (BEC) of diluted magnons occurs. The newly discovered quantum criticality and fractional magnetization phase in this ideal spin-1/2 TAF present exciting opportunities for exploring exotic quantum phenomena.

Ru-Doping-Induced Spin Frustration and Enhancement of the Room-Temperature Anomalous Hall Effect in La2/3 Sr1/3 MnO3 Films.

In transition-metal-oxide heterostructures, the anomalous Hall effect (AHE) is a powerful tool for detecting the magnetic state and revealing intriguing interfacial magnetic orderings. However, achieving a larger AHE at room temperature in oxide heterostructures is still challenging due to the dilemma of mutually strong spin-orbit coupling and magnetic exchange interactions. Here, Ru-doping-enhanced AHE in La2/3 Sr1/3 Mn1-x Rux O3 epitaxial films is exploited. As the B-site Ru doping level increases up to 20%, the anomalous Hall resistivity at room temperature can be enhanced from nΩ cm to µΩ cm scale. Ru doping leads to strong competition between the ferromagnetic double-exchange interaction and the antiferromagnetic superexchange interaction. The resultant spin frustration and spin-glass state facilitate a strong skew-scattering process, thus significantly enhancing the extrinsic AHE. The findings can pave a feasible approach for boosting the controllability and reliability of oxide-based spintronic devices.

Colossal Magnetoresistance in Ti Lightly Doped Cr2Se3 Single Crystals with a Layered Structure.

Stoichiometric Cr2Se3 single crystals are particular layer-structured antiferromagnets, which possess a noncollinear spin configuration, weak ferromagnetic moments, moderate magnetoresistance (MR ∼14.3%), and poor metallic conductivity below the antiferromagnetic phase transition. Here, we report an interesting >16 000% colossal magnetoresistance (CMR) effect in Ti (1.5 atomic percent) lightly doped Cr2Se3 single crystals. Such a CMR is approximately 1143 times larger than that of the stoichiometric Cr2Se3 crystals and is rarely observed in layered antiferromagnets and is attributed to the frustrated spin configuration. Moreover, the Ti doping not only dramatically changes the electronic conductivity of the Cr2Se3 crystal from a bad metal to a semiconductor with a gap of ∼15 meV but also induces a change in the magnetic anisotropy of the Cr2Se3 crystal from strong out-of-plane to weak in-plane. Further, magnetotransport measurements reveal that the low-field MR scales with the square of the reduced magnetization, which is a signature of CMR materials. The layered Ti:Cr2Se3 with the CMR effect could be used as two-dimensional (2D) heterostructure building blocks to provide colossal negative MR in spintronic devices.

Crystal chemistry criteria of the existence of spin liquids on the kagome lattice.

The structural-magnetic models of 25 antiferromagnetic kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2)-a perspective spin liquid-have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in lengthJ3 magnetic couplings (strongJ3(J12) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFMJ3(Jd) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality ofJ3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dualJ3 couplings with anisotropic Dzyaloshinskii-Moriya interactions are capable to suppress frustration of kagome antiferromagnetics. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighborJ1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in lengthJ3 magnetic couplings.

Emergence of metamagnetic transition, re-entrant cluster glass and spin phonon coupling in Tb2CoMnO6.

The double perovskite compound Tb2CoMnO6has been investigated using x-ray absorption spectroscopy (XAS), Raman spectroscopy, magnetic measurements andab initioband structure calculations. It is observed that both anti-ferromagnetic (AFM) and ferromagnetic (FM) phase coexist in this material. The presence of anti-site disorder (ASD) has been established from the analysis of neutron diffraction data. Moreover, a prominent metamagnetic transition is observed in theM(H) behavior that has been explained with the drastic reorientation of the pinned domain which are aligned antiparallel by the antiphase boundaries (APBs) at zero field. The ASD further gives rise to spin frustration at low temperature which leads to the re-entrant cluster glass ∼33 K. The coupling between phononic degree of freedom and spin in the system has also been demonstrated. It is observed that the theoretical calculation is consistent with that of the experimentally observed behavior.

Decacyclene Radical Anions Showing Strong Low-energy Intramolecular Absorption and Magnetic Coupling of Spins in a Hexagonal Network.

Two salts of the aromatic hydrocarbon decacyclene, {cryptand[2.2.2](Cs+ )} (decacyclene.- ) (1) and {Bu3 MeP+ }(decacyclene.- ) (2), were obtained. In both salts, decacyclene.- radical anions formed channels occupied by cations. However, corrugated hexagonal decacyclene.- layers could be outlined in the crystal structure of 1 with several side-by-side C⋅⋅⋅C approaches. The decacyclene.- radical anions showed strong distortion in both salts, deviating from the C3 symmetry owing to the repulsion of closely arranged hydrogen atoms and the Jahn-Teller effect. Radical anions showed intense unusually low energy absorption in the IR-range, with maxima at 4800 and 6000 cm-1 . According to the carculations, these bands can originate from the SOMO-LUMO+1 and SOMO-LUMO+2 transitions, respectively. Radical anions exhibited a S=1/2 spin state, with an effective magnetic moment of 1.72 µB at 300 K. The decacyclene.- spin antiferromagnetically coupled with a Weiss temperature of -11 K. Spin ordering was not observed down to 1.9 K owing to spin frustration in the hexagonal decacyclene.- layers.

The Mechanism of the Magnetodielectric Response in a Molecule-Based Trinuclear Iron Cluster Material.

Magnetodielectric response mechanisms are critical for the rational design and synthesis of molecule-based magnetodielectric materials. Herein, the magnetodielectric response was investigated in the molecule-based material [Fe3 O(CH3 COO)6 (py)3 ](py) (1). Its magnetodielectric coefficient (MD) is -2.8 % for phase transition III and -4.1 % for phase transition I. Study of the mechanism of the magnetodielectric response in 1 reveals that its magnetodielectric response at phase transition I is induced by the charge-frustration of the trinuclear iron cluster, while that at phase transition III is attributed to the spin-frustration of the trinuclear iron cluster, providing a new route for the design of magnetodielectric materials.

An [FeIII 34 ] Molecular Metal Oxide.

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe34 ] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral FeIII ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe-O-Fe angles and Fe-O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe34 ], bulk iron oxides, previous FeIII -oxo cages, and polyoxometalates (POMs), hints that much larger molecular FeIII oxides can be made.

Evidence of Spin Frustration in a Vanadium Diselenide Monolayer Magnet.

Monolayer VSe2 , featuring both charge density wave and magnetism phenomena, represents a unique van der Waals magnet in the family of metallic 2D transition-metal dichalcogenides (2D-TMDs). Herein, by means of in situ microscopy and spectroscopic techniques, including scanning tunneling microscopy/spectroscopy, synchrotron X-ray and angle-resolved photoemission, and X-ray absorption, direct spectroscopic signatures are established, that identify the metallic 1T-phase and vanadium 3d1 electronic configuration in monolayer VSe2 grown on graphite by molecular-beam epitaxy. Element-specific X-ray magnetic circular dichroism, complemented with magnetic susceptibility measurements, further reveals monolayer VSe2 as a frustrated magnet, with its spins exhibiting subtle correlations, albeit in the absence of a long-range magnetic order down to 2 K and up to a 7 T magnetic field. This observation is attributed to the relative stability of the ferromagnetic and antiferromagnetic ground states, arising from its atomic-scale structural features, such as rotational disorders and edges. The results of this study extend the current understanding of metallic 2D-TMDs in the search for exotic low-dimensional quantum phenomena, and stimulate further theoretical and experimental studies on van der Waals monolayer magnets.

Highly Spin-Frustrated Magnetism in the Topochemically Prepared Triangular Lattice Cluster Magnets Na3 A2 (MoO4 )2 Mo3 O8 (A=In, Sc).

The physical properties of novel cluster-based triangular lattice antiferromagnets Na3 A2 (MoO4 )2 Mo3 O8 (A=In, Sc), synthesized through a topochemical Na-intercalation to nonmagnetic Na2 A2 (MoO4 )2 Mo3 O8 , are reported. The S=1/2 [Mo3 ]11+ clusters form a regular triangular lattice, which gives the magnetic system a strong geometrical spin frustration effect. Despite the strong antiferromagnetic couplings among [Mo3 ]11+ clusters, they show no long-range magnetic orderings down to 0.5 K with the finite residual magnetic entropy. The ground states of Na3 A2 (MoO4 )2 Mo3 O8 have been characterized as a quantum spin liquid, owing to the strong spin frustration of cluster spins on the triangular lattice.

Magnetic Tuning of an Anionic CoII -MOF through Deionization of the Framework: Spin-Canting, Spin-Flop, and Easy-Plane Magnetic Anisotropy.

An anionic CoII -MOF, (Me2 NH2 )[Co3 (Me2 NH)3 (OH)(SDBA)3 ] (1) (H2 SDBA=4,4'-sulfonyldibenzoic acid) consisting of highly symmetric CoII3 (µ3 -OH) triangles exhibits spin-canting, spin-flop, and easy-plane magnetic anisotropy. Measurement on a single crystal shows that the ab plane of 1 is the easy magnetization plane. After structural modification through simultaneous removal of the coordinated dimethylamine (DMA) molecule at the Co center and the ionic groups DMA+ and OH- , the resulting neutral amorphous framework 2 displays an enhanced spin frustration effect. The deionization of 1 does not result in the collapse of the framework, showing the high stability of the backbone structure.

[CrF(O2 C(t) Bu)2 ]9 : Synthesis and Characterization of a Regular Homometallic Ring with an Odd Number of Metal Centers and Electrons.

The first regular homometallic ring containing an odd number of metal centers is reported. The ring was synthesized by means of amine-templated self-assembly. Extensive physical characterization studies, including magnetic measurements, powder inelastic neutron scattering (INS), and DFT calculations, show that the molecule has a near perfect match to the expected behavior for a frustrated system with the lowest energy pair of S=1/2 spin states separated by only 0.1 meV (0.8 cm(-1) ).

Studies of a Large Odd-Numbered Odd-Electron Metal Ring: Inelastic Neutron Scattering and Muon Spin Relaxation Spectroscopy of Cr8 Mn.

The spin dynamics of Cr8 Mn, a nine-membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr8 Mn is a rare example of a large odd-membered AF ring, and has an odd-number of 3d-electrons present. Odd-membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated-spin ground states. The chemical synthesis and structures of two Cr8 Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (µSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that µSR is sensitive to the ground-spin-state crossing from S=1/2 to S=3/2 in Cr8 Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin-pair correlations and scalar-spin chirality, shows a non-collinear spin structure that fluctuates between non-planar states of opposite chiralities.