Two-Dimensional Cobalt(II) Benzoquinone Frameworks for Putative Kitaev Quantum Spin Liquid Candidates

The realization and discovery of quantum spin liquid (QSL) candidate materials are crucial for exploring exotic quantum phenomena and applications associated with QSLs. Most existing metal-organic two-dimensional (2D) quantum spin liquid candidates have structures with spins arranged on the triangular or kagome lattices, whereas honeycomb-structured metal-organic compounds with QSL characteristics are rare. Here, we report the use of 2,5-dihydroxy-1,4-benzoquinone (X2dhbq, X = Cl, Br, H) as the linkers to construct cobalt(II) honeycomb lattices (NEt4)2[Co2(X2dhbq)3] as promising Kitaev-type QSL candidate materials. The high-spin d7 Co2+ has pseudospin-1/2 ground-state doublets, and benzoquinone-based linkers not only provide two separate superexchange pathways that create bond-dependent frustrated interactions but also allow for chemical tunability to mediate magnetic coupling. Our magnetization data show antiferromagnetic interactions between neighboring metal centers with Weiss constants from -5.1 to -8.5 K depending on the X functional group in X2dhbq linkers (X = Cl, Br, H). No magnetic transition or spin freezing could be observed down to 2 K. Low-temperature susceptibility (down to 0.3 K) and specific heat (down to 0.055 K) of (NEt4)2[Co2(H2dhbq)3] were further analyzed. Heat capacity measurements confirmed no long-range order down to 0.055 K, evidenced by the broad peak instead of the λ-like anomaly. Our results indicate that these 2D cobalt benzoquinone frameworks are promising Kitaev QSL candidates with chemical tunability through ligands that can vary the magnetic coupling and frustration.

Anomalous dielectric response in the triple perovskite ruthenate Ba3BiRu2O9

We have investigated the magnetic, dielectric and thermal properties of theSRu= 1 magnetic dimer Ba₃BiRu₂O₉, which is known to exhibit a spin-gap opening in conjunction with a first-order magneto-elastic phase transition at ∼175 K. Above the spin-gap temperature, the temperature dependence dielectric constant shows a peak like feature with pronounced frequency dependence. The critical slowing down behavior of this frequency dispersion suggests that a ferroelectric relaxor like electrical glassy state exists above the spin-gap opening temperature regime. The extermination of frequency dispersion-right at the magneto-elastic phase transition, is suggestive of a strong coupling between the lattice and charge-spin degrees of freedom in this triple perovskite system.

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.

Giant Anisotropic Magnetoresistance due to Purely Orbital Rearrangement in the Quadrupolar Heavy Fermion Superconductor PrV_{2}Al_{20}

We report the discovery of giant and anisotropic magnetoresistance due to the orbital rearrangement in a non magnetic correlated metal. In particular, we measured the magnetoresistance under fields up to 31.4 T in the cubic Pr-based heavy fermion superconductor PrV_{2}Al_{20} with a non magnetic Γ_{3} doublet ground state, exhibiting antiferroquadrupole ordering below 0.7 K. For the [100] direction, we find that the high-field phase appears between 12 and 25 T, accompanied by a large jump at 12 T in the magnetoresistance (ΔMR∼100%) and in the anisotropic magnetoresistivity ratio by ∼20%. These observations indicate that the strong hybridization between the conduction electrons and anisotropic quadrupole moments leads to the Fermi surface reconstruction upon crossing the field-induced antiferroquadrupole (orbital) rearrangement.

Spin-orbital entangled liquid state in the copper oxide Ba3CuSb2O9

Structure with orbital degeneracy is unstable toward spontaneous distortion. Such orbital correlation usually has a much higher energy scale than spins, and therefore, magnetic transition takes place at a much lower temperature, almost independently from orbital ordering. However, when the energy scales of orbitals and spins meet, there is a possibility of spin-orbital entanglement that would stabilize novel ground state such as spin-orbital liquid and random singlet state. Here we review on such a novel spin-orbital magnetism found in the hexagonal perovskite oxide Ba₃CuSb₂O₉, which hosts a self-organized honeycomblike short-range order of a strong Jahn-Teller ion Cu²⁺. Comprehensive structural and magnetic measurements have revealed that the system has neither magnetic nor Jahn-Teller transition down to the lowest temperatures, and Cu spins and orbitals retain the hexagonal symmetry and paramagnetic state. Various macroscopic and microscopic measurements all indicate that spins and orbitals remain fluctuating down to low temperatures without freezing, forming a spin-orbital entangled liquid state.

Spin-optotronic Properties of Organometal Halide Perovskites

Spin is an intrinsic quantum mechanical property of fundamental particles including the electron. The spin property is intimately related to electronic and optical properties of molecules and materials. The combination of spin (magnetic), electronic, and optical properties of materials, such as organometal halide perovskites (OMHP), has attracted increasing attention, which has led to a new field termed spin-optotronics based on all three key properties. This growing field has implications in emerging technological applications across disciplines, including photonics, electronics, spintronics, quantum computation, and information storage. This Perspective provides a brief introduction to this field from both experimental and computational aspects, with a focus on the effect of spin on charge carrier dynamics in OMHP, a class of materials with novel properties and promising applications in a number of fields. For instance, recent studies have demonstrated the use of ultrafast laser techniques in probing the fundamental charge carrier dynamics in relation to spin properties. Because of strong spin-orbit coupling (SOC) and broken inversion symmetry that result in Rashba and Dresselhaus effects, OMHP are considered ideal for manipulating spin states for spin-optotronics applications. In the meantime, on the basis of first-principles calculations and effective model Hamiltonians, the Rashba splitting in locally polarized domains can result in spin-forbidden recombination with significantly slow transition rate due to the mismatch of spin and momentum. We summarize the state-of-the-art first-principles methods and their current limitations for ultrafast charge and spin dynamics for realistic solid-state systems in general. To conclude, we note some promising future research and development directions for both experimental and theoretical ultrafast spin dynamics studies of OMHP.

Dynamical coupling of dilute magnetic impurities with quantum spin liquid state in the S = 3/2 dimer compound Ba3ZnRu2O9

We have investigated the dilute magnetic impurity effect on the magnetic properties of a quantum spin liquid candidate Ba₃ZnRu₂O₉ and a spin gapped compound Ba₃CaRu₂O₉. The magnetic ground state of each compound stands against 2% substitution of magnetic impurities for Zn or Ca. We have found that the magnetic response of these impurities, which behave as paramagnetic spins, depends on the host materials and the difference of the two manifests itself in the Weiss temperature, which can hardly be explained by the dilute magnetic impurities alone in the case of Ba₃ZnRu₂O₉. We consider a contribution from the Ru⁵⁺ ions which would appear only in the substituted Ba₃ZnRu₂O₉ and discuss a possible physical meaning of the observed Weiss temperature.

Emergent SU(4) Symmetry in α-ZrCl_{3} and Crystalline Spin-Orbital Liquids

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

Quantum Magnetic Properties in Perovskite with Anderson Localized Artificial Spin-1/2

Quantum magnetic properties in a geometrically frustrated lattice of spin-1/2 magnet, such as quantum spin liquid or solid and the associated spin fractionalization, are considered key in developing a new phase of matter. The feasibility of observing the quantum magnetic properties, usually found in geometrically frustrated lattice of spin-1/2 magnet, in a perovskite material with controlled disorder is demonstrated. It is found that the controlled chemical disorder, due to the chemical substitution of Ru ions by Co-ions, in a simple perovskite CaRuO3 creates a random prototype configuration of artificial spin-1/2 that forms dimer pairs between the nearest and further away ions. The localization of the Co impurity in the Ru matrix is analyzed using the Anderson localization formulation. The dimers of artificial spin-1/2, due to the localization of Co impurities, exhibit singlet-to-triplet excitation at low temperature without any ordered spin correlation. The localized gapped excitation evolves into a gapless quasi-continuum as dimer pairs break and create freely fluctuating fractionalized spins at high temperature. Together, these properties hint at a new quantum magnetic state with strong resemblance to the resonance valence bond system.

Quantum-disordered state of magnetic and electric dipoles in an organic Mott system

Strongly enhanced quantum fluctuations often lead to a rich variety of quantum-disordered states. Developing approaches to enhance quantum fluctuations may open paths to realize even more fascinating quantum states. Here, we demonstrate that a coupling of localized spins with the zero-point motion of hydrogen atoms, that is, proton fluctuations in a hydrogen-bonded organic Mott insulator provides a different class of quantum spin liquids (QSLs). We find that divergent dielectric behavior associated with the approach to hydrogen-bond order is suppressed by the quantum proton fluctuations, resulting in a quantum paraelectric (QPE) state. Furthermore, our thermal-transport measurements reveal that a QSL state with gapless spin excitations rapidly emerges upon entering the QPE state. These findings indicate that the quantum proton fluctuations give rise to a QSL—a quantum-disordered state of magnetic and electric dipoles—through the coupling between the electron and proton degrees of freedom.

The organic material κ-H₃(Cat-EDT-TTF)₂ has been suggested to exhibit a quantum spin liquid phase in which quantum fluctuations prevent the formation of magnetic order. Here, the authors show that this may be a result of fluctuations of hydrogen atoms, rather than more conventional geometric frustration.

Randomness-induced quantum spin liquid on honeycomb lattice

Quantum entanglement in magnetic materials is expected to yield a quantum spin liquid (QSL), in which strong quantum fluctuations prevent magnetic ordering even at zero temperature. This topic has been one of the primary focuses of condensed-matter science since Anderson first proposed the resonating valence bond state in a certain spin-1/2 frustrated magnet in 1973. Since then, several candidate materials featuring frustration, such as triangular and kagome lattices, have been reported to exhibit liquid-like behavior. However, the mechanisms that stabilize the liquid-like states have remained elusive. Here, we present a QSL state in a spin-1/2 honeycomb lattice with randomness in the exchange interaction. That is, we successfully introduce randomness into the organic radial-based complex and realize a random-singlet (RS) state (or valence bond glass). All magnetic and thermodynamic experimental results indicate the liquid-like behaviors, which are consistent with those expected in the RS state. Our results suggest that the randomness or inhomogeneity in the actual systems stabilize the RS state and yield liquid-like behavior.

Crystal structures, magnetic properties, and DFT calculation of B-site defected 12L-perovskites Ba2La2MW2O12 (M = Mn, Co, Ni, Zn)

The synthesis, crystal structures and magnetic properties of Ba₂La₂MW₂O₁₂ (M  =  Mn, Co, Ni, Zn) were investigated. They crystallize in the 12-layer polytype of the perovskite structure with a regular cation defect in the B-site. The results of neutron diffraction measurements reveal that they adopt a rhombohedral structure with a space group R  -  3 and have a cation ordering between Ba and La ions in the A-site. In these compounds, the magnetic M ions form the 2D triangular lattice. From the results of magnetic measurements, the ferromagnetic ordering of M²⁺ ions for M  =  Co (T _C  =  1.3 K) and Ni (6.2 K) and the paramagnetic behavior (T  >  1.8 K) with an antiferromagnetic interaction for M  =  Mn are observed. From the DFT calculation, their band structures and magnetic interactions are discussed.

Structure and interstitial iodide migration in hybrid perovskite methylammonium lead iodide

Hybrid perovskites form an emerging family of exceptional light harvesting compounds. However, the mechanism underpinning their photovoltaic effect is still far from understood, which is impeded by a lack of clarity on their structures. Here we show that iodide ions in the methylammonium lead iodide migrate via interstitial sites at temperatures above 280 K. This coincides with temperature dependent static distortions resulting in pseudocubic local symmetry. Based on bond distance analysis, the migrating and distorted iodines are at lengths consistent with the formation of I₂ molecules, suggesting a 2I⁻→I₂+2e⁻ redox couple. The actual formula of this compound is thus (CH₃NH₃)PbI_3−2x(I₂)_x where x∼0.007 at room temperature. A crucial feature of the tetragonal structure is that the methylammonium ions do not sit centrally in the A-site cavity, but disordered around two off-centre orientations that facilitate the interstitial ion migration via a gate opening mechanism.

The mechanism underpinning the photovoltaic effect in hybrid perovskite solar cells has remained unclear. Here, Green and co-workers suggest that iodide ions in methylammonium lead iodide perovskite migrate via interstitial sites and undergo a redox reaction to form molecular iodine and free electrons.

Thermal Hall Effect in a Phonon-Glass Ba_{3}CuSb_{2}O_{9}

A distinct thermal Hall signal is observed in a quantum spin liquid candidate Ba_{3}CuSb_{2}O_{9}. The transverse thermal conductivity shows a power-law temperature dependence below 50 K, where a spin gap opens. We suggest that because of the very low longitudinal thermal conductivity and the thermal Hall signals, a phonon Hall effect is induced by strong phonon scattering of orphan Cu^{2+} spins formed in the random domains of the Cu^{2+}-Sb^{5+} dumbbells in Ba_{3}CuSb_{2}O_{9}.

Spin glass behavior in frustrated quantum spin system CuAl2O4 with a possible orbital liquid state

CuAl₂O₄ is a normal spinel oxide having quantum spin, S  =  1/2 for Cu²⁺. It is a rather unique feature that the Cu²⁺ ions of CuAl₂O₄ sit at a tetrahedral position, not like the usual octahedral position for many oxides. At low temperatures, it exhibits all the thermodynamic evidence of a quantum spin glass. For example, the polycrystalline CuAl₂O₄ shows a cusp centered at ~2 K in the low-field dc magnetization data and a clear frequency dependence in the ac magnetic susceptibility while it displays logarithmic relaxation behavior in a time dependence of the magnetization. At the same time, there is a peak at ~2.3 K in the heat capacity, which shifts towards a higher temperature with magnetic fields. On the other hand, there is no evidence of new superlattice peaks in the high-resolution neutron powder diffraction data when cooled from 40 to 0.4 K. This implies that there is no long-ranged magnetic order down to 0.4 K, thus confirming a spin glass-like ground state for CuAl₂O₄. Interestingly, there is no sign of structural distortion either although Cu²⁺ is a Jahn-Teller active ion. Thus, we claim that an orbital liquid state is the most likely ground state in CuAl₂O₄. Of further interest, it also exhibits a large frustration parameter, f  =  |θ _CW/T _m| ~ 67, one of the largest values reported for spinel oxides. Our observations suggest that CuAl₂O₄ should be a rare example of a frustrated quantum spin glass with a good candidate for an orbital liquid state.

Orbital Dimer Model for the Spin-Glass State in Y_{2}Mo_{2}O_{7}

The formation of a spin glass generally requires that magnetic exchange interactions are both frustrated and disordered. Consequently, the origin of spin-glass behavior in Y_{2}Mo_{2}O_{7}-in which magnetic Mo^{4+} ions occupy a frustrated pyrochlore lattice with minimal compositional disorder-has been a longstanding question. Here, we use neutron and x-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously reported PDF, extended x-ray-absorption fine structure spectroscopy, and NMR studies, and provides a new and physical explanation of the exchange disorder responsible for spin-glass formation. We show that Mo^{4+} ions displace according to a local "two-in-two-out" rule on each Mo_{4} tetrahedron, driven by orbital dimerization of Jahn-Teller active Mo^{4+} ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O^{2-} displacements yield a distribution of Mo-O-Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.

Rearrangement of van der Waals stacking and formation of a singlet state at T = 90 K in a cluster magnet

A change of van der Waals stacking occurs spontaneously at 90 K in a cluster magnet.

Designing Quantum Spin-Orbital Liquids in Artificial Mott Insulators

Quantum spin-orbital liquids are elusive strongly correlated states of matter that emerge from quantum frustration between spin and orbital degrees of freedom. A promising route towards the observation of those states is the creation of artificial Mott insulators where antiferromagnetic correlations between spins and orbitals can be designed. We show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models. We exploit the property that massive Dirac fermions form mid-gap bound states with spin and valley degeneracies in the vicinity of a Coulomb impurity. Due to electronic repulsion, the antiferromagnetic correlations of the impurity lattice are driven by a super-exchange interaction with SU(4) symmetry, which emerges from the bound states degeneracy at quarter filling. We propose that quantum spin-orbital liquids can be engineered in artificially designed solid-state systems at vastly higher temperatures than achievable in optical lattices with cold atoms. We discuss the experimental setup and possible scenarios for candidate quantum spin-liquids in Coulomb impurity lattices of various geometries.

Topological Aspects of Symmetry Breaking in Triangular-Lattice Ising Antiferromagnets

Using a specially designed Monte Carlo algorithm with directed loops, we investigate the triangular lattice Ising antiferromagnet with coupling beyond the nearest neighbors. We show that the first-order transition from the stripe state to the paramagnet can be split, giving rise to an intermediate nematic phase in which algebraic correlations coexist with a broken symmetry. Furthermore, we demonstrate the emergence of several properties of a more topological nature such as fractional edge excitations in the stripe state, the proliferation of double domain walls in the nematic phase, and the Kasteleyn transition between them. Experimental implications are briefly discussed.

Disorder-Driven Spin-Orbital Liquid Behavior in the Ba3XSb2O9 Materials

Recent experiments on the Ba(3)XSb(2)O(9) family have revealed materials that potentially realize spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X(2+)-Sb(5+) dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, T(frz), at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba(3)CuSb(2)O(9). At T=T(frz) we find a complicated "branching" structure of superexchange-linked X(2+) clusters, which form a fractal pattern with fractal dimension d(f)=1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.

Absence of Jahn-Teller transition in the hexagonal Ba3CuSb2O9 single crystal

With decreasing temperature, liquids generally freeze into a solid state, losing entropy in the process. However, exceptions to this trend exist, such as quantum liquids, which may remain unfrozen down to absolute zero owing to strong quantum entanglement effects that stabilize a disordered state with zero entropy. Examples of such liquids include Bose-Einstein condensation of cold atoms, superconductivity, quantum Hall state of electron systems, and quantum spin liquid state in the frustrated magnets. Moreover, recent studies have clarified the possibility of another exotic quantum liquid state based on the spin-orbital entanglement in FeSc2S4. To confirm this exotic ground state, experiments based on single-crystalline samples are essential. However, no such single-crystal study has been reported to date. Here, we report, to our knowledge, the first single-crystal study on the spin-orbital liquid candidate, 6H-Ba3CuSb2O9, and we have confirmed the absence of an orbital frozen state. In strongly correlated electron systems, orbital ordering usually appears at high temperatures in a process accompanied by a lattice deformation, called a static Jahn-Teller distortion. By combining synchrotron X-ray diffraction, electron spin resonance, Raman spectroscopy, and ultrasound measurements, we find that the static Jahn-Teller distortion is absent in the present material, which indicates that orbital ordering is suppressed down to the lowest temperatures measured. We discuss how such an unusual feature is realized with the help of spin degree of freedom, leading to a spin-orbital entangled quantum liquid state.

Effect of divalent Ba cation substitution with Sr on coupled 'multiglass' state in the magnetoelectric multiferroic compound Ba3NbFe3Si2O14

(Ba/Sr)₃NbFe₃Si₂O₁₄ is a magneto-electric multiferroic with an incommensurate antiferromagnetic spiral magnetic structure which induces electric polarization at 26 K. Structural studies show that both the compounds have similar crystal structure down to 6 K. They exhibit a transition, T_N at 26 K and 25 K respectively, as indicated by heat capacity and magnetization, into an antiferromagnetic state. Although Ba and Sr are isovalent, they exhibit very different static and dynamic magnetic behaviors. The Ba-compound exhibits a glassy behavior with critical slowing dynamics with a freezing temperature of ~35 K and a critical exponent of 3.9, a value close to the 3-D Ising model above T_N, in addition to the invariant transition into an antiferromagnetic state. The Sr-compound however does not exhibit any dispersive behavior except for the invariant transition at T_N. The dielectric constant reflects magnetic behavior of the two compounds: the Ba-compound has two distinct dispersive peaks while the Sr-compound has a single dispersive peak. Thus the compounds exhibit coupled ‘multiglass’ behavior. The difference in magnetic properties between the two compounds is found to be due to modifications to super exchange path angle and length as well as anti-site defects which stabilize either ferromagnetic or antiferromagnetic interactions.

Multiferroic properties of hexagonal Ba3Ti2MnO9

Noncentrosymmetric hexagonal Ba₃Ti₂MnO₉ presents multiferroic behavior.

Evolution of ferromagnetism from a frustrated state in LixNi(2-x)O2 (0.67 < x < 0.98)

Two-dimensional triangular-lattice antiferromagnetic systems continue to be an interesting area in condensed matter physics and LiNiO2 is one such among them. Here we present a detailed experimental magnetic study of the quasi-stoichiometric LixNi2-xO2 system (0.67 < x < 0.98). It exhibits a variety of magnetic ground states-namely spin glass, cluster glass, re-entrant spin glass and ferromagnetic. This study deals with the magnetic properties of these four distinct ground states. The spin glass state is evidenced by the frequency-dependent peak shift as well as the time-dependent slow dynamics (magnetic relaxation, magnetic memory effect etc). By tuning the Li deficiency in a controlled manner, an increase in the ordering temperature is observed. Most strikingly, with the Li deficiency the nature of the magnetic ground state is changed from spin glass to ferromagnetic, with two intermediate states-namely cluster glass and re-entrant spin glass. The critical behaviour of the re-entrant spin glass is also studied here. The critical exponents (β, γ and δ) are extracted from the modified Arrot plot, Kouvel-Fisher method, and critical isotherm analysis. The critical exponents match with the long-range mean-field model. The values of the critical exponents are confirmed by the Widom scaling law: δ = 1 + γβ(-1). Furthermore, the universality class of the scaling relations is verified, where the scaled m and scaled h collapse into two branches. Finally, based on our observations, a phase diagram is constructed.

Emergent frustration in co-doped β-Mn

We investigate low-temperature spin correlations in the metallic frustrated magnet β-Mn1-xCox. Single-crystal polarized-neutron scattering experiments reveal the persistence of highly structured magnetic diffuse scattering and the absence of periodic magnetic order to T=0.05  K. We employ reverse Monte Carlo refinements and mean-field theory calculations to construct an effective Hamiltonian which accounts for the magnetic scattering. The interactions we identify describe an emergent spin structure which mimics the triangular lattice antiferromagnet, one of the canonical models of frustrated magnetism.

Noncollinear magnetic order stabilized by entangled spin-orbital fluctuations

Quantum phase transitions in the two-dimensional Kugel-Khomskii model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization Ansatz. When 3z(2)-r(2) orbitals are favored by the crystal field and Hund's exchange is finite, both methods give a noncollinear exotic magnetic order that consists of four sublattices with mutually orthogonal nearest-neighbor and antiferromagnetic second-neighbor spins. We derive an effective frustrated spin model with second- and third-neighbor spin interactions which stabilize this phase and follow from spin-orbital quantum fluctuations involving spin singlets entangled with orbital excitations.

Singlet ground state of the quantum antiferromagnet Ba(3)CuSb(2)O(9)

We present local probe results on the honeycomb lattice antiferromagnet Ba(3)CuSb(2)O(9). Muon spin relaxation measurements in a zero field down to 20 mK show unequivocally that there is a total absence of spin freezing in the ground state. Sb NMR measurements allow us to track the intrinsic susceptibility of the lattice, which shows a maximum at around 55 K and drops to zero in the low-temperature limit. The spin-lattice relaxation rate shows two characteristic energy scales, including a field-dependent crossover to exponential low-temperature behavior, implying gapped magnetic excitations.

Physics. The impact of ionic frustration on electronic order

The frustrated ordering of dipoles created by copper and antimony ions in an oxide material may help to create an exotic quantum electronic state.