Magnetic Frustration Research Articles

Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

Quantum electrodynamics in 2+1 dimensions (QED3) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated J1−J2 Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED3, in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of QED3, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by QED3. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to N=48 sites. Published by the American Physical Society 2024

J_{eff}=1/2 Hyperoctagon Lattice in Cobalt Oxalate Metal-Organic Framework.

We report the magnetic properties of a cobalt oxalate metal-organic framework featuring the hyperoctagon lattice. Our thermodynamic measurements reveal the J_{eff}=1/2 state of the high-spin Co^{2+} (3d^{7}) ion and the two successive magnetic transitions at zero field with two-stage entropy release. ^{13}C-NMR measurements reveal the absence of an internal magnetic field in the intermediate temperature phase. Multiple field-induced phases are observed before full saturation at around 40T. We argue the unique cobalt oxalate network gives rise to the Kitaev interaction and/or a bond frustration effect, providing an unconventional platform for frustrated magnetism on the hyperoctagon lattice.

Frustrated Extended Bose-Hubbard Model and Deconfined Quantum Critical Points with Optical Lattices at the Antimagic Wavelength.

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.

Excitonic instability towards a Potts-nematic quantum paramagnet

Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we focus on frustrated quantum magnets and study the nature of the quantum phase transition between a paramagnet and a magnetically ordered state with broken threefold (Z3) crystal rotation symmetry. We show that the transition can occur in two stages, giving rise to an intermediate nematic phase in which rotation symmetry is broken but the system remains magnetically disordered. Since the nematic transition is described by the three-state Potts model, the intermediate phase is a Z3 Potts-nematic phase. Our prediction of the existence of a Potts-nematic phase is based on an analysis of bound states formed from two-magnon excitations in the paramagnet, which become gapless while single-magnon excitations remain gapped. By considering three different lattice models, we demonstrate a generic instability towards two-magnon bound state formation in the Potts-nematic channel. We present both numerical results and a general analytical perturbative formula for the bound state binding energy similar to BCS theory. We further discuss a number of different materials that realize key features of the model considered, and thus provide promising venues for possible experimental observation. Published by the American Physical Society 2024

Reticular liquid crystal design: Controlling complex self-assembly of p-terphenyl rods by side-chain engineering and chirality

A series of K-shaped bolapolyphiles, consisting of a p-terphenyl core, two polar glycerol end-groups and a swallow-tailed alkyl side-chain were synthesized and investigated. By increasing the side-chain volume an astonishing variety of very different liquid crystalline (LC) phases was observed, ranging from a rectangular (Colrec/c2mm) and a square honeycomb (Colsqu/p4mm) via a highly complex zeolite-like octagon/pentagon honeycomb filled with additional strings of rod-bundles (ColrecZ/c2mm), a new 3D-hexagonal (R3‾c) double network phase, a double and even a single network cubic phase (double gyroid Cub/Ia3‾d and single diamond Cub/Fd3‾m, respectively) to a correlated lamellar phase (LamSm/c2mm). Though these LC structures are highly complex and there is a delicate balance of steric and geometric frustration determining the phase formation, there is only a small effect of permanent molecular chirality in the glycerol groups ((R,R)-configuration) on them, which is attributed to a slightly different packing density of uniformly chiral and racemic glycerols, but not to an effect of induced helicity. Compared to related T-shaped bolapolyphiles with a single linear n-alkyl side-chain, which form exclusively honeycomb phases, the complexity of self-assembly is enhanced for the K-shaped compounds due to a competition between the requirements of space filling, chain stretching and geometric frustration, and affected by the shape of the polar glycerol domains at the junctions.

Entropic sampling in frustrated magnets: Role of self-intersecting spaces

Entropic sampling in frustrated magnets: Role of self-intersecting spaces

Influence of Mn and Ni ions doping on the magnetization and dielectric properties of the CaBaCo4O7 compound

We reported the magnetic and dielectric properties of the polar magnet CaBaCo4-xMnxO7 and CaBaCo4-xNixO7 (x = 0.04, 0.08). The result shows that Mn ions exist in the sample in + 2 and + 3 valence, replacing both Co2+ and Co3+, and the Ni ions exist in + 2 valence, only replacing Co2+. Mn ion doping does not change the ratio of Co2+ to Co3+ in the crystal, leading to similar magnetic behavior to CaBaCo4O7. Ni ions increase the relative content of Co3+, which has a greater damage to the ferromagnetic interaction. Meanwhile, Mn-doping can partially release the magnetic frustration and cause the spin freezing temperature shifting to high temperature. It also slightly weakened the FIM interaction in the sample. While Ni-doping enhances the antiferromagnetic interaction and induces an additional antiferromagnetic phase at 82 K in the sample. The dielectric behavior of all samples is obviously abnormal at magnetic phase transitions, which proves the magnetodielectric effect of the samples. After Mn and Ni ions doping, the magnetodielectric properties of the samples are improved. Compared with Mn ions, Ni ions have a greater effect on the dielectric properties of CaBaCo4O7.

Modulation of skyrmion helicity by competition between Dzyaloshinskii-Moriya interaction and magnetic frustration

Modulation of skyrmion helicity by competition between Dzyaloshinskii-Moriya interaction and magnetic frustration

Kitaev-Heisenberg model on the star lattice: From chiral Majorana fermions to chiral triplons

The interplay of frustrated interactions and lattice geometry can lead to a variety of exotic quantum phases. Here we unearth a particularly rich phase diagram of the Kitaev-Heisenberg model on the star lattice, a triangle decorated honeycomb lattice breaking sublattice symmetry. In the antiferromagnetic regime, the interplay of Heisenberg coupling and geometric frustration leads to the formation of valence bond solid (VBS) phases—a singlet VBS and a bond selective triplet VBS stabilized by the Kitaev exchange. We show that the ratio of the Kitaev versus Heisenberg exchange tunes between these VBS phases and chiral quantum spin-liquid regimes. Remarkably, the VBS phases host a whole variety of chiral triplon excitations with high Chern numbers in the presence of a weak magnetic field. We discuss our results in light of a recently synthesized star lattice material and other decorated lattice systems. Published by the American Physical Society 2024

Proximity effect of emergent field from spin ice in an oxide heterostructure.

Geometrical frustration endows magnets with degenerate ground states, resulting in exotic spin structures and quantum phenomena. Such magnets, called quantum magnets, can display non-coplanar spin textures and be a viable platform for the topological Hall effect driven by "emergent field." However, most quantum magnets are insulators, making it challenging to electrically detect associated fluctuations and excitations. Here, we probe magnetic transitions in the spin ice insulator Dy2Ti2O7, a prototypical quantum magnet, as emergent magnetotransport phenomena at the heterointerface with the nonmagnetic metal Bi2Rh2O7. Angle-dependent longitudinal resistivity exhibits peaks at the magnetic phase boundaries of spin ice due to domain boundary scattering. In addition, the anomalous Hall resistivity undergoes a sign change with the magnetic transition in Dy2Ti2O7, reflecting the inversion of the emergent field. These findings, on the basis of epitaxial techniques, connect the fundamental research on insulating quantum magnets to their potential electronic applications, possibly leading to transformative innovations in quantum technologies.

Flat-band hybridization between f and d states near the Fermi energy of SmCoIn5

We present high-quality angle-resolved photoemission (ARPES) and density functional theory calculations (DFT+U) of SmCoIn5. We find broad agreement with previously published studies of LaCoIn5 and CeCoIn51,2, confirming that the Sm 4f electrons are mostly localized. Nevertheless, our model is consistent with an additional delocalized Sm component, stemming from hybridization between the 4f electrons and the metallic bands at “hot spot” positions in the Brillouin zone. The dominant hot spot, called γZ, is similar to a source of delocalized f states found in previous experimental and theoretical studies of CeCoIn51,3. In this work, we identify and focus on the role of the Co d states in exploring the relationship between heavy quasiparticles and the magnetic interactions in SmCoIn5, which lead to a magnetically ordered ground state from within an intermediate valence scenario4–6. Specifically, we find a globally flat band consisting of Co d states near E = − 0.7 eV, indicating the possibility of enhanced electronic and magnetic interactions in the “115” family of materials through localization in the Co layer, and we discuss a possible origin in geometric frustration. We also show that the delocalized Sm 4f states can hybridize directly with the Co 3dxz/3dyz orbitals, which occurs in our model at the Brillouin zone boundary point R in a band that is locally flat and touches the Fermi level from above. Our work identifies microscopic ingredients for additional magnetic interactions in the “115” materials beyond the RKKY mechanism, and strongly suggests that the Co d bands are an important ingredient in the formation of both magnetic and superconducting ground states.

Understanding Antiferromagnetic Coupling in Lead-Free Halide Double Perovskite Semiconductors.

Solution-processable semiconductors with antiferromagnetic (AFM) order are attractive for future spintronics and information storage technology. Halide perovskites containing magnetic ions have emerged as multifunctional materials, demonstrating a cross-link between structural, optical, electrical, and magnetic properties. However, stable optoelectronic halide perovskites that are antiferromagnetic remain sparse, and the critical design rules to optimize magnetic coupling still must be developed. Here, we combine the complementary magnetometry and electron-spin-resonance experiments, together with first-principles calculations to study the antiferromagnetic coupling in stable Cs2(Ag:Na)FeCl6 bulk semiconductor alloys grown by the hydrothermal method. We show the importance of nonmagnetic monovalence ions at the BI site (Na/Ag) in facilitating the superexchange interaction via orbital hybridization, offering the tunability of the Curie-Weiss parameters between -27 and -210 K, with a potential to promote magnetic frustration via alloying the nonmagnetic BI site (Ag:Na ratio). Combining our experimental evidence with first-principles calculations, we draw a cohesive picture of the material design for B-site-ordered antiferromagnetic halide double perovskites.

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration.

Shape morphing in bistable kirigami enables remarkable functionalities appealing to a diverse range of applications across the spectrum of length scale. At the core of their shape shifting lies the architecture of their repeating unit, where highly deformable slits and quasi-rigid rotating units often exhibit multiple symmetries that confer isotropic deployment obeying uniform scaling transformation. In this work, symmetry breaking in bistable kirigami is investigated to access geometric frustration and anisotropic morphing, enabling arbitrarily scaled deployment in planar and spatial bistable domains. With an analysis on their symmetry properties complemented by a systematic investigation integrating semi-analytical derivations, numerical simulations, and experiments on elastic kirigami sheets, this work unveils the fundamental relations between slit symmetry, geometric frustration, and anisotropic bistable deployment. Furthermore, asymmetric kirigami units are leveraged in planar and flat-to-3D demonstrations to showcase the pivotal role of shear deformation in achieving target shapes and functions so far unattainable with uniformly stretchable kirigami. The insights provided in this work unveil the role of slit symmetry breaking in controlling the anisotropic bistable deployment of soft kirigami metamaterials, enriching the range of achievable functionalities for applications spanning deployable space structures, wearable technologies, and soft machines.

Structural and magnetic studies of the frustrated S = 1 kagome magnet NH4Ni2Mo2O10H3

The strong geometric frustration of the kagome antiferromagnets (KAFMs) can destabilise conventional magnetic order and lead to exotic electronic states, such as the quantum spin-liquid state observed in some S=12 KAFM materials. However, the ground state of S = 1 KAFM systems are less well understood. Spin nematic phases and valence bond solid ground states have been predicted to form but a paucity of experimental realisations restricts understanding. Here, the S = 1 KAFM NH4Ni2Mo2O10H3 is presented, which has the 3-fold symmetry of the kagome lattice but significant site depletion, with ∼64% site occupancy. Frustration and a competition between exchange interactions are evidenced through the suppression of order below the Weiss temperature |θW| and observation of ferromagnetic and antiferromagnetic characteristics in the magnetisation data. A semi spin glass ground state is predicted based on the ac-field frequency dependence of the magnetic transition and ferromagnetic signal.

The dilute 3D and three site dimer Heisenberg antiferromagnet: review of some magnetic properties.

Many properties of the spin–½ kagome Heisenberg antiferromagnet remains controversial and receiving continuous attention from theorists and experimentalists due to their fascinating magnetic properties and high heterogeneity coax by the geometrical frustration. In this research we seek and compare the results obtained in our recent article [1] with that of Napel[2] where we elucidate some of the identified magnetic behaviour using the spin–½ Heisenbeg model with the application of Exact Diagonalization and classical Monte-Carlo simulation on three site dimer and 3D simple cubic lattice simulation. The results obtained shows excellent agreement in both papers reviewed with [1] establishing firmly the FM to AFM transition, having a clear transition point referred to mixed phased [2].

Superconductivity in a Layered Cobalt Oxychalcogenide Na2CoSe2O with a Triangular Lattice.

Unconventional superconductivity in bulk materials under ambient pressure is extremely rare among the 3d transition metal compounds outside the layered cuprates and iron-based family. It is predominantly linked to highly anisotropic electronic properties and quasi-two-dimensional (2D) Fermi surfaces. To date, the only known example of a Co-based exotic superconductor is the hydrated layered cobaltate, NaxCoO2·yH2O, and its superconductivity is realized in the vicinity of a spin-1/2 Mott state. However, the nature of the superconductivity in these materials is still a subject of intense debate, and therefore, finding a new class of superconductors will help unravel the mysteries of their unconventional superconductivity. Here, we report the discovery of superconductivity at ∼6.3 K in our newly synthesized layered compound Na2CoSe2O, in which the edge-shared CoSe6 octahedra form [CoSe2] layers with a perfect triangular lattice of Co ions. It is the first 3d transition metal oxychalcogenide superconductor with distinct structural and chemical characteristics. Despite its relatively low TC, this material exhibits very high superconducting upper critical fields, μ0HC2(0), which far exceeds the Pauli paramagnetic limit by a factor of 3-4. First-principles calculations show that Na2CoSe2O is a rare example of a negative charge transfer superconductor. This cobalt oxychalcogenide with a geometrical frustration among Co spins shows great potential as a highly appealing candidate for the realization of unconventional and/or high-TC superconductivity beyond the well-established Cu- and Fe-based superconductor families and opens a new field in the physics and chemistry of low-dimensional superconductors.

From flocking to glassiness in dense disordered polar active matter

AbstractLiving materials such as biological tissues or bacterial colonies are collections of heterogeneous entities of different sizes, capable of autonomous motion, and often capable of cooperating. Such a degree of complexity brings to collective motion on large scales. However, how the competition between geometrical frustration, autonomous motion, and the tendency to move cooperatively impact large-scale behavior remains an open question. We implement those three ingredients in a model of active matter and show that the system, in forming migratory patterns, can arrange in bands or develop long-range order, depending on the density of the system. We also show that the active material undergoes a reentrant glass transition triggered by the alignment interaction that typically causes only collective migratory motion. Finally, we observe that polar order destroys active phase separation, producing homogeneous, disordered moving configurations.

Magnetic properties and cryogenic magnetocaloric effect of pyrochlore structure RE2Ti2O7 (RE = Gd, Tb, and Ho) compounds

Magnetic refrigeration technology is regarded as one of the ideal solutions for cryogenic refrigeration, while magnetocaloric materials are the crucial ones. A series of polycrystalline RE2Ti2O7 (RE = Gd, Tb, and Ho) compounds were prepared by a simple one-step solid-phase reaction method in the atmosphere. The crystal structure, magnetic properties, and magnetocaloric effect (MCE) of these compounds were systematically investigated. Crystallographic research indicates that these compounds crystallized in a pyrochlore structure. Meanwhile, magnetic measurements illustrate that this class of pyrochlore oxides is highly frustrated magnetic materials and exhibits complex magnetic behavior. In addition, under the field change of 0–1 T, the values of the maximum magnetic entropy change (−ΔSMmax) and the refrigeration capacity are calculated to be 0.9 and 5.8 J/kg for Gd2Ti2O7, 9.0 and 32.9 J/kg for Tb2Ti2O7, 9.9 and 29.9 J/kg for Ho2Ti2O7, respectively. Therefore, RE2Ti2O7 (RE = Tb and Ho) pyrochlores exhibit excellent MCEs under low magnetic fields, providing candidate materials for the application of cryogenic magnetic refrigeration technology.

Intertwining of Localized (d) and Delocalized (π) Spins in Magnetically Frustrated Two-Dimensional Metal-Organic Frameworks.

Two-dimensional metal-organic frameworks (2D MOFs) are emerging as a new class of multifunctional materials for diversified applications, although magnetic properties have not been widely explored. The metal ions and organic ligands in some of the 2D MOFs are arranged in the well-known Kagome lattice, leading to geometric spin frustration. Hence, such systems could be the potential candidates to exhibit an exotic quantum spin liquid (QSL) state, as was observed in Cu3(HHTP)2 (HHTP = hexahydroxytriphenylene), with no magnetic transition down to 38 mK. Hereto, we have investigated the spin intertwining in a bimetallic 2D MOF system, M3(HHTP)2 (M = Cu/Zn), arising from the localized (d-electron) and delocalized (π-electron) S = 1/2 spins from the Cu(II) ions and the HHTP radicals, respectively. The origin of the spin frustration (down to 5K) was critically examined by varying the metal composition in bimetallic systems, CuxZn3-x(HHTP)2 (x = 1, 1.5, 2), containing both S = 1/2 and S = 0 spins. Additionally, to gain a deeper understanding, we studied the spin interaction in the pristine Zn3(HHTP)2 system containing only S = 0 Zn(II) ions. In view of the quantitative estimate of the localized and delocalized spins, the d-π spin correlation appears essential in understanding the unusual magnetic and/or other physical properties of such hybrid organic-inorganic 2D crystalline solids.

Coexistence of Long-Range Magnetic Order and Magnetic Frustration of a Novel Two-Dimensional S = 1/2 Structure: Na2Cu3(SeO3)4

Novel quantum materials offer the opportunity to expand next-generation computers, high-precision sensors, and new energy technologies. Among the most important factors influencing the development of quantum materials research is the ability of inorganic and materials chemists to grow high-quality single crystals. Here, the synthesis, structure characterization and magnetic properties of Na2Cu3(SeO3)4 are reported. It exhibits a novel two-dimensional (2D) structure with isolated layers of Cu nets. Single crystals of Na2Cu3(SeO3)4 were grown using a low-temperature hydrothermal method. Single-crystal X-ray diffraction reveals that Na2Cu3(SeO3)4 crystallizes in the monoclinic crystal system and has space group symmetry of P21/n (No.14) with a unit cell of a = 8.1704(4) Å, b = 5.1659(2) Å, c = 14.7406(6) Å, β = 100.86(2), V = 611.01(5) Å3 and Z = 2. Na2Cu3(SeO3)4 comprises a 2D Cu-O-Cu lattice containing two unique copper sites, a CuO6 octahedra and a CuO5 square pyramid. The SeO3 groups bridge the 2D Cu-O-Cu layers isolating the neighboring Cu-O-Cu layers, thereby enhancing their 2D nature. Magnetic properties were determined by measuring the magnetic susceptibility of an array of randomly oriented single crystals of Na2Cu3(SeO3)4. The temperature-dependent magnetic measurement shows an antiferromagnetic transition at TN = 4 K. These results suggest the fruitfulness of hydrothermal synthesis in achieving novel quantum materials and encourage future work on the chemistry of transition metal selenite.