Magnetic Frustration Research Articles

Pairing phase favored by magnetic frustration

Abstract The interplay between magnetic frustration and pairing is investigated by adopting a BCS-like pairing mechanism on the frustrated $J_1-J_2$ Ising model on the square lattice. The ground-state and thermal phase transitions of the model are analyzed using a fermionic formulation within a cluster mean-field method. In this approach, the lattice system is divided into identical clusters, where the intracluster dynamic is exactly solved, and the intercluster interactions are replaced by self-consistent mean fields. We introduce a framework with two pairing couplings: an intracluster local coupling, $g$, which controls the electron pairing and its mobility within the clusters, and an intercluster coupling, $g'$, which adjusts the pairing mechanism between clusters. Tuning $g'/g$ allows evaluating how the pairing phase evolves from a weak pairing coupling between clusters (clustered system) to a strong one ($g' \rightarrow g$, homogeneous system). In the range $0 \le g'/g \le 1$, we find that a gradual increase in $g'/g$ favors the pairing phase and induces a change in criticality. In particular, our results reveal the presence of tricriticality for a certain range of $g'/g$. In addition, an increase in competing magnetic interactions weakens the magnetic orders, causing the pairing phase to occur at lower strengths of pairing interactions, especially when $g' = g$. Therefore, our findings support that magnetic frustration favors the pairing phase, contributing to the onset of a superconducting state.

Origin of correlated diffuse scattering in the hexagonal manganites

We use a combination of first-principles density-functional calculations and spin-dynamics simulations to explain the unusual diffuse inelastic neutron scattering in the hexagonal multiferroic yttrium manganite, YMnO3. Using symmetry considerations, we construct a model spin Hamiltonian with parameters derived from our density-functional calculations and show that it captures the measured behavior. We then show that the observed directionality in the structured diffuse scattering in momentum space is a hallmark of the triangular geometry, and that its persistence across a wide range of temperatures, both above and below the Néel temperature TN, is a result of the strong magnetic frustration. We predict that this diffuse scattering exists in a yet-to-be-observed modulated continuum of energies, that its associated spin excitations have distinct in-plane and out-of-plane character, and that vestiges of the magnetic frustration persist into the sub−TN state. Finally, we show that visualizing the magnetic order in terms of composite trimer magnetoelectric monopoles and toroidal moments, rather than individual spins, provides insight into the real-space fluctuations, revealing clusters of emerging order in the paramagnetic state, as well as collective short-range excitations in the ordered antiferromagnetic phase. Our understanding of this directional diffuse scattering in such a wide temperature range, both below and above TN, provides new insight into the magnetic phase transitions in classical frustrated systems. Published by the American Physical Society 2024

New three-dimensional flat band candidate materials Pb2As2O7 and Pb2Sn2O7

Energy dispersion of electrons is the most fundamental property of the solid state physics. In models of electrons on a lattice with strong geometric frustration, the band dispersion of electrons can disappear due to the quantum destructive interference of the wavefunction. This is called a flat band, and it is known to be the stage for the emergence of various fascinating physical properties. It is a challenging task to realize this flat band in a real material. 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These findings underscore the importance of investigating the influence of flat bands on electronic energy dispersion, providing a crucial step toward understanding the emergence and characteristics of flat bands in novel materials.

Geometric Frustration Directs the Self-assembly of Nanoparticles with Crystallized Ligand Bundles.

Polymer-grafted nanoparticles are versatile building blocks that self-assemble into a diverse range of mesostructures. Coarse-grained molecular simulations have commonly accompanied experiments by resolving structure formation pathways and predicting phase behavior. Past simulations represented nanoparticles as spheres and the ligands as flexible chains of beads, isotropically tethered to the nanoparticles. Here, we investigate a different minimal coarse-grained model. The model consists of an attractive rod tethered to a repulsive sphere. The motivation of this rod-sphere model is to describe nanospheres with a partially crystallized, stretched polymeric bundle as well as other complex building blocks such as rigid surfactants and end-tethered nanorods. Varying the ratio of sphere size to rod radius stabilizes self-limited clusters and other mesostructures with reduced dimensionality. The complex phase behavior we observe is a consequence of geometric frustration.

Unusual spin dynamics in the van der Waals antiferromagnet FeGa2S4

Spin dynamics in the van der Waals antiferromagnet FeGa2S4with triangular lattices are investigated using magnetometry, neutron scattering, and muon spin relaxation measurements. The characteristic spin relaxation time is thoroughly clarified over thirteen orders of magnitude. Although the temperature dependence of DC and AC susceptibilities recalls a conventional spin-glass transition, nonlinear susceptibilities showing no divergences at the anomalous temperature,T∗=16.87(7) K, deny that and instead hint at other mechanisms. Elastic neutron scattering together with previously measured muon results depict a slowly fluctuated (∼10-5 s) spin state aboveT∗. In juxtaposing the underlying simplest structure among frustrated magnets with an intricate hierarchy of time scales, FeGa2S4can be a playground for studying temporal spin correlations in the two-dimensional limit.

Mitigating the Kinetic Hysteresis of Co-Free Ni-Rich Cathodes via Gradient Penetration of Nonmagnetic Silicon.

Co-free Ni-rich layered oxides are considered a promising cathode material for next-generation Li-ion batteries due to their cost-effectiveness and high capacity. However, they still suffer from the practical challenges of low discharge capacity and poor rate capability due to the hysteresis of Li-ion diffusion kinetics. Herein, based on the regulation of the lattice magnetic frustration, the Li/Ni intermixing defects as the primary origin of kinetic hysteresis are radically addressed via the doping of the nonmagnetic Si element. Meanwhile, by adopting gradient penetration doping, a robust Si-O surface structure with reversible lattice oxygen evolution and low lattice strain is constructed on Co-free Ni-rich cathodes to suppress the formation of surface dense barrier layer. With the remarkably enhanced Li-ion diffusion kinetics in atomic and electrode particle scales, the as-obtained cathodes (LiNixMn1-xSi0.01O2, 0.6≤x≤0.9) achieve superior performance in discharge capacity, rate capability, and durability. This work highlights the coupling effect of magnetic structure and interfacial chemicals on Li-ion transport properties, and the concept will inspire more researchers to conduct an intensive study.

Mitigating the Kinetic Hysteresis of Co‐Free Ni‐Rich Cathodes via Gradient Penetration of Nonmagnetic Silicon

AbstractCo‐free Ni‐rich layered oxides are considered a promising cathode material for next‐generation Li‐ion batteries due to their cost‐effectiveness and high capacity. However, they still suffer from the practical challenges of low discharge capacity and poor rate capability due to the hysteresis of Li‐ion diffusion kinetics. Herein, based on the regulation of the lattice magnetic frustration, the Li/Ni intermixing defects as the primary origin of kinetic hysteresis are radically addressed via the doping of the nonmagnetic Si element. Meanwhile, by adopting gradient penetration doping, a robust Si−O surface structure with reversible lattice oxygen evolution and low lattice strain is constructed on Co‐free Ni‐rich cathodes to suppress the formation of surface dense barrier layer. With the remarkably enhanced Li‐ion diffusion kinetics in atomic and electrode particle scales, the as‐obtained cathodes (LiNixMn1−xSi0.01O2, 0.6≤x≤0.9) achieve superior performance in discharge capacity, rate capability, and durability. This work highlights the coupling effect of magnetic structure and interfacial chemicals on Li‐ion transport properties, and the concept will inspire more researchers to conduct an intensive study.

A Frustrated Antipolar Phase Analogous to Classical Spin Liquids.

The study of magnetic frustration in classical spin systems is motivated by the prediction and discovery of classical spin liquid states. These uncommon magnetic phases are characterized by a massive degeneracy of their ground state implying a finite magnetic entropy at zero temperature. While the classical spin liquid state is originally predicted in the Ising triangular lattice antiferromagnet in 1950, this state has never been experimentally observed in any triangular magnets. The discovery of an electric analogue of classical spin liquids on a triangular lattice of uniaxial electric dipoles in EuAl12O19 is reported here. This new type of frustrated antipolar phase is characterized by a highly-degenerate state at low temperature implying an absence of long-range antiferroelectric order, despite short-range antipolar correlations. Its dynamics are governed by a thermally activated process, slowing down upon cooling toward a complete freezing at zerotemperature.

Rare-Earth Chalcogenides: An Inspiring Playground For Exploring Frustrated Magnetism

Abstract The rare-earth chalcogenide $ARECh_{2}$ family ($A =$ alkali metal or monovalent ions, $RE =$ rare earth, $Ch =$ chalcogen) has emerged as a paradigmatic platform for studying frustrated magnetism on a triangular lattice. The family members exhibit a variety of ground states, from quantum spin liquid to exotic ordered phases, providing fascinating insight into quantum magnetism. Their simple crystal structure and chemical tunability enable systematic exploration of competing interactions in quantum magnets. Recent neutron scattering and thermodynamic studies have revealed rich phase diagrams and unusual excitations, refining theoretical models of frustrated systems. This review provides a succinct introduction to $ARECh_{2}$ research. It summarizes key findings on crystal structures, single-ion physics, magnetic Hamiltonians, ground states, and low-energy excitations. By highlighting current developments and open questions, we aim to catalyze further exploration and deeper physical understanding on this frontier of quantum magnetism.

Structure and properties of mixed valent CeFe2Al8

Temperature dependent magnetic, electrical transport and thermal properties of polycrystalline orthorhombic CeFe2Al8intermetallic compound have been studied along with its isostructural La counterpart, LaFe2Al8. For the cerium compound, low fielddcmagnetization exhibits an antiferromagnetic like ordering (TN) ∼ 4 K. The main feature of the magnetic susceptibility plot is a broad hump spanning a large temperature range, indicating mixed valence of Ce in the compound, in good agreement with reported literature. However, contrary to the reported observations we find that the mixed valence state is very robust and was evident even up to very high magnetic fields (> 2 T). Further, in this work we report 3d core level photoemission spectra of cerium in CeFe2Al8, to understand the valence state of cerium ions in this system. Additionally, from resistivity measurements it is found that, CeFe2Al8is metallic with no indication of any anomaly, till the lowest temperature of measurement. Specific heat measurements show very low value of heat capacity and electronic contribution. The isostructural La analogue, LaFe2Al8compound shows broadness in susceptibility with maxima around 44 K which may be attributed to ordering of Fe moments. The comparison of Ce and La compounds brings out the role of Fe magnetic moments which may be responsible for competing with cerium moments and resulting in the dilution of long-range magnetic order, also contributing to magnetic frustration in CeFe2Al8.

Nearly linear orbital molecules on a pyrochlore lattice.

The interplay of spin-orbit coupling with other relevant parameters gives rise to the rich phase competition in complex ruthenates featuring octahedrally coordinated Ru4+. While locally, spin-orbit coupling stabilizes a nonmagnetic Jeff = 0 state, intersite interactions resolve one of two distinct phases at low temperatures: an excitonic magnet stabilized by the magnetic exchange of upper-lying Jeff = 1 states or Ru2 molecular orbital dimers driven by direct orbital overlap. Pyrochlore ruthenates A2Ru2O7 (A = rare earth, Y) are candidate excitonic magnets with geometrical frustration. We synthesized In2Ru2O7 with covalent In─O bonds. This pyrochlore ruthenate hosts a local Jeff = 0 state at high temperatures; however, at low temperatures, it forms a unique nonmagnetic ground state with nearly linear Ru─O─Ru molecules, in stark contrast to other A2Ru2O7 compounds. The disproportionation of covalent In─O bonds drives Ru2O molecule formation, quenching not only the local spin-orbit singlet but also geometrical frustration.

Polar domain walls induced by sequential symmetry breaking in frustrated mechanical metamaterials

Frustration hinders ideal local interactions in systems ranging from artificial spin ices with ice rules to mechanical metamaterials featuring regular floppy modes. While geometric frustrations have been known to promote complex ordered patterns in tessellated lattice structures, there is growing interest in global frustrations due to the topologically nontrivial geometry of metamaterials. However, multiferroic orders in globally frustrated metamaterials have remained elusive. Here, we present polar domain walls constrained in flexible mechanical metamaterials with global frustration and sequential symmetry breaking. We showcase that under simple compressive loading, competing interactions in globally frustrated metamaterials give rise to mixed deformations with high-order buckling modes described by an emergent order parameter. Utilizing an elastic mechanism model, we unveil the process of sequential symmetry breaking and capture the formation of polar domain walls exhibiting a chiral distribution within a multi-well potential landscape. We further demonstrate how to eliminate frustration through torsional loading, leading to symmetry restoration. These results provide insights into the intricate interactions between order and frustration, inspiring the modulation of domain walls in macroscopic systems.

Spin dynamics and Phonons of the Chromites CoCr2O4 and MnCr2O4

Abstract Due to the geometric magnetic frustration inherent to their lattice and the resulting complex magnetic states, the spinel compounds are of great interest in both fundamental and application-oriented perspectives. Here, we applied x-ray diffraction, magnetization, heat capacity and powder inelastic neutron scattering measurements, along with theoretical calculations, to study the exotic properties of chromite-spinel oxides, CoCr2O4 and MnCr2O4. The temperature dependence of the phonon spectra provides an insight into the correlation between oxygen motion and the magnetic order, as well as the magnetoelectric effect in the ground state of MnCr2O4. Moreover, spinwave excitations in CoCr2O4 and MnCr2O4 are compared with Heisenberg model calculations. This approach enables the precise determination of exchange energies and offers a comprehensive understanding of the spin dynamics and relevant exchange interactions in complicated spiral spin ordering.

Chemical Design of Spin Frustration to Realize Topological Spin Glasses.

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal-organic framework (MOF) platform, Ni3(pymca)3X3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni2+-based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin-spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Structural, magnetic, and magnetocaloric characterizations of geometrically-frustrated SrRE2O4 (RE = Gd, Dy, Ho, Er) oxides for low-temperature cooling applications

The magnetocaloric (MC) properties of many rare earth (RE)-based magnetic solids have been intensively investigated. This research aims to develop suitable MC materials for low-temperature cooling application and to better elucidate their intrinsic properties. We have fabricated four single-phase SrRE2O4 (RE = Gd, Dy, Ho, Er) oxides and conducted a systematic experimental investigation into their structural, magnetic, and low-temperature MC properties. All these SrRE2O4 oxides crystallize in an orthorhombic structure (space group Pnma) and exhibit typical geometrical frustration. This frustration arises from the one-dimensional RE ion zigzag ladders along the c-axis, which link the two-dimensional honeycomb lattice in the ab plane. The elements in SrRE2O4 oxides are uniformly distributed and present with valence states of Sr2+, RE3+, and O2−, respectively. Large low-temperature MC effects and notable performances are realized in these SrRE2O4 oxides, determined by the MC parameters of magnetic entropy change, refrigerant capacity, and temperature-averaged entropy change (with a lift of 5 K). These MC parameters under a magnetic field change of 0–70 kOe are as follows: 34.18 J/kgK, 275.88 J/kg, and 30.74 J/kgK for SrGd2O4; 18.13 J/kgK, 253.83 J/kg, and 17.54 J/kgK for SrDy2O4; 18.81 J/kgK, 354.77 J/kg, and 18.61 J/kgK for SrHo2O4; and 22.63 J/kgK, 284.25 J/kg, and 21.97 J/kgK for SrEr2O4. These values are comparable to those of most recently updated low-temperature MC materials with remarkable performances, making these SrRE2O4 oxides highly interesting for practical cooling applications.

Stochastic hexagonal injectors in artificial spin ice

Artificial spin ice (ASI) systems have emerged as powerful platforms for exploring the fundamental aspects of magnetic frustration and topological phenomena in condensed matter physics. In this study, we investigate the bountiful effects that result from introducing hexagonal magnetic defects into an ASI lattice. The stochastic stabilisation of a plethora of metastable states in the hexagonal defects are explored, as well as harnessing the defect magnetisation state for the selective injection of emergent monopoles of different polarities and proximities within the lattice. We demonstrate a mechanism for tailoring the ASI behaviour using the magnetic state of the defect, which is of interest to applications including magnetic memory devices and spin-based logic.

Excellent Barocaloric Effect by Modulating Geometrical Frustrations in Mn3Pt.

Barocaloric materials hold great promise for next-generation solid-state cooling devices because of their green and efficient cooling performance. The insights into low-pressure-driven barocaloric materials are expected to pave the way for the widespread application of barocaloric refrigeration technology. Here, we reveal the low-pressure-driven large barocaloric effect (BCE) modulated by geometrical frustrations in Mn3Pt. The highest sensitivity to pressure of Mn3Pt in metal BCE materials results in an excellent temperature-change strength of 9.77 K 100-1 MPa-1. Neutron powder diffraction and first-principles calculations point out the dual effect of geometrical frustration on modulating the unusual BCE, which not only induces giant volume expansion by inspiring strong spin fluctuation and magnetic moment but also enhances the sensitivity of magnetic phase transition. The model of the dual effect of geometrical frustration in magnets with geometrical frustration is established, which will promote the research progress of barocaloric refrigeration devices.

Tunable Anomalous Hall Effect in a Kagomé Ferromagnetic Weyl Semimetal.

Emerging from the intricate interplay of topology and magnetism, the giant anomalous Hall effect (AHE) is the most known topological property of the recently discovered kagomé ferromagnetic Weyl semimetal Co3Sn2S2 with the magnetic Co atoms arranged on a kagomé lattice. Here it is reported that the AHE in Co3Sn2S2 can be fine-tuned by an applied magnetic field orientated within ≈2° of the kagomé plane, while beyond this regime, it stays unchanged. Particularly, it can vanish in magnetic fields parallel to the kagomé plane and even decrease in magnetic fields collinear with the spin direction. This tunable AHE can be attributed to local spin switching enabled by the geometrical frustration of the magnetic kagomé lattice, revealing that spins in a kagomé ferromagnet change their switching behavior as the magnetic field approaches the kagomé plane. These results also suggest a versatile way to tune the properties of a kagomé magnet.

Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii Physics in the Triangular Lattice Bilayer Colbaltate.

Motivated by the experiments on the triangular lattice bilayer colbaltate K_{2}Co_{2}(SeO_{3})_{3}, we consider an extended XXZ model to explore the underlying physics. The model is composed of interacting Co^{2+} dimers on the triangular lattice, where the Co^{2+} ion provides an effective spin-1/2 local moment via the spin-orbit coupling and the crystal field effect. The intradimer interaction is dominant and would simply favor the local spin singlet, and the interdimer interactions compete with the interdimer interaction, leading to rich behaviors. With the easy-axis anisotropy, it is shown that, in the ground state manifold of the intradimer Ising interaction, the system realizes an effective quantum Ising model, where the ground state is either a three-sublattice order with a mixture of antiferromagnetic Ising order and a valence-bond spin singlet or Ising disordered. The finite temperature regime realizes the Berezinskii-Kosterlitz-Thouless physics. To explore the full excitations, we incorporate the excited state manifold of the intradimer Ising interaction and establish the emergent Kugel-Khomskii physics. Thus, the triangular lattice bilayer colbaltate is an excellent platform to explore the interplay between geometrical frustration and anisotropic interactions as well as the emergent effective models and the resulting physics.

Observation of flat bands and Dirac cones in a pyrochlore lattice superconductor

Emergent phases often appear when the electronic kinetic energy is comparable to the Coulomb interactions. One approach to seek material systems as hosts of such emergent phases is to realize localization of electronic wavefunctions due to the geometric frustration inherent in the crystal structure, resulting in flat electronic bands. Recently, such efforts have found a wide range of exotic phases in the two-dimensional kagome lattice, including magnetic order, time-reversal symmetry breaking charge order, nematicity, and superconductivity. However, the interlayer coupling of the kagome layers disrupts the destructive interference needed to completely quench the kinetic energy. Here we demonstrate that an interwoven kagome network—a pyrochlore lattice—can host a three dimensional (3D) localization of electron wavefunctions. Meanwhile, the nonsymmorphic symmetry of the pyrochlore lattice guarantees all band crossings at the Brillouin zone X point to be 3D gapless Dirac points, which was predicted theoretically but never yet observed experimentally. Through a combination of angle-resolved photoemission spectroscopy, fundamental lattice model and density functional theory calculations, we investigate the novel electronic structure of a Laves phase superconductor with a pyrochlore sublattice, CeRu2. We observe evidence of flat bands originating from the Ce 4f orbitals as well as flat bands from the 3D destructive interference of the Ru 4d orbitals. We further observe the nonsymmorphic symmetry-protected 3D gapless Dirac cone at the X point. Our work establishes the pyrochlore structure as a promising lattice platform to realize and tune novel emergent phases intertwining topology and many-body interactions.