Strong Frustration Research Articles

Exotic phases induced by RKKY interaction in the square lattice

We study a model of Ising spins in which direct exchange interactions compete with the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, which may arise effectively from itinerant electrons. We consider the model in the two-dimensional square lattice and focus on values of the RKKY coupling constant (JRKKY) and the Fermi momentum (kF) that induce strong frustration. We study the low-temperature magnetic field phase diagram using Monte Carlo simulations, considering several nearest neighbors in the RKKY interaction. Magnetic frustration yields a rich phase diagram with a variety of exotic phases. We compute the structure factors and define appropriate order parameters to describe the transitions. We also discuss the validity of the approximation made for long-range couplings and analytically demonstrate the change in the coexistence lines in the phase diagram by including up to the tenth nearest neighbors.

Breaking the vitrification limitation of monatomic metals.

The question of whether all materials can solidify into the glassy form proposed by Turnbull half a century ago remains unsolved. Some of the simplest systems of monatomic metals have not been vitrified, especially the close-packed face-centred cubic metals. Here we report the vitrification of gold, which is notoriously difficult to be vitrified, and several similar close-packed face-centred cubic and hexagonal metals using a method of picosecond pulsed laser ablation in a liquid medium. The vitrification occurs through the rapid cooling during laser ablation and the inhibition of nucleation by the liquid medium. Using this method, a large number of atomic configurations, including glassy configurations, can be generated simultaneously, from which a stable glass state can be sampled. Simulations demonstrate that the favourable stability of monatomic metals stems from the strong topological frustration of icosahedra-like clusters. Our work breaks the limitation of the glass-forming ability of matter, indicating that vitrification is an intrinsic property of matter and providing a strategy for the preparation and design of metallic glasses from an atomic configuration perspective.

Syntheses, structures, and magnetic properties of new [Co9] cluster

A new spin-cluster compound K6BaCo9(PO4H)3(PO4)6Cl2 was synthesized by the traditional solid-phase method. The fundamental magnetic unit of the compound is a coupled [Co9] cluster, which is composed of three non-coplanar triangles. These [Co9] clusters are interconnected by phosphate groups, constructing a two-dimensional framework in the ab plane. The crystal shows the clear easy-axis anisotropy. No long-range magnetic ordering was observed down to 2 K, but there is short-range spin correlation below T = 2.45 K. The Curie-Weiss temperature is about θCW = −19.38 K for the powder sample, which indicates that the dominant exchange interaction is antiferromagnetic with strong frustration (f = |θCW|/T ≈ 10). The magnetization curve presents a likely magnetic field induced transition at μ0Hc = 1.85 T.

Ba4RuMn2O10: A Noncentrosymmetric Polar Crystal Structure with Disordered Trimers.

Phase-pure polycrystalline Ba4RuMn2O10 was prepared and determined to adopt the noncentrosymmetric polar crystal structure (space group Cmc21) based on results of second harmonic generation, convergent beam electron diffraction, and Rietveld refinements using powder neutron diffraction data. The crystal structure features zigzag chains of corner-shared trimers, which contain three distorted face-sharing octahedra. The three metal sites in the trimers are occupied by disordered Ru/Mn with three different ratios: Ru1:Mn1 = 0.202(8):0.798(8), Ru2:Mn2 = 0.27(1):0.73(1), and Ru3:Mn3 = 0.40(1):0.60(1), successfully lowering the symmetry and inducing the polar crystal structure from the centrosymmetric parent compounds Ba4T3O10 (T = Mn, Ru; space group Cmca). The valence state of Ru/Mn is confirmed to be +4 according to X-ray absorption near-edge spectroscopy. Ba4RuMn2O10 is a narrow bandgap (∼0.6 eV) semiconductor exhibiting spin-glass behavior with strong magnetic frustration and antiferromagnetic interactions.

Testing structural balance theories in heterogeneous signed networks

The abundance of data about social relationships allows the human behavior to be analyzed as any other natural phenomenon. Here we focus on balance theory, stating that social actors tend to avoid establishing cycles with an odd number of negative links. This statement, however, can be supported only after a comparison with a benchmark. Since the existing ones disregard actors’ heterogeneity, we extend Exponential Random Graphs to signed networks with both global and local constraints and employ them to assess the significance of empirical unbalanced patterns. We find that the nature of balance crucially depends on the null model: while homogeneous benchmarks favor the weak balance theory, according to which only triangles with one negative link should be under-represented, heterogeneous benchmarks favor the strong balance theory, according to which also triangles with all negative links should be under-represented. Biological networks, instead, display strong frustration under any benchmark, confirming that structural balance inherently characterizes social networks.

Nonequilibrium generation of charge defects in kagome spin ice under slow cooling.

Kagome spin ice is one of the canonical examples of highly frustrated magnets. The effective magnetic degrees of freedom in kagome spin ice are Ising spins residing on a two-dimensional network of corner-sharing triangles. Due to strong geometrical frustration, nearest-neighbor antiferromagnetic interactions on the kagome lattice give rise to a macroscopic number of degenerate classical ground states characterized by ice rules. Elementary excitations at low temperatures are defect-triangles that violate the ice rules and carry an additional net magnetic charge relative to the background. We perform large-scale Glauber dynamics simulations to study the nonequilibrium dynamics of kagome ice under slow cooling. We show that the density of residual charge defects exhibits a power-law dependence on the quench rate for the class of algebraic cooling protocols. The numerical results are well captured by the rate equationfor the charge defects based on the reaction kinetics theory. As the relaxation time of the kagome ice phase remains finite, there is no dynamical freezing as in the Kibble-Zurek scenario. Instead, we show that the power-law behavior originates from a thermal excitation that decays algebraically with time at the late stage of the cooling schedule. Similarities and differences in quench dynamics of other spin ice systems are also discussed.

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.

Highly entangled polyradical nanographene with coexisting strong correlation and topological frustration.

Open-shell nanographenes exhibit unconventional π-magnetism arising from topological frustration or strong electron-electron interaction. However, conventional design approaches are typically limited to a single magnetic origin, which can restrict the number of correlated spins or the type of magnetic ordering in open-shell nanographenes. Here we present a design strategy that combines topological frustration and electron-electron interactions to fabricate a large fully fused 'butterfly'-shaped tetraradical nanographene on Au(111). We employ bond-resolved scanning tunnelling microscopy and spin-excitation spectroscopy to resolve the molecular backbone and reveal the strongly correlated open-shell character, respectively. This nanographene contains four unpaired electrons with both ferromagnetic and anti-ferromagnetic interactions, harbouring a many-body singlet ground state and strong multi-spin entanglement, which is well described by many-body calculations. Furthermore, we study the magnetic properties and spin states in the nanographene using a nickelocene magnetic probe. The ability to imprint and characterize many-body strongly correlated spins in polyradical nanographenes paves the way for future advancements in quantum information technologies.

Observation of Topological Hall Effect in a Chemically Complex Alloy.

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Unusual magnetic behavior of cubic double perovskite Ba2YIrO6 with Ir5+(5d 4) ions

Using density functional calculations, we investigate the electronic structure and magnetism of double-perovskite Ba2YIrO6 to explore the origin of its unusual magnetic behavior. Our results show that the breakdown of expected j = 0 nonmagnetic state of Ir5+(5d 4) in Ba2YIrO6 is induced by both bandwidth and exchange interaction. In addition, the bandwidth effect makes the system behave like metal, while the antiferromagnetic interaction between Ir ions should be responsible for the insulator behavior. Moreover, the strong geometrical frustration in Ir triangular unit prevents the formation of long-range magnetic order.

Magnetism and metallicity in moiré transition metal dichalcogenides.

The ability to control the properties of twisted bilayer transition metal dichalcogenides in situ makes them an ideal platform for investigating the interplay of strong correlations and geometric frustration. Of particular interest are the low energy scales, which make it possible to experimentally access both temperature and magnetic fields that are of the order of the bandwidth or the correlation scale. In this manuscript, we analyze the moiré Hubbard model, believed to describe the low energy physics of an important subclass of the twisted bilayer compounds. We establish its magnetic and the metal-insulator phase diagram for the full range of magnetic fields up to the fully spin-polarized state. We find a rich phase diagram including fully and partially polarized insulating and metallic phases of which we determine the interplay of magnetic order, Zeeman-field, and metallicity, and make connection to recent experiments.

Building Peace after Self-Determination and Partition: Faulty Assumptions?

Abstract Since the 1990s, scholars have debated whether partition, the most radical solution to ethnic conflicts, promotes peace or not. Drawing on the peacebuilding and war recurrence literature, I contribute to this debate by theorizing reasons that newly independent states emerging from partition are likely to suffer from new conflicts between former pro-independence allies. At the domestic level, former pro-independence groups, assumed to be a unitary actor by partition proponents, are likely to fragment as their unity was based on achieving the goal of independence. Furthermore, newly independent states tend to suffer from very weak institutions, and citizens develop strong frustrations toward their new states because their unrealistically high expectations are unmet. At the international level, international peacebuilders tend to wrongly assume that the unity within the pro-independence camp will last after independence and that the pro-independence people are essentially “good guys.” As a result, they often misunderstand the post-conflict political dynamics of new states, which reduces the effectiveness of their peacebuilding efforts. My arguments are illustrated through analyzing why Timor-Leste and South Sudan, the closest to typical partition cases in the twenty-first century, faced the 2006 Crisis and the 2013 Civil War, respectively.

Low-temperature antiferromagnetism in quaternary Mn2FeSi0.5Al0.5 alloys

In this work, the quaternary Mn2FeSi0.5Al0.5 alloys are prepared for the first time in the form of cylinder-shaped ingots by traditional induction melting technique followed by homogenization annealing at 773 K for 100 h. The microstructural and magnetic properties of as-cast and annealed Mn2FeSi0.5Al0.5 samples are analyzed in detail and compared to the Mn2FeSi and Mn2FeAl ternary alloys. The Mn2FeSi0.5Al0.5 ingots are two-phase both before and after annealing, and their diffractograms correspond to the primitive cubic β-Mn structure. Obtained lattice constant of 0.6274 nm is only slightly lower than that of Mn2FeAl alloy (0.6339 nm) and different from Mn2FeSi (0.5672 nm). The existence of both phases enriched in Si at the expense of Al and Mn was confirmed by differential thermal analysis showing two endothermic and exothermic peaks at temperatures of 1363 K and 1407 K. The magnetic properties of both quaternary samples studied in wide temperature range from 5 K to 573 K indicate paramagnetic behavior at room and elevated temperatures. The annealed system has the values of Curie temperature and effective paramagnetic moment comparable to the ternary Mn2FeAl alloy. The transition to antiferromagnetic state occurring at Néel temperatures of 34 K (as-cast sample) and 37 K (annealed sample) is caused by strong geometric frustration of β-Mn structure. The magnetic transitions observed in both samples between Néel and room temperature are discussed in terms of the existence of Griffiths phase.

Eleven competing phases in the Heisenberg-Gamma ( JΓ ) ladder

The spin-orbit generated Γ interaction is known to induce strong frustration and to be significant in realistic models of materials. To gain an understanding of the possible phases that can arise from this interaction, it is of considerable interest to focus on a limited part of parameter space in a quasi one-dimensional model where high precision numerical results can be obtained. Here we study the Heisenberg–Gamma ( JΓ ) ladder, determining the complete zero temperature phase diagram by analyzing the entanglement spectrum (ES) and energy susceptibility. A total of 11 different phases can be identified, among them the well known rung-singlet (RS) phase and 5 other phases, FM, FM-Z, FM-XY, AF and AF-Z, with conventional long-range magnetic order. The 3 ferromagnetic phases, FM, FM-Z and FM-XY simultaneously have non-zero scalar chirality. Two other phases, the antiferromagnetic Gamma (AΓ) and ferromagnetic Gamma (FΓ) phases, have previously been observed in the Kitaev–Gamma ladder, demonstrating that the AΓ-phase is a symmetry protected topological phase (SPT) protected by TR ×Rb symmetry, the product of time-reversal (TR) and π rotation around the b-axis ( Rb ), while the FΓ-phase is related to the RS phase through a local unitary transformation. The 3 remaining phases, ϒ, Ω and δ show no conventional order, a doubling of the ES and for the ϒ and Ω-phases a gap is clearly present. The δ-phase has a significantly smaller gap and displays incommensurate correlations, with a peak in the static structure factor, S(k) continuously shifting from k/π=2/3 to k=π . In the Ω-phase we find pronounced edge-states consistent with a SPT phase protected by the same TR ×Rb symmetry as the AΓ-phase. The precise nature of the ϒ and δ-phases is less clear.

Thermodynamic Properties and DFT Study on Highly Frustrated Cr3BO6: Coexistence of Spin-Singlets with Long-Range Magnetic Order.

The triangle-based magnetic subsystem of borates with the mineral norbergite structure M3BO6 (M = Fe, Cr, V) makes these compounds unique to investigate rare quantum ground states influenced by strong magnetic frustration. In this work, we investigated the thermal and magnetic properties of Cr3BO6 to find that despite very large negative Weiss temperature Θ = -160.7 K, it orders only at TN = 4.5 K and experiences a spin-flop transition at µ0H = 5 T. Density functional theory (DFT) calculations of exchange interaction parameters allow for suggesting the model of magnetic subsystem in chromium borate Cr3BO6. The results prove the decisive role of magnetic frustration on the formation of long-range order, providing therefore a basis for future study. Both experimental data and first-principles calculations point to the coexistence of chromium spin-singlets with long-range antiferromagnetic order.

Near Room-Temperature Intrinsic Exchange Bias in an Fe Intercalated ZrSe2 Spin Glass.

Some magnetic systems display a shift in the center of their magnetic hysteresis loop away from zero field, a phenomenon termed exchange bias. Despite the extensive use of the exchange bias effect, particularly in magnetic multilayers, for the design of spin-based memory/electronics devices, a comprehensive mechanistic understanding of this effect remains a longstanding problem. Recent work has shown that disorder-induced spin frustration might play a key role in exchange bias, suggesting new materials design approaches for spin-based electronic devices that harness this effect. Here, we design a spin glass with strong spin frustration induced by magnetic disorder by exploiting the distinctive structure of Fe intercalated ZrSe2, where Fe(II) centers are shown to occupy both octahedral and tetrahedral interstitial sites and to distribute between ZrSe2 layers without long-range structural order. Notably, we observe behavior consistent with a magnetically frustrated and multidegenerate ground state in these Fe0.17ZrSe2 single crystals, which persists above room temperature. Moreover, this magnetic frustration leads to a robust and tunable exchange bias up to 250 K. These results not only offer important insights into the effects of magnetic disorder and frustration in magnetic materials generally, but also highlight as design strategy the idea that a large exchange bias can arise from an inhomogeneous microscopic environment without discernible long-range magnetic order. In addition, these results show that intercalated TMDs like Fe0.17ZrSe2 hold potential for spintronic technologies that can achieve room temperature applications.

Incommensurate Antiferromagnetic Order in Weakly Frustrated Two-Dimensional van der Waals Insulator CrPSe3.

Although magnetic order is suppressed by a strong frustration, it appears in complex forms such as a cycloid or spin density wave in weakly frustrated systems. Herein, we report a weakly magnetically frustrated two-dimensional (2D) van der Waals material CrPSe3. Polycrystalline CrPSe3 was synthesized at an optimized temperature of 700 °C to avoid the formation of any secondary phases (e.g., Cr2Se3). The antiferromagnetic transition appeared at TN ≈ 127 K with a large Curie-Weiss temperature θCW ≈ -301 K via magnetic susceptibility measurements, indicating weak frustration in CrPSe3 with a frustration factor of f (|θCW|/TN) ≈ 2.4. Evidently, the formation of a long-range incommensurate antiferromagnetic order was revealed by neutron diffraction measurements at low temperatures (below 120 K). The monoclinic crystal structure of the C2/m symmetry is preserved over the studied temperature range down to 20 K, as confirmed by Raman spectroscopy measurements. Our findings on the incommensurate antiferromagnetic order in 2D magnetic materials, not previously observed in the MPX3 family, are expected to enrich the physics of magnetism at the 2D limit, thereby opening opportunities for their practical applications in spintronics and quantum devices.

K2Ni(SeO3)2: A Perfect S = 1 Triangular-Lattice Antiferromagnet with Strong Geometric Frustration and Easy-Plane Anisotropy

We synthesized a single crystal of K2Ni(SeO3)2 (S = 1) with an equilateral triangular lattice (space group R-3m). The magnetic susceptibility χ(T) and heat capacity Cp(T) show that the compound is antiferromagnetically ordered at TN ≈ 7 K. The Curie–Weiss temperature is about θCW = −72.41 and −71.83 K when the field is applied along the ab plane (H//ab) and parallel to the c axis (H//c), respectively, indicating a strong geometric frustration (f ≈ 10). Both the χ(T) and M(H) point to the presence of easy-plane anisotropy. Density functional theory (DFT) calculations estimate the intraplane exchange (J/kB = −19.04 K) and the interplane exchange (J′/kB = −0.01 K), proving the excellent two-dimensionality. The 50 T high-field magnetization M(H) at 2 K indicates a sign of 1/3 magnetization plateau. The high-field electron spin resonance demonstrates the antiferromagnetic resonance modes with easy-plane anisotropy, yielding J highly consistent with the DFT result. Thus, K2Ni(SeO3)2 is a perfect triangular-lattice antiferromagnet with strong frustration and easy-plane anisotropy.

The experience of closeness and distance in the therapeutic relationship of patients with different attachment classifications: an exploration of prototypical cases.

Individuals with different attachment classifications (Secure, Avoidant and Preoccupied) may experience emotional closeness differently, in their intimate relationships but also as clients in psychotherapy. However, evidence for this assumption almost exclusively comes from research with self-report questionnaires. In this paper, we use observer-rated measures to explore in depth how patients with different attachment classifications experience closeness and distance from the therapist in different phases of therapy. Three patients' and their therapists' narratives about the therapeutic relationship at three time points during therapy were extracted and analyzed with two transcript-based observational measures: The Patient Attachment Coding System (PACS), which classifies patients' attachment according to their discourse behavior, and the therapeutic-Distance Scale-Observer version (TDS-O), which assesses the therapeutic relationship in terms of closeness, distance, autonomy and engagement. Cases were chosen from a larger research project due to their different prototypical attachment classification on the PACS. The narratives were obtained from Relationship Anecdote Paradigm (RAP) interviews in which the patients and their therapists narrated separately about meaningful interactions with each other, at early, middle and late phases of therapy. In addition, we followed patients self-report of the alliance and symptoms (OQ-45). Although all patients reported experiencing discomfort with feeling distant from the therapist the therapeutic distance, the secure patient was able to reflect on his feelings and, in the therapist's recollection, was able to share them with the therapist. This allowed the therapist to harness these feelings for the benefit of the therapy. The avoidant and the preoccupied patients both experienced the therapist as distant, but the avoidant patient prevented closeness by a minimal expression of feelings, and the preoccupied described strong frustration with the therapist in a one-sided manner that prevented collaborative processing and left the therapist confused. It appears that patient discourse is a stable (trait-like) component of attachment, while the therapeutic-distance is a process (state-like) component that may change along therapy. The discourse of insecure patients may hinder therapists' ability to adjust the therapeutic-distance to patients' needs. Therapists' knowledge about the ways patients with different attachment classifications communicate their proximity wishes may improve their attunement.

Excitonic topological order in imbalanced electron-hole bilayers.

Correlation and frustration play essential roles in physics, giving rise to novel quantum phases1-6. A typical frustrated system is correlated bosons on moat bands, which could host topological orders with long-range quantum entanglement4. However, the realization of moat-band physics is still challenging. Here, we explore moat-band phenomena in shallowly inverted InAs/GaSb quantum wells, where we observe an unconventional time-reversal-symmetry breaking excitonic ground state under imbalanced electron and hole densities. We find that a large bulk gap exists, encompassing a broad range of density imbalances at zero magnetic field (B), accompanied by edge channels that resemble helical transport. Under an increasing perpendicular B, the bulk gap persists, and an anomalous plateau of Hall signals appears, which demonstrates an evolution from helical-like to chiral-like edge transport with a Hall conductance approximately equal to e2/h at 35 tesla,where e is the elementarycharge and h is Planck's constant. Theoretically, we show that strong frustration from density imbalance leads to a moat band for excitons, resulting in a time-reversal-symmetry breaking excitonic topological order, which explains all our experimental observations. Our work opens up a new direction for research on topological and correlated bosonic systems in solid states beyond the framework of symmetry-protected topological phases, including but not limited to the bosonic fractional quantum Hall effect.