Strong Geometric Frustration Research Articles

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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Both compounds have electronic states close to flat bands, but the band width is significantly larger than that of Pb2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}Sb2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_7$$\\end{document} shown in previous research. Nevertheless, the density of states at the Fermi level of Pb2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}As2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_7$$\\end{document} is large enough to cause the system to undergo a ferromagnetic transition. In the case of Pb2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}Sn2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_7$$\\end{document}, pseudo-gap behavior near the Fermi level was observed. 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.

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.

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.

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.

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.

Nontrivial spin textures induced remarkable topological Hall effect and extraordinary magnetoresistance in kagome magnet TmMn6Sn6

Kagome magnets RMn6Sn6 (R = lanthanides) manifest novel topological phases and field-induced transitions, owing to the interplay between strong correlations and geometrical frustration among the corner-sharing-triangle intralayers. Here we report the magnetometry and magnetoelectric transport properties of TmMn6Sn6 single crystal, which coexists with Tm and Mn magnetic sublattices. We reveal that this compound displays multiple magnetic structures with the increase of in-plane magnetic field. The combination of non-collinear magnetic structure and real-space Berry curvature leads to a remarkable topological Hall effect over an extensive temperature range. The in-plane magnetic transition is accompanied by a large magnetoresistance effect of -32 ∼ -17% from 10 K to 300 K at 7 T, and the magnetoresistance manifests two peaks with increasing the in-plane field. These observations suggest a robust Mn - Tm magnetic coupling, which provides a nontrivial ferrimagnetic network for the further investigation of new emergent topological magnetic structures.

Signatures of spin-liquid state in a 3D frustrated lattice compound KSrFe2(PO4)3 with S = 5/2

A quantum spin-liquid is a spin disordered state of matter in which spins are strongly correlated and highly entangled with low-energy excitations. It has been often found in two-dimensional S = ½, highly frustrated spin networks but rarely observed in three-dimensional (3D) frustrated quantum magnets. Here, KSrFe2(PO4)3, forming a complicated 3D frustrated lattice with a spin moment S = 5/2, is investigated by thermodynamic, neutron diffraction measurements and electronic structure calculations. Despite the relatively sizable Curie–Weiss temperature θCW = −70 K, a conventional magnetic long-range order is confirmed to be absent down to 0.19 K. The magnetic heat capacity data follow the power-law behavior at the lowest temperature region, supporting gapless excitations in a 3D spin-liquid state. Strong geometrical spin frustration responsible for the spin-liquid feature is understood as originating from the almost comparable five competing nearest-neighbor antiferromagnetic exchange interactions, which form the complicated 3D frustrated spin network. All these results suggest that the compound KSrFe2(PO4)3, representing a unique 3D spin frustrated network, could be a rare example of forming a gapless spin-liquid state even with a large spin moment of S = 5/2.

Incommensurate magnetic ordering in CrB2

Incommensurate magnetism in CrB2 is studied in terms of a spin model based on density functional theory calculations. Heisenberg exchange interactions derived from the paramagnetic phase using the disordered local moment (DLM) theory show significant differences compared with those resulting from the treatment of the material as a ferromagnet; of these two methods, the DLM theory is found to give a significantly more realistic description. We calculate strongly ferromagnetic interactions between Cr planes but largely frustrated interactions within Cr planes. Although we find that the ground state ordering vector is sensitive to exchange interactions over a large number of neighbour shells, the q-vector of the incommensurate spin spiral state is satisfactorily reproduced by the theory (0.213 compared with the known ordering vector along Γ–). The strong geometric frustration of the exchange interactions causes a rather low Néel temperature (about 97 K), also in good agreement with experiment.

Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials

A simple yet paradigmatic model for the interplay of strong electronic correlations and geometric frustration is the triangular lattice Hubbard model. Recently it was proposed that moir\'e structures of transition metal dichalcogenides can be used to simulate extended versions that include non-local density-density interactions. We study competing instabilities of interacting electrons in such an extended Hubbard model on the triangular lattice near a filling where the density of states has a Van Hove singularity. We employ a truncated-unity functional renormalization group approach to investigate two cases: a paradigmatic minimally extended Hubbard model and a specific model with parameters that are applicable to hetero-bilayers of transition metal dichalcogenides. We unravel rich phase diagrams, including tendencies to spin-density-wave order and unconventional pairing, which can give rise to topological superconductivity. We classify the symmetry of the superconducting instabilities according to their irreducible representations and show that higher lattice harmonics are dominant when the nearest-neighbor interaction is sizable indicating pair formation between second-nearest neighbors. The phenomenological consequences can be enhanced spin and thermal quantum Hall responses in a topological superconductor.

Optical Conductivity Spectra of Charge-Crystal and Charge-Glass States in a Series of θ-Type BEDT-TTF Compounds

In the 3/4-filled band system θ-(BEDT-TTF)2X with a two-dimensional triangular lattice, charge ordering (CO) often occurs due to strong inter-site Coulomb repulsion. However, the strong geometrical frustration of the triangular lattice can prohibit long-range CO, resulting in a charge-glass state in which the charge configurations are randomly distributed. Here, we investigate the charge-glass states of orthorhombic and monoclinic θ-type BEDT-TTF salts by measuring the electrical resistivity and optical conductivity spectra. We find a substantial difference between the charge-glass states of the orthorhombic and monoclinic systems. The charge-glass state in the orthorhombic system with an isotropic triangular lattice exhibits larger low-energy excitations than that in the monoclinic one with an anisotropic triangular lattice and becomes more metallic as the isotropy of the triangular lattice increases. These results can be understood by the different charge-glass formation mechanisms in the two systems: in the orthorhombic system, the charge-glass state originates from geometric frustration due to the equilateral triangular lattice, leading to metallic 3-fold COs, whereas in the monoclinic system, the charge-glass formation originates from geometric frustration of the isosceles triangular lattice, in which the charge-glass state is described by the superposition of insulating 2-fold stripe COs.

Open-Framework Iron Fluoride Phosphates Based on Chain, Trinuclear, and Tetranuclear Chain FeIII Building Units: Crystal Structures and Magnetic Properties.

We report the synthesis and characterization of a series of new open-framework iron fluoride-fluorophosphates based on linear, trinuclear, and tetranuclear chain FeIII building units. KFe2(PO3F)2F3 (I) consists of {Fe2(O3F)2F2}10- zigzag chains interconnected by P(O/F)4 tetrahedra forming a three-dimensional (3D) open framework. K2Fe(PO2.5F1.5)2F2 (II) is built up by {Fe(PO2.5F1.5)2F2}2- chains separated by K+ cation layers. The framework for K3Fe3(PO4)(PO3F)2F5 (III) contains two-dimensional {Fe3O4F4(PO3F)2}2- sheets, which are built from trimeric Fe-octahedra insulated by PO3F tetrahedra. The macroanionic framework of K3Fe4(PO4)2F9 (IV) comprises linear {Fe4O8F9}10- chains consisting of tetranuclear magnetic clusters of [Fe4O8F9]10- formed via corner-sharing fluorine atoms decorated with PO4 groups. The magnetic characterization of three iron fluorophosphates reveals diversified magnetism: S = 5/2 spin chains for I, antiferromagnetically coupled triangular Fe units for III, and coupled tetrahedral S = 5/2 spin chains for IV. IV shows strong geometric frustration thanks to its spin motifs of corner-shared tetrahedral clusters.

Mixed-valent metallic pyrochlore iridate: A possible route to non-Fermi liquids

Non-Fermi liquid behavior in some fermionic systems has attracted significant interest in last few decades. Certain pyrochlore iridates with stronger spin-orbit coupling strength have recently been added to the list. Here, we provide evidence of such a non-Fermi liquid ground state in another mixed-valent metallic pyrochlore iridate ${\mathrm{Pb}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$, through the combined investigation of electronic, magnetic, and thermodynamic properties as a function of temperature ($T$) and applied magnetic field ($H$). Resistivity measurement showed a linear temperature dependence down to 15 K below which it shows $\ensuremath{\rho}\ensuremath{\sim}{T}^{3/2}$ dependence while magnetic susceptibility diverges as $\ensuremath{\chi}(T$) $\ensuremath{\sim}{T}^{\ensuremath{-}\ensuremath{\alpha}}$ ($\ensuremath{\alpha}<1$) below 10 K. While a strong negative ${\mathrm{\ensuremath{\Theta}}}_{\text{CW}}$ has been observed from Curie-Weiss fitting, the absence of any long-range order down to 80 mK only indicates the presence of strong inherent geometric frustration in the system. Heat capacity data showed ${C}_{p}\ensuremath{\sim}Tln({T}_{0}/T)+\ensuremath{\beta}{T}^{3}$ dependence below 15 K down to 1.8 K. More importantly spin-orbit coupling strength by x-ray absorption spectroscopy was found to be weaker in ${\mathrm{Pb}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ compared to other pyrochlore iridates. In the absence of any large moment rare earth magnetic ion, ${\mathrm{Pb}}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ presents a rare example of an iridate system showing non-Fermi liquid behavior due to disordered distribution of ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$ having markedly different strengths of spin-orbit coupling which might offer a prescription for achieving new non-Fermi liquid systems.

Quantum phases and transitions of spin-1/2 quantum compass chain

Quantum phases (QPs) and quantum phase transitions (QPTs) are very important parts of the strongly correlated quantum many-body systems in condensed matter. To study the QPs and QPTs, the systems should include rich quantum phase diagram. In this sense, the corresponding quantum spin models should have strong quantum fluctuation, strong geometric frustration, complicated spin-spin exchange or orbital degrees of freedom, which induces a variety of spontaneous symmetry breaking (SSB) or hidden spontaneous symmetry breaking. The QPs induced by the SSB can be characterized by local order parameters, a concept that originates from Landau-Ginzburg-Wilson paradigm (LGW). However, there is also a novel class of topological QPs beyond LGW, which has aroused one’s great interest since the Haldane phase was found. Such QPs can be characterized only by topological long-range nonlocal string correlation order parameters instead of local order parameters. In this paper, we investigate a spin-1/2 quantum compass chain model (QCC) with orbital degrees of freedom in <i>x</i>, <i>y</i> and <i>z</i> components. The prototype of QCC is the quantum compass model including novel topological QPs beyond LGW, and consequently one can also anticipate the existence of novel topological QPs in QCC. However, very little attention has been paid to the QPs and QPTs for QCC, which deserves to be further investigated. By using the infinite time evolving block decimation in the presentation of matrix product states, we study the QPs and QPTs of QCC. To characterize QPs and QPTs of QCC, the ground state energy, local order parameter, topological long-range nonlocal string correlation order parameters, critical exponent, correlation length and central charge are calculated. The results show the phase diagram of QCC including local antiferromagnetic phase, local stripe antiferromagnetic phase, oscillatory odd Haldane phase and monotonic odd Haldane phase. The QPTs from oscillatory odd Haldane phase to local stripe antiferromagnetic phase and from local antiferromagnetic phase to monotonic odd Haldane phase are continuous; on the contrary, QPTs from local stripe antiferromagnetic phase to local antiferromagnetic phase and from oscillatory odd Haldane phase to monotonic odd Haldane phase are discontinuous. The crossing point where the line of continuous QPTs meets with the line of discontinuous QPTs is the multiple critical point. The critical exponents <i>β</i> of local antiferromagnetic order parameter, local stripe antiferromagnetic order parameter, topological long-range nonlocal oscillatory odd string correlation order parameter, and topological long-range nonlocal monotonic odd string correlation order parameter are all equal to 1/8. Moreover, <inline-formula><tex-math id="M3">\begin{document}$\beta =1/8$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20211433_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20211433_M3.png"/></alternatives></inline-formula> and the central charges <inline-formula><tex-math id="M4">\begin{document}$c = 1/2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20211433_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20211433_M4.png"/></alternatives></inline-formula> at the critical points show that the QPTs from local phases to nonlocal phases belong to the Ising-type universality class.

Unraveling the Electrical and Magnetic Properties of Layered Conductive Metal‐Organic Framework With Atomic Precision

AbstractThis paper describes structural elucidation of a layered conductive metal‐organic framework (MOF) material Cu3(C6O6)2 by microcrystal electron diffraction with sub‐angstrom precision. This insight enables the first identification of an unusual π‐stacking interaction in a layered MOF material characterized by an extremely short (2.73 Å) close packing of the ligand arising from pancake bonding and ordered water clusters within pores. Band structure analysis suggests semiconductive properties of the MOF, which are likely related to the localized nature of pancake bonds and the formation of a singlet dimer of the ligand. The spin of CuII within the Kagomé arrangement dominates the paramagnetism of the MOF, leading to strong geometrical magnetic frustration.

Unraveling the Electrical and Magnetic Properties of Layered Conductive Metal-Organic Framework With Atomic Precision.

This paper describes structural elucidation of a layered conductive metal-organic framework (MOF) material Cu3 (C6 O6 )2 by microcrystal electron diffraction with sub-angstrom precision. This insight enables the first identification of an unusual π-stacking interaction in a layered MOF material characterized by an extremely short (2.73 Å) close packing of the ligand arising from pancake bonding and ordered water clusters within pores. Band structure analysis suggests semiconductive properties of the MOF, which are likely related to the localized nature of pancake bonds and the formation of a singlet dimer of the ligand. The spin of CuII within the Kagomé arrangement dominates the paramagnetism of the MOF, leading to strong geometrical magnetic frustration.

Physical and magnetic properties of frustrated triangular-lattice antiferromagnets R3Cu (R = Ce, Pr)

We report the synthesis, crystal structure, and thermodynamic properties of the two binary laves phases Ce3Cu and Pr3Cu, which crystallize in the tetragonal I4/mmm (space group: 139). We have investigated the compounds using dc magnetic susceptibility χdc(T), ac magnetic susceptibility χac(T), isothermal magnetization M(B) and specific heat Cp(T) measurements. Both compounds show features of strong geometrical frustration, which is driven by the arrangement of the rare-earth ions on triangular lattice sites. Ce3Cu shows a phase transition at TN = 5 K and its M(B) at 2 K reveals the presence of a metamagnetic transition near 2 T. Pr3Cu, on the other hand, shows a spin-glass behaviour with a freezing temperature of Tf1 ≃ 12 K and with an irreversible behavior in zero-field-cooled (ZFC) and field-cooled (FC) χdc(T) below about 13 K. The real part of χac(T) reveals a frequency dependence of Tf. The result, however shows the presence of another frequency-dependent phase below Tf2 ≃ 9.35 K, a feature which signals a re-entrant spin-glass behaviour in the compound. Furthermore, the frequency dependence of Tf1 follows the Vogel-Fulcher law, with an activation energy Ea∕kB = 5.3 K. This observation along with the estimated relative shift in Tf1 per decade in frequency δTf = 0.0105, irreversible behaviour in ZFC-FC χdc(T) and a slow decay in thermo-remnant magnetization provide supports for the formation of a cluster spin-glass in Pr3Cu. In addition, we observe the enhancement of the Sommerfeld coefficient, γ in both compounds with values of 0.1892(5) J/(molCe K2) and 0.5078(1) J/(molPr K2). The estimation of the Sommerfeld-Wilson ratio WR yield values of 0.576 and 1.17 for Ce3Cu and Pr3Cu, respectively.

Exchange Bias in a Layered Metal-Organic Topological Spin Glass.

The discovery of conductive and magnetic two-dimensional (2D) materials is critical for the development of next generation spintronics devices. Coordination chemistry in particular represents a highly versatile, though underutilized, route toward the synthesis of such materials with designer lattices. Here, we report the synthesis of a conductive, layered 2D metal–organic kagome lattice, Mn3(C6S6), using mild solution-phase chemistry. Strong geometric spin frustration in this system mediates spin freezing at low temperatures, which results in glassy magnetic dynamics consistent with a rare geometrically frustrated (topological) spin glass. Notably, we show that this geometric frustration engenders a large, tunable exchange bias of 1625 Oe in Mn3(C6S6), providing the first example of exchange bias in a coordination solid or a topological spin glass. Exchange bias is a critical component in a number of spintronics applications, but it is difficult to rationally tune, as it typically arises due to structural disorder. This work outlines a new strategy for engineering exchange bias systems using single-phase, crystalline lattices. More generally, these results demonstrate the potential utility of geometric frustration in the design of new nanoscale spintronic materials.

Structure and frustrated magnetism of the two-dimensional triangular lattice antiferromagnet Na2BaNi(PO4)2 * *Project supported by the National Natural Science Foundation of China (Grant No. 11804137) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2020YQ03 and ZR2018BA026).

A new frustrated triangular lattice antiferromagnet Na2BaNi(PO4)2 was synthesized by high temperature flux method. The two-dimensional triangular lattice is formed by the Ni2+ ions with S = 1. Its magnetism is highly anisotropic with the Weiss constants θ CW = –6.615 K (H ⊥ c) and –43.979 K (H ∥ c). However, no magnetic ordering is present down to 0.3 K, reflecting strong geometric spin frustration. Our heat capacity measurements show substantial residual magnetic entropy existing below 0.3 K at zero field, implying the presence of low energy spin excitations. These results indicate that Na2BaNi(PO4)2 is a potential spin liquid candidate with spin-1.