Geometrical Spin Frustration Research Articles

Magnetic excitation in the hyperkagome antiferromagnet Mn3RhSi

In a paramagnetic state of a hyperkagome lattice antiferromagnet Mn3RhSi, magnetic diffuse scattering by magnetic short-range order is observed over a wide temperature range of approximately 500 K above the Néel temperature of 190 K. We have studied the magnetic excitation with a single crystal in a wide energy range from 0.3 to 140 meV by inelastic neutron scattering, where the prominent inelastic neutron-scattering signal is observed at Q=(2,0,0). The inelastic scattering intensity integrated for two of twelve magnon modes leads to a localized magnetic moment of about 5 μB per Mn site, although the long-range ordered magnetic moment is only 2.61 μB at 4 K. The result suggests that a large part of the magnetic moment does not order in Mn3RhSi, possibly due to the geometrical spin frustration of the hyperkagome lattice. Published by the American Physical Society 2024

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.

Signature of elementary excitations in Se-substituted layered triangular-lattice antiferromagnet CuCrS2

Geometrical spin frustration in a layered triangular-lattice system prohibits the long-range magnetic order and could give rise to unusual spin-disordered states of matter in which spins are strongly correlated and highly entangled with low-energy excitations. Here we investigate the low-temperature magnetic and specific heat properties of the layered triangular-lattice system CuCr(S1-xSex)2 within the entire Se-for-S substitution range. In magnetization measurements, the x = 0 phase exhibits a sharp cusp-like antiferromagnetic transition at 38 K, while for all the Se-substituted samples a broad maximum along with a spin-glass-like freezing at low temperatures is seen. The Curie-Weiss temperature systematically increases from −122 K for x = 0 to + 15 K for x = 1. These observations suggest that the magnetic ground state is determined by the competition between antiferromagnetic direct exchange interactions and ferromagnetic super-exchange interactions. For x = 0, the magnetic contribution to heat capacity exhibits a sharp jump at the magnetic transition temperature indicative of 3D long-range magnetic order, while for the x > 0 samples it increases smoothly across the magnetic transition range following a power-law (∼T2.1) behavior. All these results are in line with an existence of unusual gapless spin-liquid like excitations originating from the spin frustrations and competing nearest-neighbor interactions in CuCr(S,Se)2.

Interplay of spin and orbital ordering in a frustrated spinel chromite

Geometric Spin Frustration, when sufficiently strong, provides a platform for novel spin textures with emergent phenomena, such as ferroelectricity. This article investigates NiCr2O4, a spinel chromite co-hosting the frustration of Cr3+ spins with orbital frustration of Ni2+ ions, with the latter expected to eradicate the spin frustration by lowering lattice symmetry. Detailed experiments unveil an intriguing reentrant-spin-glass-like behavior alongside the previously known canted ferrimagnetism. Our analysis focuses on the ordering of Cr3+ spins at two distinct sublattices, with one contributing to canted ferrimagnetism, while the other exhibits a local (spin-frustrated) texture, potentially inducing spin-glass behavior. Density functional theory calculations corroborate the experimental findings, establishing as the ground state of NiCr2O4. This study presents new prospects for ferroelectricity driven by exchange striction in orbitally ordered spinel chromites.

Generalized spin σ-SCF method.

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3-7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Structural and Magnetic Properties of the B-Site-Ordered Double Perovskites Ln2NiTiO6 (Ln = La, Pr, and Nd)

Abstract Structural and magnetic properties of B-site-ordered double perovskites Ln2NiTiO6 (Ln = La, Pr, and Nd) were investigated. The charge formulas were revealed to be Ln23+Ni2+Ti4+O6, which gave a geometrically frustrated face-centered cubic lattice consisting of magnetic Ni2+ (S = 1) cations. In spite of the geometrical spin frustration of Ni2+ spins, the samples show an antiferromagnetic-like magnetic transition at temperatures TN close to their absolute values of the Weiss temperature θ, giving small frustration indices f = |θ|/TN ∼ 1. The small f values are considered to be due to some amount of anti-site disorder between Ni2+ and Ti4+ originating in the small valence difference. The suppression of magnetic ordering in the geometrically frustrated system is strongly affected by the B-site cation ordering in the double perovskites.

Quantum geometric spin frustration of antiferromagnetic CuFeO2 enables photocatalytic applications

Photocatalysis, containing a potential solution to the global crises of energy shortage and the greenhouse effect, has been studied extensively in recent years. The CuFeO2 (abbreviated as CFO) is a material with a Delafossite structure, and has also been widely studied because of its triangular lattice antiferromagnets. The triangular lattice composed of Fe3+ ions, along with strong antiferromagnetic spin coupling between the Fe3+ ions, leads to a geometric spin frustration. Furthermore, CFO is also a potential candidate for the photocatalytic material due to its narrow band gap of 1.1–1.6 eV, electrochemical stability in an aqueous environment, high charge carrier mobility, flat-band potential positioned at ∼ 1 eV, and contains an abundance of raw materials in the earth. In this study, we successfully grew the size and highly-quality CFO single crystals using the optical floating-zone technique. Powder x-ray diffraction (XRD) and Rietveld refinement indicate that the CFO is a rhombohedral structure with a space group of R3̅m, consisting of edge-shared FeO6 octahedron to form the FeO2 layer, and the Cu cations occupied between the two FeO2 layers. The core-level electron energy loss (EEL) spectra found the valence of Fe and Cu in CFO is +3 and +1, respectively. The low-loss EEL spectrum observed two volume plasmons at ∼5 eV and ∼23 eV contributed from the collective oscillation of Cu-O antibonding states σCu−O* and mixed nonbonding Cu 3dxy, σCu−O bonding states, and Fe-O, respectively, based on the density function theory calculation. The optical absorption spectrum measured the energy bandgap for CFO is about 1.5 eV. The Raman spectrum shows significant Eg and A1 g vibration modes corresponding to the in-plane Fe-O and out-of-plane Cu-O vibrations, respectively. Both magnetic susceptibility, χ(T), with the applied magnetic field along the c-axis and specific heat capacity reveal the two magnetic phase transition temperatures at low temperatures: TN1 = 13.5 K when transition from paramagnetic (PM) phase to partially disordered antiferromagnetic, and TN2 = 10.5 K when complete transition from partially disordered antiferromagnetic to antiferromagnetic phase. The additional calculation of magnetic entropy change is 0.15, which is roughly close to 0.2, meaning that only 1/5 of the Fe3+ spins are disordered when transforming from PM states to partially disordered at T < TN1 in this study. The presence of instantaneous ferromagnetic spin arrangement (↑↑↓) extends the residence time of H2O on the surface of CFO, facilitating electron exchange with CFO and promoting photocatalytic water splitting reactions.

Towards frustration in Eu(II) Archimedean tessellations.

Self-assembly of trans-{EuI2} nodes and ditopic ligands leads to isoreticular 2D frameworks featuring a rare, non-kagome Archimedean tessellation. The topology and intra-layer Eu(II)-Eu(II) antiferromagnetic interactions provide the prerequisites for geometrical spin frustration, which, due to the spin state degeneracy, is key for novel phenomena such as enhanced magnetic refrigeration.

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.

Unconventional spin frustration due to two competing ferromagnetic interactions of a spin-1/2 Ising-Heisenberg model on martini and martini-diced lattices.

The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattices is exactly solved using a star-triangle transformation, which affords an exact mapping correspondence to an effective spin-1/2 Ising model on a triangular lattice. The ground-state phase diagram of both investigated quantum spin models display two spontaneously ordered ferromagnetic phases and one macroscopically degenerate disordered phase. In contrast to a classical ferromagnetic phase where the spontaneous magnetization of the Ising as well as Heisenberg spins acquire fully saturated values, the spontaneous magnetization of the Heisenberg spins is subject to a quantum reduction to one-third of its saturated value within a quantum ferromagnetic phase. The spontaneous magnetization and logarithmic divergence of the specific heat as the most essential features of both ferromagnetic phases disappear whenever the investigated quantum spin model is driven to the highly degenerate disordered phase. The disordered phase with nonzero residual entropy originates either from a geometric spin frustration caused by antiferromagnetic interactions or more strikingly it may also alternatively arise from a competition of the ferromagnetic Ising and Heisenberg interactions of easy-axis and easy-plane type, respectively. All three available ground states coexist together at a single triple point, around which anomalous magnetic and thermodynamic behavior can be detected.

Geometrical Spin Frustration and Monoclinic-Distortion-Induced Spin Canting in the Double Perovskites Ln2LiFeO6 (Ln = La, Nd, Sm, and Eu) with Unusually High Valence Fe5.

We discovered new B-site-ordered double perovskites Ln2LiFeO6 (Ln = La, Nd, Sm, and Eu) with most likely unusually high valence Fe5+, which was stabilized by strong oxidizing high-pressure synthesis. Despite large antiferromagnetic interactions between Fe5+ spins in these compounds, the magnetic ordering is strongly suppressed due to the geometrical frustration of Fe5+ located in a face-centered cubic lattice. In addition, canted magnetic structures are stabilized only in those with Ln = Sm and Eu, which is most likely due to significant Dzyaloshinskii Moriya interaction caused by large monoclinic structural distortion. These results provide a deep understanding of the structure-property relationships in geometrically frustrated B-site-ordered double perovskites.

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.

Atomistic simulations of the magnetic properties of IrxMn1−x alloys

Iridium manganese (IrMn) is arguably the most important antiferromagnetic material for device applications due to its metallic nature, high N\'eel temperature, and exceptionally high magnetocrystalline anisotropy. Despite its importance, its magnetic properties are poorly understood due to its intrinsic complexity and the interplay between structural and magnetic properties. Here we present a unifying atomistic model of ${\mathrm{Ir}}_{x}{\mathrm{Mn}}_{(1\ensuremath{-}x)}$ alloys which reproduces the key experimental facts of the material, while providing unprecedented understanding of the compositional and structural origins of its magnetic ground state and thermodynamic properties. We find that the N\'eel temperature is strongly dependent on the nature of the ground-state magnetic order which varies with $x$ from a triangular to tetrahedral spin structure, leading to different levels of geometric spin frustration. The N\'eel temperature increases linearly with manganese concentration for the disordered phase, while the ordered phases show a peak for ${\mathrm{Ir}}_{50}{\mathrm{Mn}}_{50}$ followed by a decrease due to increased spin frustration. The ground-state tetrahedral spin structure of the disordered phase is composition independent for manganese concentrations in the 50--95% range, while the degree of spin order varies strongly in the same range. For low manganese concentrations, we find antiferromagnetic spin-glass and ferromagnetic ground-state spin structures. The magnetic anisotropy energy exhibits a complex dependence on the lattice symmetry, presenting easy-plane, cubic, and unconventional symmetries for the principal phases, and a similarly complex variation of magnitude. The complexity of behavior represents a dual blessing and a curse in that the properties of a particular sample depend strongly on the degree of order and composition, while also providing a large state space to engineer an antiferromagnet with optimal symmetry, magnetic anisotropy, and thermal stability. Such effects are important for the future development of nanoscale sensor devices and antiferromagnetic spintronics.

Magnetic interactions in the tripod kagome antiferromagnet Mg2Gd3Sb3O14 probed by static magnetometry and high-field ESR spectroscopy

We report an experimental study of the static magnetization $M(H,T)$ and high-field electron spin resonance (ESR) of polycrystalline \MgGd, a representative member of the newly discovered class of the so-called tripod-kagome antiferromagnets where the isotropic Gd$^{3+}$ spins ($S = 7/2$) form a two-dimensional kagome spin-frustrated lattice. It follows from the analysis of the low-$T$ $M(H)$-curves that the Gd$^{3+}$ spins are coupled by a small isotropic antiferromagnetic (AFM) exchange interaction $|J| \approx$ 0.3\,K. The $M(H,T)$-dependences measured down to 0.5\,K evidence a long-range AFM order at $T_{\text{N}} = 1.7$\,K and its rapid suppression at higher fields $\geq 4$\,T. ESR spectra measured in fields up to 15\,T are analyzed considering possible effects of demagnetizing fields, single-ion anisotropy and spin-spin correlations. While the demagnetization effects due to a large sample magnetization in high fields and its shape anisotropy become relevant at low temperatures, the broadening of the ESR line commencing already at $T\lesssim 30$\,K may indicate the onset of the spin-spin correlations far above the ordering temperature due to the geometrical spin frustration in this compound.

Synthesis and Characterization of Cu(II) and Mixed-Valence Cu(I)Cu(II) Clusters Supported by Pyridylamide Ligands.

A group of copper complexes supported by polydentate pyridylamide ligands H2bpda and H2ppda were synthesized and characterized. The two Cu(II) dimers [CuII2(Hbpda)2(ClO4)2] (1) and [CuII2(ppda)2(DMF)2] (2) were constructed by using neutral ligands to react with Cu(II) salts. Although the dimers showed similar structural features, the second-sphere interactions affect the structures differently. With the application of Et3N, the tetranuclear cluster (HNEt3)[CuII4(bpda)2(μ3-OH)2(ClO4)(DMF)3](ClO4)2 (3) and hexanuclear cluster (HNEt3)2[CuII6(ppda)6(H2O)2(CH3OH)2](ClO4)2 (4) were prepared under similar reaction conditions. The symmetrical and unsymmetrical arrangement of the ligand donors in ligands H2bpda and H2ppda led to the dramatic conformation difference of the two Cu(II) complexes. As part of our effort to explore mixed-valence copper chemistry, the triple-decker pentanuclear cluster [CuII3CuI2(bpda)3(μ3-O)] (5) was prepared. XPS examination demonstrated the localized mixed-valence properties of complex 5. Magnetic studies of the clusters with EPR evidence showed either weak ferromagnetic or antiferromagnetic interactions among copper centers. Due to the trigonal-planar conformation of the trinuclear Cu(II) motif with the μ3-O center, complex 5 exhibits geometric spin frustration and engages in antisymmetric exchange interactions. DFT calculations were also performed to better interpret spectroscopic evidence and understand the electronic structures, especially the mixed-valence nature of complex 5.

Canting Antiferromagnetic Spin-Order (TN = 102 K) in a Monomer Mott Insulator (ET)Ag4(CN)5 with a Diamond Spin-Lattice

Abstract The ET•+ molecules in a charge-transfer salt (ET)Ag4(CN)5 form a three-dimensional diamond spin-lattice with S = 1/2 (ET: bis(ethylenedithio)tetrathiafulvalene), where a geometrical spin-frustration is expected when an appropriate spin interaction is realized. A metallic nature has been proposed for this salt based on both band calculation and electron paramagnetic resonance measurements. We studied the crystal and band structures, optical spectra, resistivity, magnetic, and NMR measurements and found the salt to be a three-dimensional monomer Mott insulator with a resistivity of 1.8 × 102 Ω cm at room temperature (// c), though the calculated band structure showed a Dirac-like semimetallic dispersion. 1H NMR and magnetic susceptibility measurements reveal an antiferromagnetic spin ordering at TN = 102 K, above which characteristic temperature insensitive behaviors of T1−1 and spin susceptibility are observed. A weak ferromagnetism is detected below TN with a spin canting angle of ∼0.01°, possibly arising from a Dzyaloshinskii-Moriya interaction due to a lowering of the crystal symmetry. This is the first example of a weak ferromagnetic three-dimensional diamond spin-lattice among the organic charge-transfer solids.

Substitution Effects on Magnetic Ground States with Geometrical Spin Frustration in Triangular Spin Tubes Formed in CsCrF4 and α-KCrF4

A chemical-impurity substitution in a geometrical spin-frustrated antiferromagnet often produces an unconventional antiferromagnetic state, because the ground states of the pure systems maintain a ...

Dipolar Cairo lattice: Geometrical frustration and short-range correlations

We have studied low-energy configurations in two-dimensional arrays consisting of Ising-type dipolar coupled nanomagnets lithographically defined onto a two-dimensional Cairo lattice, thus dubbed the dipolar Cairo lattice. Employing synchrotron-based photoemission electron microscopy (PEEM), we perform real-space imaging of moment configurations achieved after thermal annealing. These states are then characterized in terms of vertex populations, spin- and emergent magnetic charge correlations, and a topology-enforced emergent ice rule. The results reveal a strong dominance of short-range correlations and the absence of long-range order, reflecting the high degree of geometrical spin frustration present in this example of an artificial frustrated spin system.

A new pnictidehalide with van der Waals host–guest interactions exhibiting both geometric spin frustration and resistive humidity sensitivity

The structure and electric and magnetic properties of a new metal pnictidehalide (Hg6P4)(CrCl6)Cl are reported in detail. The weak van der Waals interactions in its structure are responsible for its geometric spin frustration and good resistive humidity sensitivity.