Geometrical Spin Frustration Research Articles

Ultrahigh magnetic field phases in the frustrated triangular-lattice magnet CuCrO2

The magnetic phases of a triangular-lattice antiferromagnet ${\mathrm{CuCrO}}_{2}$ were investigated in magnetic fields along the $c$ axis, $H\ensuremath{\parallel}[001]$, up to 120 T. Faraday rotation and magnetoabsorption spectroscopy were used to unveil the rich physics of magnetic phases. An up-up-down (UUD) magnetic structure phase was observed around 90--105 T at temperatures around 10 K. Additional distinct anomalies adjacent to the UUD phase were uncovered and the $\mathsf{Y}$-shaped and the $\mathsf{V}$-shaped phases are proposed to be viable candidates. These ordered phases emerged as a result of the interplay of geometrical spin frustration, single-ion anisotropy, and thermal fluctuations in an environment of extremely high magnetic fields.

Highly Spin-Frustrated Magnetism in the Topochemically Prepared Triangular Lattice Cluster Magnets Na3 A2 (MoO4 )2 Mo3 O8 (A=In, Sc).

The physical properties of novel cluster-based triangular lattice antiferromagnets Na3 A2 (MoO4 )2 Mo3 O8 (A=In, Sc), synthesized through a topochemical Na-intercalation to nonmagnetic Na2 A2 (MoO4 )2 Mo3 O8 , are reported. The S=1/2 [Mo3 ]11+ clusters form a regular triangular lattice, which gives the magnetic system a strong geometrical spin frustration effect. Despite the strong antiferromagnetic couplings among [Mo3 ]11+ clusters, they show no long-range magnetic orderings down to 0.5 K with the finite residual magnetic entropy. The ground states of Na3 A2 (MoO4 )2 Mo3 O8 have been characterized as a quantum spin liquid, owing to the strong spin frustration of cluster spins on the triangular lattice.

Design and Preparation of a Quantum Spin Liquid Candidate κ-(ET)2Ag2(CN)3 Having a Nearby Superconductivity

Abstract Similar to the first quantum spin liquid (QSL) candidate, κ-(ET)2Cu2(CN)3 (1), newly prepared κ-(ET)2Ag2(CN)3 (2) is a dimer Mott insulator with a QSL ground state at ambient pressure and exhibits metallic and superconducting states next to the QSL state under pressure, where ET is bis(ethylenedithio)tetrathiafulvalene. The packing of the ET dimer, which corresponds to a single spin site (S = 1/2), in 2 is similar to that in 1. Salt 2 afforded a two-dimensional equilateral triangular spin lattice having strong geometrical spin frustration (t′/t = 0.967) similar to 1 (t′/t = 1.09), where t and t′ are the interdimer transfer interactions. The geometric relationship between the spin site and the opening in the anion layer in 2 is considerably different from that in 1, resulting in more dispersed packing of ET dimers, narrower bandwidth W, and larger on-site Coulomb repulsion energy U for 2 than 1. As a consequence, 2 has a higher electron correlation U/W, more robust QSL state for wider pressure range and is allocated far away from the itinerant region compared to those of 1. The narrower bandwidth is consistent with a higher superconducting critical temperature for 2 than 1 under pressure.

Hidden transition in multiferroic and magnetodielectric CuCrO2 evidenced by ac-susceptibility

Ferroelectric polarization, magnetic-field dependence of the dielectric constant and ac and dc magnetizations of frustrated CuCrO2 have been measured. A new spin freezing transition below 32 K is observed which is thermally driven. The nature of the spin freezing is to be a single-ion process. Dilution by the replacements of Cr ions by magnetic Mn ions showed suppression of the spin freezing transition suggesting it to be fundamentally a single-ion freezing process. The observed freezing, which is seemingly associated to geometrical spin frustration, represents a novel form of magnetic glassy behavior.

Interaction of spin-orbital-lattice degrees of freedom: Vibronic state of the corner-sharing-tetrahedral frustrated spin system HoBaFe4O7 by dynamical Jahn-Teller effect

A powder inelastic neutron-scattering study of ${\mathrm{HoBaFe}}_{4}{\mathrm{O}}_{7}$ (HBFO) revealed characteristic magnetic excitations associated with geometrical spin frustration. Dispersionless excitations in energy ($\ensuremath{\omega}$) and wave-vector ($Q$) space are observed at several discrete energies. Some of them can be attributed to crystal-field excitations of ${\mathrm{Ho}}^{3+}$ in octahedral symmetry, but the others are explained instead by the vibronic state of the ${\mathrm{Fe}}^{2+}$ dynamical Jahn-Teller effect with orbit-spin coupling, indicating interaction among the spin, the orbital, and the lattice degree of freedom. The antiferromagnetic HBFO lattice has cubic symmetry, and both ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ reside on corner-sharing tetrahedra with a number ratio of 3:1. Even though ${\mathrm{Fe}}^{2+}$ is a Jahn-Teller active ion in tetrahedral symmetry, the system does not exhibit any static lattice distortion to the lowest temperature studied (4 K). The observed excitations can be understood by considering the dynamical interaction among spin-orbital-lattice degrees of freedom, indicating that spin fluctuation due to the frustration effect induces the dynamical Jahn-Teller effect, although in most cases a Jahn-Teller active ion ${\mathrm{Fe}}^{2+}$ takes the static Jahn-Teller effect in a magnetic oxide system.

Geometric Spin Frustration in Zn1-xNixCr2O4 System

At room temperature, the cubic spinel ZnCr2O4 is known as the typical geometrically frustrated spin system. Upon cooling this compound undergoes a crystal structure change driven by removing the frustrated degenerated states, accompanying with the magnetic ordering. In the tetragonal phase the c-axis is larger than the a-axis. Another spinel compound NiCr2O4 takes the cubic structure above 310 K. Below 310 K NiCr2O4 is tetragonally distorted (c/a < 1) due to cooperative Jahn-Teller ordering. In the previous reports, the geometrical frustrated spin fluctuations still exist in NiCr2O4. In this report we investigated how the geometrical frustration changes and how the ratio of the crystal axis, c/a changes in Zn1-xNixCr2O4 system by the low temperature x-ray diffraction measurement and the SQUID magnetometer.

Strong spin frustration and negative magnetization in LnCu3(OH)6Cl3 (Ln = Nd and Sm) with triangular lattices: the effects of lanthanides.

Herbertsmithite- and kapellasite-type compounds with triangular lattices (i.e. Kagomé) as the most promising candidates for realizing the exotic quantum spin liquid (QSL) state have recently attracted significant attention in condensed matter physics and materials science but are often adversely affected by dimensional imperfections arising from significant cation mixing. Also, interaction mechanisms between the Kagomé lattices and ionic impurities remain unclear. Herein we report on the synthesis, crystal structures and magnetic properties of a new class of kapellasite-type compounds LnCu3(OH)6Cl3 (Ln = Nd and Sm) with two overlapped triangular lattices. These compounds are characterized by the triangular lattices of Cu2+ superimposed by another triangular lattice of paramagnetic Ln3+. The magnetic properties of LnCu3(OH)6Cl3 feature strong spin frustrations as well as antisymmetrical Dzyaloshinskii-Moriya interactions resulting in canted antiferromagnetic ordering with the Néel temperature (TN) of ∼20 K and ∼18 K for NdCu3(OH)6Cl3 and SmCu3(OH)6Cl3, respectively. Moreover, negative magnetization at low temperatures was firstly observed in Kagomé lattice compounds, arising from geometrical spin frustration and competing interactions within two overlapped triangular lattices.

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg distorted diamond chain

The mixed spin-(1,1/2) Ising-Heisenberg model on a distorted diamond chain with the spin-1 nodal atoms and the spin-1/2 interstitial atoms is exactly solved by the transfer-matrix method. An influence of the geometric spin frustration and the parallelogram distortion on the ground state, magnetization, susceptibility and specific heat of the mixed-spin Ising-Heisenberg distorted diamond chain are investigated in detail. It is demonstrated that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and one-half of the saturation magnetization. The temperature dependence of the specific heat may have up to three distinct peaks at zero magnetic field and up to four distinct peaks at a non-zero magnetic field. The origin of multipeak thermal behavior of the specific heat is comprehensively studied.

Geometrical Spin Frustration of Unusually High Valence Fe(5+) in the Double Perovskite La2LiFeO6.

A double perovskite-structure oxide La2LiFeO6 with unusually high-valence Fe(5+) was synthesized using a high-pressure technique. The Li(+) and Fe(5+) ions at the B site in the rhombohedral R3̅ perovskite structure are ordered in a rock salt manner, and the resultant tetrahedral network of Fe(5+) gives geometrical spin frustration, which is consistent with a large frustration index f (|θ|/TN) ≈ 10. Mg(2+) substitution for Li(+) produces Fe(4+) from some Fe(5+) and changes the magnetic properties. The Weiss temperature is increased from -119 to 21 K by the substitution of only 1%, significantly decreasing the frustration index. The geometrical frustration of the Fe(5+) spin sublattice cannot be tolerant for even a very small amount of Fe(4+) disturbance.

New Family of Six Stable Metals with a Nearly Isotropic Triangular Lattice of Organic Radical Cations and Diluted Paramagnetic System of Anions: κ(κ⊥)-(BDH-TTP)4MX4·Solv, where M = CoII, MnII; X = Cl, Br, and Solv = (H2O)5, (CH2X2)

A new family of six paramagnetic metals, namely, κ-(BDH-TTP)4CoCl4·(H2O)5 (I), κ-(BDH-TTP)4Co0.54Mn0.46Cl4·(H2O)5 (II), κ-(BDH-TTP)4MnCl4·(H2O)5 (III), κ⊥-(BDH-TTP)4CoBr4·(CH2Cl2) (IV), κ⊥-(BDH-TTP)4MnBr4·(CH2Cl2) (V), and κ⊥-(BDH-TTP)4MnBr4·(CH2Br2) (VI), has been synthesized and characterized by X-ray crystallography, four-probe conductivity measurements, SQUID magnetometry, and calculations of electronic structure. The newly discovered κ⊥-type packing motif of organic layers differs from the parent κ-type by a series of longitudinal shifts of BDH-TTP radical cations in the crystal structure. Salts I–VI form two isostructural groups: I–III (κ) and IV–VI (κ⊥). Salts I–III are isostructural to the previously discovered κ-(BDH-TTP)2FeIIIX4 (X = Cl, Br) even though the charge of FeX4– anions is half that of the MX42– (M = Co, Mn) anions. The tetrahedral anions are disordered in I–III but completely ordered in IV–VI. The type of included solvent molecule is solely determined by the anion size. The paramagnetic subsystem is effectively spin diluted either by anion disorder (I–III) or by spatial separation (IV–VI). The Weiss constants are virtually zero for all compounds (e.g., θ(III) = 0.0056 K, θ(V) = −0.076 K). Curie constants are dominated by anion paramagnetic centers indicating high spin states 5/2 for MnII and 3/2 for CoII with large spin–orbital coupling. All compounds retain metallic properties down to 4.2 K. There is a magnetic breakdown gap of width (w) in the chiral salts IV–VI: w(IV) > w(V) ≈ w(VI) but no gap in the centrosymmetric salts I–III. Electronic structure calculations at room temperature revealed a nearly isotropic triangular lattice in I–III and a honeycomb lattice in IV–VI with an extreme geometric spin frustration exceeding the level reported for the quantum “spin liquid” κ-(BEDT-TTF)2Cu2(CN)3.

Observation of the influence of dipolar and spin frustration effects on the magnetocaloric properties of a trigonal prismatic {Gd7} molecular nanomagnet.

We report the synthesis and structure of a molecular {Gd7} cage of the formula (iPr2NH2)6[Gd7(μ3-OH)3(CO3)6(O2C t Bu)12] which has crystallographic C3h symmetry. Low temperature specific heat and adiabatic demagnetization experiments (the latter achieving temperatures below 100 mK), lead to the observation of the effects of both intramolecular dipolar interactions and geometric spin frustration. The dipolar interaction leads to a massive rearrangement of energy levels such that specific heat and entropy below 2 K are strongly modified while magnetic susceptibility and magnetization above 2 K are not affected. The consequences of these phenomena for low temperature magnetocaloric applications are discussed.

Electronic and magnetic structures of the ferroelectric compoundPbBaFe2O5

By using first-principles electronic and magnetic as well as ferroelectric property calculations on the ferroelectric compound ${\mathrm{PbBaFe}}_{2}{\mathrm{O}}_{5}$, we find that the ground states of the two ${\mathrm{PbBaFe}}_{2}{\mathrm{O}}_{5}$ phases, the space group $Imma$ and $Pnma$ phases, exhibit an antiferromagnetic structure with a propagation vector $[0,\frac{1}{2},\frac{1}{2}]$ state and the magnetic moment of $3.99 {\ensuremath{\mu}}_{B}$ on Fe atoms, which are in good agreement with neutron diffraction experiments. In addition, we find that this magnetic ordering state is an insulating state with an energy gap of 2.24 (2.62) eV for the $Imma (Pnma)$ phase. These findings can be tested by future optical measurements. Furthermore, the parameters of magnetic exchange coupling are also evaluated to illustrate the nature of frustrated magnetic behaviors based on the localized Heisenberg model. Finally, we discuss whether the presence of an improper geometric spin frustration causes the appearance of ferroelectricity.

Specific Heats of Triangular Spin Tube in Magnetic Fields

In this study, the temperature (T) dependence of specific heat (Cp) is investigated in an equilateral triangular spin tube CsCrF4 above T = 0.38K under several magnetic fields (B). At B = 0 T, no λ-type anomaly of the temperature dependence [Cp(T)] appears over the entire temperature range. However, the DC and AC magnetic susceptibilities exhibit a small anomaly, which is interpreted as an antiferromagnetic phase transition at TN∼4.5K. This difference may indicate that the large magnetic entropy at B = 0 T is spent far below TN, because a large fluctuated spin state due to geometrical spin frustration may have occurred at T = 0K. Under different magnetic fields, the Cp(T)/T curves present shoulders and/or broad peaks above B = 1 T. The electronic specific heat coefficient decreases with increasing B indicating that the magnetic ground state consists of an antiferromagnetic ordered state with large spin fluctuations, rather than a gapless spin-liquid state, and their fluctuations are sensitively suppressed by the magnetic fields.

A three dimensional magnetically frustrated metal-organic framework via the vertices augmentation of underlying net.

In our efforts to fabricate magnetically frustrated materials, a feasible vertices augmentation method was successfully used to construct a 4-fold interpenetrating three dimensional metal-organic framework (MOF) with rare topology by linking [Fe3(μ3-O)(μ-O2CCH3)6](+) triangular moieties through the pure anti,anti acetate ligands. Strong antiferromagnetic interactions were found to exist between the neighboring Fe(III) ions without long-range magnetic ordering above 2.2 K, indicating the strong geometric spin frustration nature of this MOF.

Magnetic domain growth in geometrically frustrated Ising antiferromagnetsCo1−xMgxNb2O6(x=0 and 0.004)as seen via time-resolved neutron diffraction measurements

We have investigated anomalously slow magnetic domain growth in an antiferromagnetic (AF) phase of isosceles triangular lattice Ising antiferromagnets ${\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$ with $x=0$ and 0.004, by means of time-resolved neutron diffraction measurements. Applying the multi-profile-deconvolution analysis to the observed diffraction profiles, we have revealed that time evolutions of spin correlation lengths along the $a$ and $b$ axes, ${\ensuremath{\xi}}_{a}$ and ${\ensuremath{\xi}}_{b}$, are well described by a power-law scaling form of ${\ensuremath{\xi}}_{0\ensuremath{\alpha}}+{L}_{\ensuremath{\alpha}}{(t/{\ensuremath{\tau}}_{\ensuremath{\alpha}})}^{n}$ $(\ensuremath{\alpha}=a,b)$ with a universal growth exponent of $n=0.2$. The characteristic time scale of the domain growth, ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$, was found to exhibit Arrhenius-type temperature dependence in the AF phase. A comparison between the results of the $x=0$ and 0.004 samples has revealed that the nonmagnetic substitution significantly reduces the initial correlation length, ${\ensuremath{\xi}}_{0\ensuremath{\alpha}}$, and the activation energy in the Arrhenius-type temperature dependence of ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$. We have also found that magnetic domain growth in a magnetic-field-induced ferrimagnetic phase also follows the power law with the growth exponent of $n=0.2$. On the basis of these results, we have concluded that the existence of ferromagnetic Ising spin chains running along the $c$ axis and the geometrical spin frustration in the $ab$ plane are the keys to the domain growth kinetics in this system. The former and the latter govern the characteristic time scale and the growth exponent, respectively.

Uniaxial-pressure control of geometrical spin frustration in an Ising antiferromagnetCoNb2O6via anisotropic deformation of the isosceles lattice

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Multiple magnetic interactions in ordered perovskite-structure oxides

Cation ordering in transition-metal oxides often drastically modifies their properties. We focus on A-and-B-site-ordered quadruple perovskite-structure oxides AA'3B2B'2O12, in which transition-metal ions are included at the A', B, and B' sites in an ordered manner. In such compounds A'-A', A'-B, A'-B', and B-B' interactions compete with each other and play important role in giving rise to unusual properties. The A-and-B-site-ordered quadruple perovskite CaCu3Fe2Sb2O12with magnetic Fe3+at the B site and nonmagnetic Sb5+at the B' site was successfully synthesized under a high-pressure and high-temperature condition. The B-site Fe3+spin sublattice adapts a tetrahedral framework and the Fe3+-Fe3+antiferromagnetic interaction causes geometrical spin frustration as seen in the double perovskite Ca2FeSbO6. With the introduction of Cu2+into the A' site, the frustration is relieved by strong antiferromagnetic A'(Cu2+)-B(Fe3+) interaction, leading to a ferrimagnetic ordering below 160 K. When B'-site Sb5+was replaced with Re5+, another A-and-B-site-ordered quadruple perovskite CaCu3Fe2Re2O12was synthesized by a high-pressure technique. The compound contains magnetic Fe3+at the B site and Re5+at the B' sites, and strong antiferromagnetic A'(Cu2+)-B'(Re5+) interaction overcomes the A'(Cu2+)-B(Fe3+) interaction, leading to a ferrimagnetism with the ferromagnetic A'(Cu2+)-B(Fe3+) spin arrangement below 550 K. More importantly, the electronic structure of CaCu3Fe2Re2O12is half metallic and the compound shows large magnetoresistance by the spin-dependent transport.

Geometrical spin frustration in Pr5Ni2Si3 composed of triangular crystal lattices

We have studied the transport, magnetic and thermal properties of Pr5Ni2Si3 with complex triangular lattices under various magnetic fields. The ferromagnetic transitions in the basal plane were observed at TC1 = 52 K and TC2 = 65 K. A decrease in magnetization below 30 K and the reduced paramagnetic Curie temperature θP are indicative of the development of antiferromagnetic correlation. These features are well understood by the frustration effect of the magnetic moments of Pr ions which constitute the triangular structural unit. The frustration caused the rapid rise of electrical resistivity below 30 K and an enormous entropy in low-temperature regions. The antiferromagnetic correlation acting between the frustrated Pr ions never causes any long-range order down to 0.6 K.

Unusual spin fluctuations and magnetic frustration in olivine and non-olivine LiCoPO4detected byP31andLi7nuclear magnetic resonance

We report $^{31}\mathrm{P}$ and $^{7}\mathrm{Li}$ nuclear magnetic resonance (NMR) studies in new non-olivine LiZnPO${}_{4}$-type LiCoPO${}_{4}^{\mathrm{tetra}}$ microcrystals, where the Co${}^{2+}$ ions are tetrahedrally coordinated. Olivine LiCoPO${}_{4}$, which was directly transformed from LiCoPO${}_{4}^{\mathrm{tetra}}$ by an annealing process, was also studied and compared. The uniform bulk magnetic susceptibility and the $^{31}\mathrm{P}$ Knight shift obey the Curie-Weiss law for both materials with a high spin Co${}^{2+}$ ($3{d}^{7}$, $S=3/2$), but the Weiss temperature $\ensuremath{\Theta}$ and the effective magnetic moment ${\ensuremath{\mu}}_{\mathrm{eff}}$ are considerably smaller in LiCoPO${}_{4}^{\mathrm{tetra}}$. The spin-lattice relaxation rate ${T}_{1}^{\ensuremath{-}1}$ reveals a quite different nature of the spin dynamics in the paramagnetic state of both materials. Our NMR results imply that strong geometrical spin frustration occurs in tetrahedrally coordinated LiCoPO${}_{4}$, which may lead to the incommensurate magnetic ordering.

Geometrical Spin Frustration and Ferromagnetic Ordering in (MnxPb2–x)Pb2Sb4Se10

Engineering the atomic structure of an inorganic semiconductor to create isolated one-dimensional (1D) magnetic subunits that are embedded within the semiconducting crystal lattice can enable chemical and electronic manipulation of magnetic ordering within the magnetic domains, paving the way for (1) the investigation of new physical phenomena such as the interactions between electron transport and localized magnetic moments at the atomic scale and (2) the design and fabrication of geometrically frustrated magnetic materials featuring cooperative long-range ordering with large magnetic moments. We report the design, synthesis, crystal structure and magnetic behavior of (MnxPb2-x)Pb2Sb4Se10, a family of three-dimensional manganese-bearing main-group metal selenides featuring quasi-isolated [(MnxPb2-x)3Se30]∞ hexanuclear magnetic ladders coherently embedded and uniformly distributed within a purely inorganic semiconducting framework, [Pb2Sb4Se10]. Careful structural analysis of the magnetic subunit, [(MnxPb2-x)3Se30]∞ and the temperature dependent magnetic susceptibility of (MnxPb2-x)Pb2Sb4Se10, indicate that the compounds are geometrically frustrated 1D ferromagnets. Interestingly, the degree of geometrical spin frustration (f) within the magnetic ladders and the strength of the intrachain antiferromagnetic (AFM) interactions strongly depend on the concentration (x value) and the distribution of the Mn atom within the magnetic substructure. The combination of strong intrachain AFM interactions and geometrical spin frustration in the [(MnxPb2-x)3Se30]∞ ladders results in a cooperative ferromagnetic order with exceptionally high magnetic moment at around 125 K. Magnetotransport study of the Mn2Pb2Sb4Se10 composition over the temperature range from 100 to 200 K revealed negative magnetoresistance (NMR) values and also suggested a strong contribution of magnetic polarons to the observed large effective magnetic moments.