Effects Of Geometrical Frustration Research Articles

Magnetic properties of strongly frustrated and correlated systems

While consequences of frustration of magnetic interactions are much studied in localized spin systems, much less studies have been performed on frustrated metallic systems. However, several effects of strong geometrical frustration in metallic correlated system have also been experimentally observed in rare-earth or transition metal compounds: coexistence of magnetic and non-magnetic sites in ordered magnetic structure, heavy fermion behaviour and anomalous Hall effect due to spin chirality are consequences of frustration. An overview of the experimental observations and of the proposed models is given. Other interesting effects due to magnetic frustration in metallic systems, which have been predicted theoretically, are also reviewed.

Geometrical Frustration and Glass Formation

The effect of geometrical frustration in the atomic structure on the formability of bulk metallic glasses is discussed from a general point of view. It is pointed out that there are two distinct and complementing pathways to easy glass formation: stabilizing the glass itself and destabilizing the corresponding crystalline state. While the discussions in the field tend to focus on the first one, the second in fact is a more effective approach. Examples of both will be discussed using soft-sphere, rather than hard-sphere, packing concepts.

Frustration effects in antiferromagnets on planar random graphs

We consider the effect of geometric frustration induced by the random distribution of loop lengths in the ``fat'' graphs of the dynamical triangulations model on coupled antiferromagnets. While the influence of such connectivity disorder is rather mild for ferromagnets in that an ordered phase persists and only the properties of the phase transition are substantially changed in some cases, any finite-temperature transition is wiped out due to frustration for some of the antiferromagnetic models. A wealth of different phenomena is observed: While for the annealed average of quantum gravity some graphs can adapt dynamically to allow the emergence of a N\'eel ordered phase, this is not possible for the quenched average, where a zero-temperature spin-glass phase appears instead. We relate the latter to the behavior of conventional spin-glass models coupled to random graphs.

Substitution effect on the two-dimensional triangular-lattice systemCuCrS2

We have studied the magnetic susceptibility and specific heat of polycrystallineCuCr1−xVxS2, the mothercompound of which, CuCrS2, has a nearly two-dimensional structure in which the triangular-latticeCrS2 layer and the Cu-ion layer are stacked alternately. The temperaturedependence of the magnetic susceptibility revealed that only the Crions have local magnetic moment, and the V ions are nonmagnetic.CuCrS2 shows a long-range antiferromagnetic ordering atTN = 39 K, which is found to be suppressed quickly by the V substitution. Abovex = 0.2, the ordered state is replaced by a spin-glass behaviour with the transition temperatureTg decreasing graduallywith increasing x. Tg is one order of magnitude smaller than the Weiss temperatureθ, implying the dominant effect of geometrical frustration. The specific heatC of the spin-glasssystem, CuCr0.7V0.3S2 (x = 0.3), is found to vary as below 10 K, similarly to those two-dimensional spin-liquid systems.

Charge Fluctuations in Geometrically Frustrated Charge Ordering System

Effects of geometrical frustration in low-dimensional charge ordering systems are theoretically studied, mainly focusing on dynamical properties. We treat extended Hubbard models at quarter-filling, where the frustration arises from competing charge ordered patterns favored by different intersite Coulomb interactions, which are effective models for various charge transfer-type molecular conductors and transition metal oxides. Two different lattice structures are considered: (a) one-dimensional chain with intersite Coulomb interaction of nearest neighbor V_1 and that of next-nearest neighbor V_2, and (b) two-dimensional square lattice with V_1 along the squares and V_2 along one of the diagonals. From previous studies, charge ordered insulating states are known to be unstable in the frustrated region, i.e., V_1 \simeq 2V_2 for case (a) and V_1 \simeq V_2 for case (b), resulting in a robust metallic phase even when the interaction strenghs are strong. By applying the Lanczos exact diagonalization to finite-size clusters, we have found that fluctuations of different charge order patterns exist in the frustration-induced metallic phase, showing up as characteristic low energy modes in dynamical correlation functions. Comparison of such features between the two models are discussed, whose difference will be ascribed to the dimensionality effect. We also point out incommensurate correlation in the charge sector due to the frustration, found in one-dimensional clusters.

High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO3 is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μB (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ2) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO3. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.

Specific heat study on a spin-one-half frustrated diamond chain

The specific heat of S = 1 / 2 frustrated diamond-spin chain has been examined by means of the Green's function theory combined with the Jordan–Wigner transformation, and the particular emphasis is laid on the investigation of the effect of geometric frustration, which is generated by the competition between the exchange interactions along the spin chain. It is found that the interplay between the geometric frustration and quantum effects gives rise to non-trivial behaviors in the curves of the specific heat: in the absence of the external magnetic field, the temperature dependence of the specific heat shows a double-peak structure for different strength of the frustration, and in the presence of the external field, the curves of the specific heat display as a three-peak structure due to the field-induced splitting of the energy levels related to the frustrated spins, which are in good agreement with the exact analytical approach based on the generalized decoration–iteration map method.

Geometric frustration in the class of exactly solvable Ising–Heisenberg diamondchains

Ground-state and finite-temperature properties of the mixed spin- and spin-S Ising–Heisenberg diamond chains are examined within an exact analytical approachbased on the generalized decoration–iteration map. A particular emphasis is laidon the investigation of the effect of geometric frustration, which is generatedby the competition between Heisenberg- and Ising-type exchange interactions.It is found that an interplay between the geometric frustration and quantumeffects gives rise to several quantum ground states with entangled spin states inaddition to some semi-classically ordered ones. Among the most interesting results toemerge from our study one could mention rigorous evidence for quantized plateauxin magnetization curves, an appearance of the round minimum in the thermaldependence of susceptibility times temperature data, double-peak zero-field specific heatcurves, or an enhanced magnetocaloric effect when the frustration comes intoplay. The triple-peak specific heat curve is also detected when applying smallexternal field to the system driven by the frustration into the disordered state.

Theoretical Aspects of Charge Ordering in Molecular Conductors

Theoretical studies on charge ordering phenomena in quarter-filled molecular (organic) conductors are reviewed. Extended Hubbard models including not only the on-site but also the inter-site Coulomb repulsion are constructed in a straightforward way from the crystal structures, which serve for individual study on each material as well as for their systematic understandings. In general the inter-site Coulomb interaction stabilizes Wigner crystal-type charge ordered states, where the charge localizes in an arranged manner avoiding each other, and can drive the system insulating. The variety in the lattice structures, represented by anisotropic networks in not only the electron hopping but also in the inter-site Coulomb repulsion, brings about diverse problems in low-dimensional strongly correlated systems. Competitions and/or co-existences between the charge ordered state and other states are discussed, such as metal, superconductor, and the dimer-type Mott insulating state which is another typical insulating state in molecular conductors. Interplay with magnetism, e.g., antiferromagnetic state and spin gapped state is considered as well. Distinct situations are pointed out: influences of the coupling to the lattice degree of freedom and effects of geometrical frustration which exists in many molecular crystals. Some related topics, such as charge order in transition metal oxides and its role in new molecular conductors, are briefly remarked.

Geometrical magnetic frustration in rare-earth chalcogenide spinels

We have characterized the magnetic and structural properties of the $\mathrm{Cd}{\mathit{Ln}}_{2}{\mathrm{Se}}_{4}$ $(\mathit{Ln}=\mathrm{Dy},\mathrm{Ho})$, and $\mathrm{Cd}{\mathit{Ln}}_{2}{\mathrm{S}}_{4}$ $(\mathit{Ln}=\mathrm{Ho},\mathrm{Er},\mathrm{Tm},\mathrm{Yb})$, spinels. We observe all compounds to be normal spinels, possessing a geometrically frustrated sublattice of lanthanide atoms with no observable structural disorder. Fits to the high-temperature magnetic susceptibilities indicate these materials to have effective antiferromagnetic interactions, with Curie-Weiss temperatures ${\ensuremath{\Theta}}_{\mathrm{W}}\ensuremath{\sim}\ensuremath{-}10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, except $\mathrm{Cd}{\mathrm{Yb}}_{2}{\mathrm{S}}_{4}$ for which ${\ensuremath{\Theta}}_{\mathrm{W}}\ensuremath{\sim}\ensuremath{-}40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The absence of magnetic long-range order or glassiness above $T=1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ strongly suggests that these materials are a different venue in which to study the effects of strong geometrical frustration, potentially as rich in interesting physical phenomena as that of the pyrochlore oxides.

Doping effects of hexagonal manganitesEr1−xYxMnO3with triangular spin structure

We have studied doping effects of hexagonal manganites ${\mathrm{Er}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}\mathrm{Mn}{\mathrm{O}}_{3}$, which are found to have 2D triangular spin structure for all the samples studied here. Upon doping Er at the Y site, the magnetic structure changes gradually from the ${\ensuremath{\Gamma}}_{1}$ representation of $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ to the ${\ensuremath{\Gamma}}_{2}$ representation of $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_{3}$ while the ordered moment remains almost unchanged in magnitude over the whole doping range. Despite the gradual change in the magnetic structure with doping, geometrical frustration effects expected of the 2D triangular spin structure with antiferromagnetic interaction between nearest neighbors show very strong doping dependence. For example, although $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ shows all the signs of Mn moments being geometrically frustrated in the susceptibility and neutron diffraction data, such evidence of frustration effects is nearly absent in $\mathrm{Er}\mathrm{Mn}{\mathrm{O}}_{3}$. We suggest that magnetic coupling along the $c$ axis between Er and Mn moments should be responsible for the drastic doping dependence of the geometrical frustration effects.

Quantum melting of charge order due to frustration in two-dimensional quarter-filled systems

The effect of geometrical frustration in a two-dimensional 1/4-filled strongly correlated electron system is studied theoretically, motivated by layered organic molecular crystals. An extended Hubbard model on the square lattice is considered, with competing nearest neighbor Coulomb interaction, V, and that of next-nearest neighbor along one of the diagonals, V', which favor different charge ordered states. Based on exact diagonalization calculations, we find a metallic phase stabilized over a broad window at V' ~ V even for large Coulomb repulsion strengths as a result of frustrating the charge ordered states. Slightly modifying the lattice geometry relevant to the actual organic compounds does not alter the results, suggesting that this `quantum melting' of charge order is a robust feature of frustrated strongly correlated 1/4-filled systems.

Possible pairing symmetry in the two-dimensional t– J model on square and triangular lattices

To investigate effects of geometrical frustration on the possibility of superconductivity and its pairing symmetry in the strongly correlated electron system, we calculate the high-temperature series for the equal-time pairing correlation in the two-dimensional t– J model on square and triangular lattices. In the square lattice where the d-wave superconductivity is expected in the ground state, it is found that d-wave pairing correlation really grows with lowering the temperature. In the triangular lattice with t > 0 , d-wave pairing correlation also shows an enhancement. Since resonating valence bond (RVB)-like behavior is observed in this case, we speculate that the RVB superconductivity is realized. In contrast, in the case of t < 0 on the triangular lattice, various pairing symmetries compete with each other. Particularly in the low-density region where the Fermi surface is disconnected, we find the possibility of f-wave superconductivity, which seems to be related to the ferromagnetic tendency in small J region.

Spin Frustration and Orbital Order in Vanadium Spinels

We present the results of our theoretical study on the effects of geometrical frustration and the interplay between spin and orbital degrees of freedom in vanadium spinel oxides $A$V$_2$O$_4$ ($A$ = Zn, Mg or Cd). Introducing an effective spin-orbital-lattice coupled model in the strong correlation limit and performing Monte Carlo simulation for the model, we propose a reduced spin Hamiltonian in the orbital ordered phase to capture the stabilization mechanism of the antiferromagnetic order. Orbital order drastically reduces spin frustration by introducing spatial anisotropy in the spin exchange interactions, and the reduced spin model can be regarded as weakly-coupled one-dimensional antiferromagnetic chains. The critical exponent estimated by finite-size scaling analysis shows that the magnetic transition belongs to the three-dimensional Heisenberg universality class. Frustration remaining in the mean-field level is reduced by thermal fluctuations to stabilize a collinear ordering.

Quasiparticle vanishing driven by geometrical frustration

We investigate the single hole dynamics in the triangular t-J model. We study the structure of the hole spectral function, assuming the existence of a 120 magnetic Neel order. Within the self-consistent Born approximation (SCBA) there is a strong momentum and t sign dependence of the spectra, related to the underlying magnetic structure and the particle-hole asymmetry of the model. For positive t, and in the strong coupling regime, we find that the low energy quasiparticle excitations vanish outside the neighbourhood of the magnetic Goldstone modes; while for negative t the quasiparticle excitations are always well defined. In the latter, we also find resonances of magnetic origin whose energies scale as (J/t)^2/3 and can be identified with string excitations. We argue that this complex structure of the spectra is due to the subtle interplay between magnon-assisted and free hopping mechanisms. Our predictions are supported by an excellent agreement between the SCBA and the exact results on finite size clusters. We conclude that the conventional quasiparticle picture can be broken by the effect of geometrical magnetic frustration.

Quantum effects on charge order

Charge ordering in strongly correlated 1/4-filled systems, such as charge transfer organic conductors and transition metal oxides, is discussed from a theoretical point of view. Strong electron-electron Coulomb interaction especially that between neighboring molecules induces Wigner crystal-type charge order, which competes with another insulating state due to strong correlation in these systems, i.e., the dimer Mott insulating state. Based on such idea, new aspects of the charge ordering phenomenon are pointed out, where full quantum mechanical treatments are required. One case is the interplay between electron-phonon interaction leading to a novel co-existence of charge order and spin-Peierls lattice distortion, and the other is the effect of geometrical frustration resulting in a quantum melting of the charge order.

Effect of geometrical frustration on the magnetic properties of the triangular-layer systemTb2C2I2: a neutron diffraction investigation

Powder neutron diffraction on Tb2C2I2 reveals strong resolution-limited magnetic Bragg reflections below 60 K due tocommensurate antiferromagnetic (afm) long range ordering. Between 60 and 85 K themagnetic reflections broaden beyond instrumental resolution and the propagation vectorbecomes incommensurate. Above K magnetic scattering is only seen as a diffuse ridge which we ascribe to short-rangecorrelations within the triangular Tb atom planes. With decreasing temperature anadditional Lorentzian shaped reflection grows on top of the decaying edge of this diffuseridge. We analyse the diffuse scattering by fitting a Warren-type lineshape and aLorentzian shaped Bragg reflection. The results of the fits indicate that, with divergingintra-plane correlations, significant inter-plane afm correlations build up close to 85 K.Above 95 K inter-plane correlations are essentially limited to nearest-neighbour Tb atomdouble layers only.

New issues in zero dimensions: magnetic molecules

Abstract We discuss some major features of isolated magnetic molecules where intermolecular magnetic interactions are negligible and the magnetic properties are determined using a Heisenberg model of intramolecular exchange between a relatively small number of diverse paramagnetic ions. We survey some of the more challenging issues and results that have emerged to date, including the spectrum of excitations, effects of geometric frustration, and critical slowing down of the spin dynamics at low temperatures. Primary attention is given to realizable magnetic molecules.

新機能材料開発と構造科学 ２．新しい構造物性の芽 スピンアイスにおける磁場によって誘起される新しい巨視的縮退

Pyrochlore oxides have attracted much interest because their crystal structures include the corner-sharing tetrahedra. This represents an ideal system for studying the effect of geometrical frustration in the limit of low disorder. Recently, a new class of magnetic state known as“spin ice”is discovered in the pyrochlore rare-earth oxides. Recent our study reveals a new macroscopically degenerate ground state in the spin ice induced by a magnetic field. This is called“kagome ice”.

パイロクロア酸化物超伝導体における構造と物性の特異な相関

Pyrochlore oxides have the general chemical formula A2B2O7 or A2B2O6O', where A is a larger cation and B is a smaller transition metal cation. The ideal pyrochlore structure contains a tetrahedral network called the pyrochlore lattice, which has been studied extensively in order to elucidate the effect of geometrical frustration on the properties of localized spin and itinerant electron systems. Recently, superconductivity was found in Cd2Re2O7 at Tc= 1.0 K for the first time in the family of pyrochlore oxides. Although the mechanism of the superconductivity appears to be conventional, it exhibits unique successive structural phase transitions at high temperatures accompanied by large changes in physical properties. Very recently, new pyrochlore oxides AOs2O6 with A = K, Rb, and Cs were discovered, which show superconductivity at 9.6 K, 6.3 K, and 3.3 K, respectively. Although the nature of superconductivity on these β-pyrochlore superconductors is not clear at the moment, we believe that interesting physics is involved on the basis of electron correlations on the pyrochlore lattice.