Effects Of Geometrical Frustration Research Articles

Ferroelectricity from iron valence ordering in rare earth ferrites?

AbstractThe possibility of multiferroicity arising from charge ordering in LuFe2O4 and structurally related rare earth ferrites is reviewed. Recent experimental work on macroscopic indications of ferroelectricity and microscopic determination of coupled spin and charge order indicates that this scenario does not hold. Understanding the origin of the experimentally observed charge and spin order will require further theoretical work. Other aspects of recent research in these materials, such as geometrical frustration effects, possible electric‐field‐induced transitions, or orbital order are also briefly treated.magnified imageBilayer subunit in R Fe2O4 compounds with proposed charge order rendering it polar.(© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Synthesis and magnetic properties of a new series of triangular-lattice magnets, Na2BaMV2O8 (M = Ni, Co, and Mn)

A new series of triangular-lattice magnets, Na2BaMV2O8 (M = Ni, Co, and Mn), are reported. These three compounds crystallize with the Ag2BaMnV2O8 type structure, where the magnetic M2+ ions form a two-dimensional triangular lattice. The magnitude of the exchange interactions in these compounds is moderate because the nonmagnetic VO4 tetrahedra interrupt direct connections between MO6 octahedra. The magnetic susceptibilities of Na2BaNiV2O8 and Na2BaCoV2O8 reveal ferromagnetic transitions at 8.4 and 3.9 K, respectively. In contrast, the magnetic susceptibility of Na2BaMnV2O8 exhibits a broad maximum at around 2.3 K, which suggests antiferromagnetic nearest-neighbour interactions and a significant effect of geometric frustration. The specific heat and magnetization curve of Na2BaMnV2O8 indicate that magnetic long-range ordering appears below 1.5 K.

X-ray Diffraction and Absorption Spectroscopy in Pulsed High Magnetic Fields

Recent results of high-magnetic-field X-ray diffraction and absorption spectroscopy experiments using pulsed magnets are reviewed. Pulsed magnetic fields of up to 30–40 T are utilized. Structural changes induced by magnetic fields in rare-earth intermetallic compounds, transition-metal oxides and low-dimensional quantum spin compounds are presented as results of X-ray diffraction experiments. The structural changes are interpreted by several mechanisms such as the interspin distance dependence of exchange interactions, the symmetry change owing to the geometrical frustration effect, and the Jahn–Teller effect. In addition to the Thomson scattering experiment, a magnetic X-ray scattering experiment on TbB4 has been conducted at 30 T. Regarding X-ray absorption spectroscopy, the valence state transition in magnetic fields is observed in Yb-, Ce-, and Eu-based intermetallic compounds. Magnetic-field-induced changes in the structural and electronic states in transition-metal and rare-earth compounds were inve...

Theories on Frustrated Electrons in Two-Dimensional Organic Solids

Two-dimensional quarter-filled organic solids are a promising class of materials to realize the strongly correlated insulating states called dimer Mott insulator and charge order. In their conducting layer, the molecules form anisotropic triangular lattices, harboring geometrical frustration effect, which could give rise to many interesting states of matter in the two insulators and in the metals adjacent to them. This review is concerned with the theoretical studies on such issue over the past ten years, and provides the systematic understanding on exotic metals, dielectrics, and spin liquids, which are the consequences of the competing correlation and fluctuation under frustration.

Spin-Disorder and Non-Degenerate Energy States in Geometrically Frustrated Materials

We have studied chalcogenide Ni <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , showing geometrical frustration effect. M-H curves at 4.2 K reveal that the disordered spins cannot be rotated completely along the direction of high external field of 5 T, since these spins are strongly constrained in the triangular lattice. H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> increases with increasing Fe concentration, being consistent with the enhanced antiferromagnetic (AFM) spin-spin interactions and the suppressed spin-fluctuation due to the increase in freezing temperature T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> . The specific heat (C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> /T) measurement do not show any phase transformation between 2 and 160 K and there is no clear indication of gap in the temperature dependent C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sub> curve between 0 and 7 T, because the atomic short-range ordering of the strained spin in the geometrically frustrated triangular lattice exists at low temperature. Though typical geometrically frustrated magnet shows degeneracy, Mossbauer analysis at 4.2 K shows that 5D of 3d orbit in the samples studied here is splitted into <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2g</sub> and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2g</sub> , and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2g</sub> is further splitted into singlet and doublet by large electric quadrupole splitting. This suggests that Fe <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2+</sup> ionic state has no absolute degenerate energy states in all samples due to Jahn-Teller effect.

Single-crystal study of the kagome antiferromagnet U3Ru4Al12

A ternary intermetallic compound, U${}_{3}$Ru${}_{4}$Al${}_{12}$ in a single-crystal form, was studied by measurement of susceptibility, magnetization, electrical resistivity, magnetoresistivity, thermopower, and heat capacity, as well as neutron diffraction, revealing that this aluminide is an antiferromagnetically ordered (${T}_{\mathrm{N}}$ $=$ 9.5 K) dense Kondo system (${T}_{\mathrm{K}}$ \ensuremath{\approx} 30 K) with a considerable enhancement of the Sommerfeld coefficient $\ensuremath{\gamma}$(0) of about $200\phantom{\rule{0.28em}{0ex}}{\mathrm{mJ}\phantom{\rule{0.28em}{0ex}}\mathrm{mol}}_{\mathrm{U}}^{\ensuremath{-}1}\phantom{\rule{0.28em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$. The electrical resistivity and thermopower of U${}_{3}$Ru${}_{4}$Al${}_{12}$ show characteristic features of the interplay between anisotropic magnetic exchange, Kondo, and crystal field effects. A pronounced in-plane anisotropy and a unique noncollinear antiferromagnetic structure in the (a,b) hexagonal plane, found by neutron diffraction, are discussed in view of the effect of geometrical frustration caused by the distorted kagome lattice of a Gd${}_{3}$Ru${}_{4}$Al${}_{12}$-type crystal structure. Thus, the overall behavior of U${}_{3}$Ru${}_{4}$Al${}_{12}$ resembles that observed for the orthorhombic compound UCu${}_{5}$In, reported earlier as a spin density wave material.

Magnetic properties and relaxation dynamics of a frustrated Ni7 molecular nanomagnet

The Ni7 nanomagnet represents an ideal model system for investigating the effects of geometrical frustration in magnetic interactions. The Ni ions in the magnetic core are arranged on two corner-sharing tetrahedra and interact through antiferromagnetic exchange couplings. We show that the high degree of frustration leads to a magnetic energy spectrum with large degeneracies which result in unusual static and dynamical magnetic properties. In particular, the relaxation dynamics of the magnetization is characterized by several distinct characteristic times. We also discuss the possible interest of Ni7 for magnetocaloric refrigeration.

Spin cluster operator theory for the kagome lattice antiferromagnet

The spin-1/2 quantum antiferromagnet on the Kagome lattice provides a quintessential example in the strongly correlated electron physics where both effects of geometric frustration and quantum fluctuation are pushed to their limit. Among possible non-magnetic ground states, the valence bond solid (VBS) with a 36-site unit cell is one of the most promising candidates. A natural theoretical framework for the analysis of such VBS order is to consider quantum states on a bond connecting the nearest-neighboring sites as fundamental quantum modes of the system and treat them as effectively independent "bond particles." While correctly describing the VBS order in the ground state, this approach, known as the bond operator theory, significantly overestimates the lowest spin excitation energy. To overcome this problem, we take a next logical step in this paper to improve the bond operator theory and consider extended spin clusters as fundamental building blocks of the system. Depending on two possible configurations of the VBS order, various spin clusters are considered: (i) in the VBS order with staggered hexagonal resonance, we consider one spin cluster for a David star and two spin clusters with each composed of a perfect hexagon and three attached dimers, and (ii) in the VBS order with uniform hexagonal resonance, one spin cluster composed of a David star and three attached dimers. It is shown that the majority of low-energy spin excitations are nearly or perfectly flat in energy. With most of its weight coming from the David star, the lowest spin excitation has a gap much lower than the previous value obtained by the bond operator theory, narrowing the difference against exact diagonalization results.

Regular Packings on Periodic Lattices

We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction φ(d)(X). It is proved to be continuous with an infinite number of singular points X(ν)(min), X(ν)(max), ν = 0, ±1, ±2,…. In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of φ(d)(X) is discussed in the context of geometrical frustration effects, transitions in the contact numbers, and number-theoretical properties. Implications and generalizations for more general packing problems are outlined.

Geometrical frustration effects on charge-driven quantum phase transitions

The interplay of Coulomb repulsion and geometrical frustration on charge-driven quantum phase transitions is explored. The ground state phase diagram of an extended Hubbard model on an anisotropic triangular lattice relevant to quarter-filled layered organic materials contains homogeneous metal, 'pinball' and three-fold charge ordered metallic phases. The stability of the 'pinball' phase occurring for strong Coulomb repulsions is found to be strongly influenced by geometrical frustration. A comparison with a spinless model reproduces the transition from the homogeneous metallic phase to a pinball liquid, which indicates that the spin correlations should play a much smaller role than the charge correlations in the metallic phase close to the charge ordering transition. Spin degeneracy is, however, essential to describe the dependence of the system on geometrical frustration. Based on finite temperature Lanczos diagonalization we find that the effective Fermi temperature scale, T*, of the homogeneous metal vanishes at the quantum phase transition to the ordered metallic phase driven by the Coulomb repulsion. Above this temperature scale 'bad' metallic behavior is found which is robust against geometrical frustration in general. Quantum critical phenomena are not found whenever nesting of the Fermi surface is strong, possibly indicating a first order transition instead. 'Reentrant' behavior in the phase diagram is encountered whenever the 2kF-CDW instability competes with the Coulomb driven three-fold charge order transition. The relevance of our results to the family of quarter-filled materials: theta-(BEDT-TTF)2X is discussed.

Quantum Monte Carlo study of molecular polarization and antiferroelectric ordering in squaric acid crystals

Effects of geometrical frustration and quantum fluctuation are theoretically investigated for the proton ordering in a quasi-two-dimensional hydrogen-bonded system, squaric acid crystal. We elucidate the phase diagram for an effective model, the transverse-field Ising model on a frustrated checkerboard lattice, by using quantum Monte Carlo simulation. A crossover to liquidlike paraelectric state with well-developed molecular polarizations is identified, distinguishably from long-range ordering. Emergence of long-range order from the liquidlike state exhibits peculiar aspects originating from the lifting of quasi-macroscopic degeneracy, such as colossal enhancement of the transition temperature and a vanishingly small anomaly in the specific heat.

Successive Magnetic Phase Transitions of Component Orderings in DyB4

The successive magnetic phase transitions in DyB 4 have been studied in detail by microscopic measurements using resonant X-ray diffraction and neutron scattering. It is shown that the a b -plane component of the magnetic moment is short-range-ordered in the intermediate phase where the c -axis component is long-range-ordered. It is estimated that this short-range order is dynamically fluctuating with a time scale between ∼10 -8 to ∼10 -11 s. Crystal field excitation has also been investigated by inelastic neutron scattering. To qualitatively understand the phase-transition phenomenon, we have studied a simple two-sublattice model with an antiferromagnetic interaction by mean-field calculation. The calculation, though without a quadrupolar interaction, successfully explains the occurrence of double phase transition, magnetic specific heat and entropy, magnetic susceptibility, and the huge elastic softening in the intermediate phase. The general success of the mean-field calculation, except for the short-range order, suggests that there is little effect of geometrical frustration on the macroscopic properties at zero magnetic field.

Magnetic phase diagrams of classical triangular and kagome antiferromagnets

We investigate the effect of geometrical frustration on theH–T phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagomelattices. The phase diagrams for the two models are obtained from large-scale Monte Carlosimulations. For the kagome antiferromagnet, thermal fluctuations are unable to liftdegeneracy completely and stabilize translationally disordered multipolar phases. We find asubstantial difference in the temperature scales of the order by disorder effect related todifferent degeneracy of the low- and the high-field classical ground states in thekagome antiferromagnet. In the low-field regime, the Kosterlitz–Thouless transitioninto a spin-nematic phase is produced by unbinding of half-quantum vortices.

Structural, electronic and magnetic properties of negative thermal expansion material Mn 3Cu 1− xSn xN

We have investigated the structural, electronic and magnetic properties of Mn 3Cu 1− x Sn x N( x=0, 0.5) using first-principles density functional theory within the generalized gradient approximation (GGA) + U schemes. The crystal structure of the compounds is tetragonal crystal for x=0 while it is a cubic crystal for x=0.5. Our spin-polarized calculations give a metallic ground state for the x= 0, 0.5 in agreement with experiments. From the charge density and density of states(DOS), the coupling between Sn 5p with Mn 3d and spin geometrical frustration effect are the main reasons for magnetic transition in Mn 3Cu 1− x Sn x N.

Magnetic frustration effects in uranium intermetallics

The effect of geometrical frustration on the development of the heavy-fermion state and quantum criticality is studied in UAuCu4, UAuPt4, UAu3Ni2 samples through measurements of their magnetic susceptibility, heat capacity, and electrical resistivity. In addition, since lattice disorder can play a large role in defining magnetic properties in frustrated systems, extended X-ray absorption fine structure (EXAFS) data have also been obtained. The local structure results show a strong correlation with the magnetic properties in these samples.

Numerical study of geometrical frustration: From square to triangular lattices

In this work we study the effects of geometrical frustration in square lattice which can be measured by the diagonal hopping integral. In the framework of the Hubbard model, we use quantum Monte Carlo method to calculate spin susceptibility and focus on magnetic fluctuations in this system. We find that in two filling regions, the effects of geometrical frustration are quite different. As a measure of geometrical frustration between square and triangular lattices, the diagonal hopping suppresses the anti-ferromagnetic fluctuation at half filling and enhances ferromagnetic fluctuation at 1.5 filling.

Partial Kondo Screening in Frustrated Kondo Lattice Systems

We investigate the effect of geometrical frustration on the competition between the Kondo coupling and the Ruderman-Kittel-Kasuya-Yosida interaction in Kondo lattice systems. By variational MonteCarlo simulations, we reveal an emergent quantum phase with partial ordering in which the frustration is relieved by forming a magnetic order on a sublattice and leaving the rest in the Kondo screening with spin-singlet formation. The role of quantum fluctuations and spin-charge interplay is elucidated.

Chirality-spin separation in the Hubbard model on the kagome lattice

Effect of geometrical frustration in strongly-correlated metallic region is studied for the Hubbard model on the kagome lattice at half filling by a cluster extension of the dynamical mean-field theory combined with a continuous-time auxiliary-field quantum Monte Carlo method. We find that the electron correlation enhances the spin chirality in both vector and scalar channels. The chirality grows as decreasing temperature and exhibits a peak at a low temperature, indicating a new energy scale under strong correlation. The peak temperature is considerably lower than that for the local spin moment, namely, the characteristic temperatures for the chirality and the local moment are well separated. This is a signature of separation between spin and chiral degrees of freedom in the correlated metallic regime under geometrical frustration.

Quantum Fluctuation and Geometrical Frustration Effects on Electric Polarization

We examine theoretically a possibility of ferroelectricity caused by electronic charge order without inversion symmetry, motivated by layered iron oxides. Quantum electronic models in a paired-triangular lattice are analyzed by utilizing the variational Monte Carlo simulation. Our calculation demonstrates that combined effects of electron transfer between the layers, corresponding to quantum fluctuation between the potential minima, and geometrical frustration promote appearance of an electric polarization. Present results are in contrast to the conventional manner of quantum fluctuation in ferroelectricity.

Yb2(Pd1-xNix)2Sn: Interplay of Geometrical Frustration and Kondo Effect in Quantum Spin System

Single crystals of Yb 2 (Pd 1- x Ni x ) 2 Sn with x =0, 0.1, and 0.2 were prepared to clarify the effects of pressure on Yb 2 Pd 2 Sn which is considered to reside near the quantum critical point. The magnetization and specific heat measurements revealed that their ground states are regarded as an S =1/2 XY-like spin system. Although nondoped Yb 2 Pd 2 Sn shows no magnetic transition down to 0.5 K owing to the Kondo effect, Ni-doped Yb 2 Pd 2 Sn exhibits a distinct magnetic transition. Furthermore, the magnetic susceptibility of Ni-doped Yb 2 Pd 2 Sn exhibits a broad peak in the temperature range higher than the magnetic transition temperature, which is not explained by the S =1/2 Coqblin–Schrieffer model, suggesting the effect of geometrical frustration arising from the characteristic structure of these compounds, i.e., the Shastry–Sutherland lattice.