Effects Of Geometrical Frustration Research Articles

Effects of geometrical frustration on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice

The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ($n \gtrsim 7/4$), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized only for these values of frustration parameters, which lead to the single peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band egde the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.

Real-space investigation of short-range magnetic correlations in fluoride pyrochlores NaCaCo2F7 and NaSrCo2F7 with magnetic pair distribution function analysis

We present time-of-flight neutron total scattering and polarized neutron scattering measurements of the magnetically frustrated compounds NaCaCo$_2$F$_7$ and NaSrCo$_2$F$_7$, which belong to a class of recently discovered pyrochlore compounds based on transition metals and fluorine. The magnetic pair distribution function (mPDF) technique is used to analyze and model the total scattering data in real space. We find that a previously-proposed model of short-range XY-like correlations with a length scale of 10-15 \AA, combined with nearest-neighbor collinear antiferromagnetic correlations, accurately describes the mPDF data at low temperature, confirming the magnetic ground state in these materials. This model is further verified by the polarized neutron scattering data. From an analysis of the temperature dependence of the mPDF and polarized neutron scattering data, we find that short-range correlations persist on the nearest-neighbor length scale up to 200 K, approximately two orders of magnitude higher than the spin freezing temperatures of these compounds. These results highlight the opportunity presented by these new pyrochlore compounds to study the effects of geometric frustration at relatively high temperatures, while also advancing the mPDF technique and providing a novel opportunity to investigate a genuinely short-range-ordered magnetic ground state directly in real space.

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.

High-Pressure Synthesis of the Cobalt Pyrochlore Oxide Pb2Co2O7 with Large Cation Mixed Occupancy.

The novel A2B2O7-type compound Pb2Co2O7 was synthesized at 8 GPa and 1673 K. Synchrotron X-ray diffraction shows a cubic pyrochlore structure with space group Fd3̅m. Rietveld structural analysis reveals a large cation mixed occupancy at both A and B sites by about 40%, the greatest value found in the pyrochlore family. In combination with the X-ray absorption spectroscopy results, the specific chemical composition and charge states are determined to be (Co0.6Pb0.4)3+2(Pb0.6Co0.4)4+2O7, in which both the A-site Co3+ and the B-site Co4+ are low-spin. Due to the tetrahedral geometric frustration effects as well as the random Co4+ and Pb4+ distribution at the B site, spin glassy behavior is well observed following the conventional critical slowing down feature in Pb2Co2O7.

Crystal growth and magnetic properties of a kagomé compound Cs2NaMn3F12

Cs2NaMn3F12, one of manganese based fluorides A2A′Mn3F12 (A=Rb, Cs; A′=Li, Na, K), has been found to exhibit a typical kagomé structure. Here, we report the first successful growth of large-sized single crystals of Cs2NaMn3F12 by means of a hydrothermal method. Good quality of grown crystals is confirmed by the XRD and EDS techniques. Magnetic measurements suggest that Cs2NaMn3F12 possesses an antiferromagnetic ordering at 2.5K and a remarkably geometrical frustration effect in the system.

Magnetic Structure and Quadrupolar Order Parameter Driven by Geometrical Frustration Effect in NdB4

Neutron diffraction experiments have been carried out to characterize the magnetic structures and order parameters in an intermediate phase of NdB4 showing the successive phase transitions at T0 = 17.2 K, TN1 = 7.0 K, and TN2 = 4.8 K. We have revealed the antiferromagnetic ordering with the propagation vectors \(\textbf{q}_{0} = (0,0,0)\), q0 and \(\textbf{q}_{\text{s}1} = (\delta ,\delta ,0.4)\) (δ ∼ 0.14), and q0 and \(\textbf{q}_{\text{s}2} = (0.2,0,0.4)\) in phase II (TN1 < T < T0), phase III (TN2 < T < TN1), and phase IV (T < TN2), respectively. The observed patterns in phase II are successfully explained by postulating a coplanar structure with static magnetic moments in the tetragonal ab-plane. We have found that the magnetic structure in phase II can be uniquely determined to be a linear combination of antiferromagnetic “all-in/all-out”-type (Γ4) and “vortex”-type (Γ2) structures, consisting of a Γ4 main component (77%) with a small amplitude of Γ2 (23%). We propose that the quadrupolar interactio...

Switchable Multiple Spin States in the Kondo description of Doped Molecular Magnets

We show that introducing electrons in magnetic clusters and molecular magnets lead to rich phase diagrams with a variety of low-spin and high-spin states allowing for multiple switchability. The analysis is carried out for a quantum spin-fermion model using the exact diagonalization, and the cluster mean-field approach. The model is relevant for a number of molecular magnets with triangular motifs consisting of transition metal ions such as Cr, Cu and V. Re-entrant spin-state behavior and chirality on-off transitions exist over a wide parameter regime. A subtle competition among geometrical frustration effects, electron itinerancy, and Kondo coupling at the molecular level is highlighted. Our results demonstrate that electron doping provides a viable mean to tame the magnetic properties of molecular magnets towards potential technological applications.

Extensive degeneracy, Coulomb phase and magnetic monopoles in artificial square ice.

Artificial spin-ice systems are lithographically patterned arrangements of interacting magnetic nanostructures that were introduced as way of investigating the effects of geometric frustration in a controlled manner. This approach has enabled unconventional states of matter to be visualized directly in real space, and has triggered research at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite efforts to create an artificial realization of the square-ice model-a two-dimensional geometrically frustrated spin-ice system defined on a square lattice-no simple geometry based on arrays of nanomagnets has successfully captured the macroscopically degenerate ground-state manifold of the model. Instead, square lattices of nanomagnets are characterized by a magnetically ordered ground state that consists of local loop configurations with alternating chirality. Here we show that all of the characteristics of the square-ice model are observed in an artificial square-ice system that consists of two sublattices of nanomagnets that are vertically separated by a small distance. The spin configurations we image after demagnetizing our arrays reveal unambiguous signatures of a Coulomb phase and algebraic spin-spin correlations, which are characterized by the presence of 'pinch' points in the associated magnetic structure factor. Local excitations-the classical analogues of magnetic monopoles-are free to evolve in an extensively degenerate, divergence-free vacuum. We thus provide a protocol that could be used to investigate collective magnetic phenomena, including Coulomb phases and the physics of ice-like materials.

Geometric frustration effects in the spin-1 antiferromagnetic Ising model on the kagome-like recursive lattice: exact results

The antiferromagnetic spin-1 Ising model is studied on the Husimi lattice constructed from elementary triangles with coordination number z = 4. It is found that the model has a unique solution for arbitrary values of the magnetic field as well as for all temperatures. A detailed analysis of the magnetization is performed and it is shown that in addition to the standard plateau-like ground states, the model also contains well-defined single-point ground states related to definite values of the magnetic field. Exact values of the residual entropies for all ground states are found. The properties of the susceptibility and the specific heat of the model are also discussed. The existence of the Schottky-type behavior of the specific heat and the strong magnetocaloric effect for low enough temperatures and for the external magnetic field close to the values at which the single-point ground states exist are identified.

Anomalous Magnetothermopower in a Metallic Frustrated Antiferromagnet.

We report the temperature T and magnetic field H dependence of the thermopower S of an itinerant triangular antiferromagnet PdCrO_{2} in high magnetic fields up to 32T. In the paramagnetic phase, the zero-field thermopower is positive with a value typical of good metals with a high carrier density. In marked contrast to typical metals, however, S decreases rapidly with increasing magnetic field, approaching zero at the maximum field scale for T>70 K. We argue here that this profound change in the thermoelectric response derives from the strong interaction of the 4d correlated electrons of the Pd ions with the short-range spin correlations of the Cr^{3+} spins that persist beyond the Néel ordering temperature due to the combined effects of geometrical frustration and low dimensionality.

Effect of geometrical frustration on inverse freezing.

The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor (J_{1}) and second-neighbor (J_{2}) intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings (J) among clusters. We obtain phase diagrams of temperature versus J_{1}/J in two cases: the absence of J_{2} interaction and the isotropic limit J_{2}=J_{1}, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J_{1}/J in both cases. The J_{1} interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF.

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.

Doping Dependence of Meissner Effect in Triangular-Lattice Superconductors

In the spin-excitation-mediated pairing mechanism for superconductivity, the geometric frustration effects not only the spin configuration but also the superconducting-state properties. Within the framework of the kinetic-energy-driven superconducting mechanism, the doping and temperature dependence of the Meissner effect in triangular-lattice superconductors is investigated. It is shown that the magnetic-field-penetration depth exhibits an exponential temperature dependence due to the absence of the d-wave gap nodes at the Fermi surface. However, in analogy to the dome-like shape of the doping dependence of the superconducting transition temperature, the superfluid density increases with increasing doping in the lower doped regime, and reaches a maximum around the critical doping, then decreases in the higher doped regime.

Ising antiferromagnet on the Archimedean lattices.

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Cooling through quantum criticality and many-body effects in condensed matter and cold gases

This article reviews some recent developments for new cooling technologies in the fields of condensed matter physics and cold gases, both from an experimental and theoretical point of view. The main idea is to make use of distinct many-body interactions of the system to be cooled which can be some cooling stage or the material of interest itself, as is the case in ultracold gases. For condensed matter systems, we discuss magnetic cooling schemes based on a large magnetocaloric effect as a result of a nearby quantum phase transition and consider effects of geometrical frustration. For ultracold gases, we review many-body cooling techniques, such as spin-gradient and Pomeranchuk cooling, which can be applied in the presence of an optical lattice. We compare the cooling performance of these new techniques with that of conventional approaches and discuss state-of-the-art applications.

First order phase transitions in the antiferromagnetic Ising model on a pure Husimi lattice

Abstract The antiferromagnetic spin-1/2 Ising model on the pure Husimi lattice with three sites in the elementary polygon ( p = 3 ) and the coordination number z = 6 is investigated which represents the simplest approximation of the antiferromagnetic Ising model on the regular triangular lattice which takes into account effects of geometric frustration. The region of parameters is found in which two physical phases coexist. In addition, the existence of the first order phase transitions between these two coexisting phases is demonstrated and investigated in detail. A detailed analysis of the magnetization properties of the model is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed.

Effects of geometrical frustration on the spin-glass transition

Randomness and frustration are important for the spin-glass transitions. Ising antiferromagnet on a stacked triangular lattice is a highly frustrated system. Phase diagram is obtained within a cluster approximation for the system with randomness in the interaction between Ising spins. To see the frustration effects, the phase diagram of the antiferromagnet is compared with the corresponding one of the ferromagnet. Spin-glass phase of the antiferromagnet appears much more easily by the randomness than that of the ferromagnet.

ChemInform Abstract: Theories on Frustrated Electrons in Two‐Dimensional Organic Solids

AbstractReview: 112 refs.

Triangular spin tubes with bond randomness

We performed X-ray diffraction, magnetic susceptibility, and magnetization experiments on nonequilateral triangular spin tubes composed of α-KCr1−x Fe x F4 (x = 0∼0.13), which consisted of one-dimensional Heisenberg antiferromagnets coexisting with geometrically-frustrated spin systems with bond randomness. The variation of lattice parameters with x may indicate that the Fe3+ ions constitute the low-spin state (S = 1/2). As a result of analyses of the frustration factor and the spin-flop transition field, we found that the effect of geometrical spin frustration was enhanced and that the magnetic anisotropy was weakened as x was increased. Because these results are remarkably similar to the previous results for α-KCr1−x Al x F4, the effect of the chemical impurity substitutions, whether they are magnetic or nonmagnetic ions, on α-KCrF4 is clearly understood.

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 &amp; Co. KGaA, Weinheim)