Strong Geometric Frustration Research Articles

Heavy-fermion behavior of itinerant frustrated systems: β-Mn, Y(Sc)Mn<sub>2</sub>, and LiV<sub>2</sub>O<sub>4</sub>

These three metallic systems do not exhibit any magnetic ordering despite experiments show the existence of localized moments with large antiferromagnetic exchange: this is a consequence of the strong geometric frustration (Y(Sc)Mn_{2} and LiV_{2}O_{4} have the Pyrochlore structure, while beta-Mn has a more complicated frustrated structure). Another common feature is their very large specific heat coefficient \gamma =C/T (420 mJ mole^{-1} K^{-2} for LiV_{2}O_{4}). Several explanations have been proposed for this ''3d heavy fermion behavior'', including a 3d-Kondo effect. However the similarities between the three compounds indicate that frustration plays a big role. We propose a new model which takes into account the existence of two types of 3d-electrons (localized and itinerant) and a frustrated antiferromagnetic exchange between the localized 3d electrons.

Magnets with strong geometric frustration

A non-technical introduction to the theory of magnets with strong geometric frustration is given, concentrating on magnets on corner-sharing (kagome, pyrochlore, SCGO and GGG) lattices. Their rich behaviour is traced back to a large ground-state degeneracy in model systems, which renders them highly unstable towards perturbations. A systematic classification according to properties of their ground states is discussed. Other topics addressed in this overview article include a general theoretical framework for thermal order by disorder; the dynamics of how the vast regions of phase space accessible at low temperature are explored; the origin of the featureless magnetic susceptibility fingerprint of geometric frustration; the role of perturbations; and spin ice. The rich field of quantum frustrated magnets is also touched on.

A polarised neutron scattering study of the magnetic correlations in the kagome antiferromagnet [formula omitted

This paper reports a full three-directional ( XYZ) polarisation analysis study of the short- and long-range order in D 3OFe 3(SO 4) 2(OD) 6 and KFe 3(SO 4) 2(OD) 6 performed on the D7 Diffractometer at the ILL. Both compounds belong to the jarosite family of minerals. The Fe 3+ ions in these materials are arranged in a two-dimensional kagome lattice which exhibits, in the case of antiferromagnetic superexchange, a strong geometric frustration. Only short-range magnetic correlations down to 1.5 K have been observed in the D 3O salt, in contrast to the successive long-range magnetic ordering transitions seen in the K salt at T N1 ≈65 K and T N2 ≈50 K , respectively. The diffuse scattering observed in the deuteronium salt is compared with the theoretical predictions for the magnetic structure factor for a kagome lattice with the nearest-neighbour antiferromagnetic exchange.

Antiferromagnetic ordering in the novel Ho3Ge5 and HoGe1.85 compounds studied by X-ray and neutron diffraction

The crystal structures and magnetic ordering of the novel binary compounds Ho3Ge5 (Y3Ge5structure type, space group Fdd2) and HoGe1.85 (DyGe1.85 structure type, space group Cmcm) have been studied by X-ray and neutron powder diffraction. Both compounds have two rare-earth sites which order simultaneously below TN=6 K for Ho3Ge5 and 12 K for HoGe1.85. Ho3Ge5 orders with the wave vector q=(1/2 1/2 1/2) or with an eightfold cell enlargement (2a×2b×2c) with a canted antiferromagnetic arrangement comprising ten sublattices. The two Ho-sites split into six independent sets (orbits), two for Ho1:8(a) (1, 2) and four for Ho2:16(b) (1′–4′). The two Ho1 orbits have a uniaxial moment arrangement along the z-axis, the four Ho2 orbits have their moments in general directions and two distinct moment values. The ordered moment values at 1.4 K for the three (1, 2), (1′, 2′) and (3′, 4′) Ho-orbits decrease in the sequence μ1=10.3(2) μB/Ho>μ3′=7.3(2) μB/Ho>μ1′=6.1(2) μB/Ho. The opposite relation holds for the tilt angle of the moments away from the z-axis: φ1z=0<φ3z′=47(6)°<φ1z′=56(3)°. The total canted antiferromagnetic structure is described by the triclinic magnetic space group Fs1 and results from the strong geometrical frustration of the Ho moments due to triangular atomic arrangement with negative interactions. HoGe1.85 orders antiferromagnetically below TN=12 K with the wave vector q=(1/2 1/2 0). The two 4(a) Ho-sites order simultaneously with a uniaxial moment arrangement along the z-axis described by the monoclinic magnetic space group C11(21/m)i. At 1.4 K the ordered magnetic moment value is 7.87(6) μB/Ho. A comparison of the magnetic ordering of several studied compounds of the RGe2−δ series is made.

Magnetic ordering in triangulated kagomélattice compound, Cu 9Cl 2(cpa) 6 · nH 2O

A triangulated kagomélattice compound Cu 9Cl 2(cpa) 6 · nH 2O was found to show an anomalous magnetic properties due to strong geometrical frustration. In spite of a strong antiferromagnetic interaction among S = ½ Cu 2+ moments deduced from magnetic susceptibility at high temperatures and the g-factor measured by ESR, no long-range magnetic order was detected down to 2 K. The Curie constant decreases remarkably at low temperatures and the magnetization in an external magnetic field of 38 T amounts to only 0.3 μ B . These facts suggest strongly the reduction in the number of magnetic moments at low temperatures due to the local formation of singlet state.

Spin frustration in Y(Sc)Mn 2

The relaxation rate of muon polarization of Y0.97Sc0.03Mn2 with a magnetic lattice composed of corner‐shared tetrahedrons shows a broad peak around 2.5 K indicating a random spin freezing at low temperatures. The substitution by nonmagnetic Al atoms for 10% Mn atoms raises the spin freezing temperature to 45 K. The present work shows clearly that due to the strong geometrical frustration, the ground state of the system is singlet tetrahedrons mixed with frozen paramagnetic tetrahedrons.

LOW-TEMPERATURE SPECIFIC HEAT OF YMn2 IN THE PARAMAGNETIC AND ANTIFERROMAGNETIC PHASES

The low-temperature specific heat of YMn2 has been measured at applied pressures of 0 to 7.7 kbar. A paramagnetic state is stabilized for moderate values of the applied pressure (of the order of 1.6 kbar). A large linear term in the specific heat, which decreases regularly with increasing pressure, is observed in this phase. It is ascribed to giant spin fluctuations associated with a magnetic-non magnetic instability and a strong geometrical spin frustration.