The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. The authors show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations that only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. The authors illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, the chiral parameter of the constituent molecules that determines the macroscopic pitch of cholesterics is identified. [S0034-6861(99)00255-X] CONTENTS

The nature of the ordering of a quantum spin-1/2 Heisenberg antiferromagnet is considered in the presence of the strong lattice frustration associated with the pyrochlore lattice. A field theory indicates that quantum fluctuations lead to a state having dimerization that has long-range static correlations not in 〈S〉 but rather in 〈S(r)⋅S(r+δ)〉. A sublattice ordering is found that is consistent with results obtained using degenerate perturbation theory to analyze the ground-state manifold.

We develop a microscopic magnetoelectric coupling in Ni3V2O8 (NVO) which gives rise to the trilinear phenomenological coupling used previously to explain the phase transition in which magnetic and ferroelectric order parameters appear simultaneously. Using combined neutron scattering measurements and first-principles calculations of the phonons in NVO, we determine eleven phonons which can induce the observed spontaneous polarization. Among these eleven phonons, we find that a few of them can actually induce a significant dipole moment. Using the calculated atomic charges, we find that the required distortion to induce the observed dipole moment is very small ( 0.001 A) and therefore it would be very difficult to observe the distortion by neutron-powder diffraction. Finally, we identify the derivatives of the exchange tensor with respect to atomic displacements which are needed for a microscopic model of a spin-phonon coupling in NVO and which we hope will be obtained from a fundamental quantum calculation such as LDA+U. We also analyze two toy models to illustrate that the Dzyaloskinskii-Moriya interaction is very important for coexisting of magnetic and ferroelectric order but it is not the only mechanism when the local site symmetry of the system is low enough.

Eight new triterpene glycosides named cimiracemosides A-H, respectively, and eight known triterpene glycosides were isolated from the rhizome extracts of black cohosh (Cimicifuga racemosa). The new compounds were determined by spectral data to be 21-hydroxycimigenol-3-O-alpha-L-arabinopyranoside (1), 21-hydroxycimigenol-3-O-beta-D-xylopyranoside (2), cimigenol-3-O-alpha-L-arabinopyranoside (3), 12beta-acetoxycimigenol-3-O-alpha-L-arabinopyranoside (4), 24-acetylisodahurinol-3-O-beta-D-xylopyranoside (5), 20(S),22(R), 23(S),24(R)-16beta:23;22:25-diepoxy-12beta-acetoxy-3be ta,23, 24-trihydroxy-9,19-cycloanost-7-ene-3-O-beta-D-xylopyranoside (6), 20(S),22(R),23(S),24(R)-16beta:23;22:25-diepoxy-12beta -acetoxy-3beta, 23,24-trihydroxy-9,19-cycloanost-7-en-3-O-alpha-L-arabinopyrano side (7), and 20(S),22(R),23(S), 24(R)-16beta:23;22:25-diepoxy-12beta-acetoxy-3beta,23, 24-trihydroxy-9,19-cycloanostane-3-O-beta-D-xylopyranoside (8).

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Yildirim et al. Reply: The Skanthakumar et al. Comment [1] draws attention to the existing evidence in favor of the noncollinear spin structure of Nd2Cu04 (NCO), and we agree that this evidence is compelling [2]. The aim of our Letter [3] was to understand microscopic origins of

Landau theory and symmetry considerations lead us to propose an explanation for several seemingly paradoxical behaviors of charge ordering (CO) and spin ordering (SO) in the mixed valence compound LuFe 2 O 4 . Both SO and CO are highly frustrated. We analyze a lattice gas model of CO within mean-field theory and determine the magnitude of several of the phenomenological interactions. We show that the assumption of a continuous phase transitions at which CO or SO develops implies that both CO and SO are incommensurate. To explain how ferroelectric fluctuations in the charge-disordered phase can be consistent with an antiferroelectric-ordered phase, we invoke an electron-phonon interaction in which a low-energy (20 meV) zone-center transverse phonon plays a key role. The energies of all the zone center phonons are calculated from first principles. We give a Landau analysis which explains SO and we discuss a model of interactions which stabilizes the SO state, if it is assumed commensurate. However, we suggest a highresolution experimental determination to see whether this phase is really commensurate, as believed up to now. The applicability of representation analysis is discussed. A tentative explanation for the sensitivity of the CO state to an applied magnetic field in field-cooled experiments is given. Landau theory and symmetry considerations lead us to propose an explanation for several seemingly paradoxical behaviors of charge ordering ͑CO͒ and spin ordering ͑SO͒ in the mixed valence compound LuFe 2 O 4 . Both SO and CO are highly frustrated. We analyze a lattice gas model of CO within mean-field theory and determine the magnitude of several of the phenomenological interactions. We show that the assumption of a continuous phase transitions at which CO or SO develops implies that both CO and SO are incommensurate. To explain how ferroelectric fluctuations in the charge-disordered phase can be consistent with an antiferroelectric-ordered phase, we invoke an electron-phonon interaction in which a low-energy ͑20 meV͒ zone-center transverse phonon plays a key role. The energies of all the zone center phonons are calculated from first principles. We give a Landau analysis which explains SO and we discuss a model of interactions which stabilizes the SO state, if it is assumed commensurate. However, we suggest a high-resolution experimental determination to see whether this phase is really commensurate, as believed up to now. The applicability of representation analysis is discussed. A tentative explanation for the sensitivity of the CO state to an applied magnetic field in field-cooled experiments is given. Disciplines Physical Sciences and Mathematics | Physics

Molecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like ferroelectric liquid crystals. This paper will review some recent advances in our understanding of the connection between the chiral geometry of individual molecules and the important phenomenological parameters that determine macroscopic chiral structure. It will then consider chiral structure in columnar systems and propose a new equilibrium phase consisting of a regular lattice of twisted ropes.