arXiv subjects

A. B. Harris

Publications and source records attributed to A. B. Harris.

At least 55 records · Page 3Linked to original sources

arXiv2003

Hidden Symmetries and their Consequences in $t_{2g}$ Cubic Perovskites

The five-band Hubbard model for a $d$ band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e. g. cubic) symmetry. In that case, if the crystal field splitting is large one may consider excitations confined to the lowest threefold degenerate $t_{2g}$ orbital states. When the electron hopping matrix element ($t$) is much smaller than the on-site Coulomb interaction energy ($U$), the Hubbard model can be mapped onto the well-known effective Hamiltonian (at order $t^{2}/U$) derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support long range spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying three-band Hubbard model. Using these symmetries we develop a rigorous Mermin-Wagner construction, which shows that the three-band Hubbard model does not support spontaneous long-range spin order at any nonzero temperature and at any order in $t/U$ -- despite the three-dimensional lattice structure. Introduction of spin-orbit coupling does allow spin ordering, but even then the excitation spectrum is gapless due to a subtle continuous symmetry. Finally we showed that these hidden symmetries dramatically simplify the numerical exact diagonalization studies of finite clusters.

cond-mat.str-el↗

arXiv2003

Unusual Symmetries in the Kugel-Khomskii Hamiltonian

The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between $d^1$ ions having three-fold degenerate $t_{2g}$ orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to the orbital planes, the total number of electrons in $|α>$ orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.

cond-mat.str-el↗

arXiv2002

Rotational and Vibrational Dynamics of Interstitial Molecular Hydrogen

The calculation of the hindered roton-phonon energy levels of a hydrogen molecule in a confining potential with different symmetries is systematized for the case when the rotational angular momentum $J$ is a good quantum number. One goal of this program is to interpret the energy-resolved neutron time of flight spectrum previously obtained for H$_{2}$C$_{60}$. This spectrum gives direct information on the energy level spectrum of H$_2$ molecules confined to the octahedral interstitial sites of solid C$_{60}$. We treat this problem of coupled translational and orientational degrees of freedom a) by construction of an effective Hamiltonian to describe the splitting of the manifold of states characterized by a given value of $J$ and having a fixed total number of phonon excitations, b) by numerical solutions of the coupled translation-rotation problem on a discrete mesh of points in position space, and c) by a group theoretical symmetry analysis. Results obtained from these three different approaches are mutually consistent. The results of our calculations explain several hitherto uninterpreted aspects of the experimental observations, but show that a truly satisfactory orientational potential for the interaction of an H$_2$ molecule with a surrounding array of C atoms has not yet been developed.

cond-mat↗

arXiv2001

Two-Stage Rotational Disordering of a Molecular Crystal Surface: C60

We propose a two-stage mechanism for the rotational surface disordering phase transition of a molecular crystal, as realized in C$_{60}$ fullerite. Our study, based on Monte Carlo simulations, uncovers the existence of a new intermediate regime, between a low temperature ordered $(2 \times 2)$ state, and a high temperature $(1 \times 1)$ disordered phase. In the intermediate regime there is partial disorder, strongest for a subset of particularly frustrated surface molecules. These concepts and calculations provide a coherent understanding of experimental observations, with possible extension to other molecular crystal surfaces.

cond-mat↗

arXiv2000

Neutron Scattering study of Sr_2Cu_3O_4Cl_2

We report a neutron scattering study on the tetragonal compound Sr_2Cu_3O_4Cl_2, which has two-dimensional (2D) interpenetrating Cu_I and Cu_{II} subsystems, each forming a S=1/2 square lattice quantum Heisenberg antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the inter-subsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show that quantum fluctuations lift the degeneracy and cause a 2D Ising ordering of the Cu_{II} subsystem. Due to quantum fluctuations a dramatic increase of the Cu_I out-of-plane spin-wave gap is also observed. The temperature dependence and the dispersion of the spin-wave energy are quantitatively explained by spin-wave calculations which include quantum fluctuations explicitly. The values for the nearest-neighbor superexchange interactions between the Cu_I and Cu_{II} ions and between the Cu_{II} ions are determined experimentally to be J_{I-II} = -10(2)meV and J_{II}= 10.5(5)meV, respectively. Due to its small exchange interaction, J_{II}, the 2D dispersion of the Cu_{II} SLQHA can be measured over the whole Brillouin zone with thermal neutrons, and a novel dispersion at the zone boundary, predicted by theory, is confirmed. The instantaneous magnetic correlation length of the Cu_{II} SLQHA is obtained up to a very high temperature, T/J_{II}\approx 0.75. This result is compared with several theoretical predictions as well as recent experiments on the S=1/2 SLQHA.

cond-mat.str-el↗

arXiv2000

Quantum Fluctuations in the Frustrated Antiferromagnet Sr_2Cu_3O_4Cl_2

Sr_2Cu_3O_4Cl_2 is an antiferromagnet consisting of weakly coupled CuO planes which comprise two weakly interacting antiferromagnetic subsystems, I and II, which order at respective temperatures T_I \approx 390K and T_{II} \approx 40K. Except asymptotically near the ordering temperature, these systems are good representations of the two-dimensional quantum spin 1/2 Heisenberg model. For T< T_{II} there are four low-energy modes at zero wave vector, three of whose energies are dominated by quantum fluctuations. For T_{II} < T < T_I there are two low energy modes. The mode with lower energy is dominated by quantum fluctuations. Our calculations of the energies of these modes (including dispersion for wave vectors perpendicular to the CuO planes) agree extremely well with the experimental results of inelastic neutron scattering (in the accompanying paper) and for modes in the sub meV range observed by electron spin resonance. The parameters needed to describe quantum fluctuations are either calculated here or are taken from the literature. These results show that we have a reasonable qualitative understanding of the band structure of the lamellar cuprates needed to calculate the anisotropic exchange constants used here.

cond-mat.str-el↗

arXiv2000

Direct Observation of the Quantum Energy Gap in S = 1/2 Tetragonal Cuprate Antiferromagnets

Using an electron spin resonance spectrometer covering a wide range of frequency and magnetic field, we have measured the low energy excitations of the S=1/2 tetragonal antiferromagnets, Sr_{2}CuO_{2}Cl_{2} and Sr_{2}Cu_{3}O_{4}Cl_{2}. Our observation of in-plane energy gaps of order 0.1 meV at zero external magnetic field are consistent with a spin wave calculation, which includes several kinds of quantum fluctuations that remove frustration. Results agree with other experiments and with exchange anisotropy parameters determined from a five band Hubbard model.

cond-mat↗

arXiv1999

Molecular Chirality and Chiral Parameters

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We 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 which 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. We 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, we identify the chiral parameter of the constituent molecules which determines the macroscopic pitch of cholesterics.

cond-mat.stat-mech↗

arXiv1998

Quantum Theory of Chiral Interactions in Cholesteric Liquid Crystals

We study the effective chiral interaction between molecules arising from quantum dispersion interactions within a model in which a) the dominant excited states of a molecule form a band whose width is small compared to the average excitation energy and b) biaxial orientational correlation between adjacent molecules can be neglected. Previous treatments of quantum chiral interactions were based on a multipole expansion of the intermolecular interaction. However, because real liquid crystals are composed of elongated molecules, we utilize an expansion in terms of only coordinates transverse to the long molecular axes. We identify two distinct physical limits depending on whether one or both of the interacting molecules are excited in the virtual state. When both molecules are excited, our results are similar to those found previously by van der Meer et al. Previously unidentified terms in which only one molecule is excited involve the interactions of local dipole moments, which exist even when the global dipole moment of the molecule vanishes. We present analytic and numerical results for helical molecules. Our results do not indicate whether the dominant chiral interaction in cholesterics results from quantum or from steric interactions.

cond-mat.soft↗

arXiv1997

Chirality in Liquid Crystals: from Microscopic Origins to Macroscopic Structure

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.

cond-mat.soft↗

arXiv1997

On the Microscopic Origin of Cholesteric Pitch

We present a microscopic analysis of the instability of the nematic phase to chirality when molecular chirality is introduced perturbatively. We show that previously neglected short-range biaxial correlations play a crucial role in determining the cholesteric pitch. We propose an order parameter which quantifies the chirality of a molecule.

cond-mat.soft↗

arXiv1996

A complete devil's staircase in the Falicov-Kimball model

We consider the neutral, one-dimensional Falicov-Kimball model at zero temperature in the limit of a large electron--ion attractive potential, U. By calculating the general n-ion interaction terms to leading order in 1/U we argue that the ground-state of the model exhibits the behavior of a complete devil's staircase.

cond-mat↗

arXiv1996

Complete wetting in the three-dimensional transverse Ising model

We consider a three-dimensional Ising model in a transverse magnetic field, $h$ and a bulk field $H$. An interface is introduced by an appropriate choice of boundary conditions. At the point $(H=0,h=0)$ spin configurations corresponding to different positions of the interface are degenerate. By studying the phase diagram near this multiphase point using quantum-mechanical perturbation theory we show that that quantum fluctuations, controlled by $h$, split the multiphase degeneracy giving rise to an infinite sequence of layering transitions.

cond-mat↗

arXiv1996

Periodic Molecular Arrangements from Space Groups

We demonstrate, using examples from $2$ and $3$-dimensions, a systematic method of finding all possible periodic arrangements of a given molecule or molecules such that the arrangements have the symmetry of a given space group. The technique is based on work by Rabson {\it et.\ al.\}. We give tables of generators which facilitate such work.

cond-mat↗

arXiv1995

Magnetic anisotropies and general on--site Coulomb interactions in the cuprates

This paper derives the anisotropic superexchange interactions from a Hubbard model for excitations within the copper 3d band and the oxygen 2p band of the undoped insulating cuprates. We extend the recent calculation of Yildirim et al. [Phys. Rev. B {\bf VV}, pp, 1995] in order to include the most general on--site Coulomb interactions (including those which involve more than two orbitals) when two holes occupy the same site. Our general results apply when the oxygen ions surrounding the copper ions form an octahedron which has tetragonal symmetry (but may be rotated as in lanthanum cuprate). For the tetragonal cuprates we obtain an easy--plane anisotropy in good agreement with experimental values. We predict the magnitude of the small in--plane aniso

cond-mat↗

arXiv1995

Lifting of Multiphase Degeneracy by Quantum Fluctuations

We study the effect of quantum fluctuations on the multiphase point of the Heisenberg model with first- and second-neighbor competing interactions and strong uniaxial spin anisotropy $D$. By studying the structure of perturbation theory we show that the multiphase degeneracy which exists for $S=\infty$ (i.e., for the ANNNI model) is lifted and that the effect of quantum fluctuations is to stabilize a sequence of phases of wavelength 4,6,8,...~. This sequence is probably an infinite one. We also show that quantum fluctuations can mediate an infinite sequence of layering transitions through which an interface can unbind from a wall.

cond-mat↗

arXiv1995

Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions

This paper contains the details of Phys. Rev. Lett. 73, 2919 (1994) and, to a lesser extent, Phys. Rev. Lett. 72, 3710 (1994). We treat a Hubbard model which includes all the 3d states of the Cu ions and the 2p states of the O ions. We also include spin-orbit interactions, hopping between ground and excited crystal field states of the Cu ions, and rather general Coulomb interactions. Our analytic results for the spin Hamiltonian, H, are corroborated by numerical evaluations of the energy splitting of the ground manifold for two holes on either a pair of Cu ions or a Cu-O-Cu complex. In the tetragonal symmetry case and for the model considered, we prove that H is rotationally invariant in the absence of Coulomb exchange. When Coulomb exchange is present, each bond Hamiltonian has full biaxial anisotropy, as expected for this symmetry. For lower symmetry situations, the single bond spin Hamiltonian is anisotropic at order t**6 for constant U and at order t**2 for nonconstant U. (Constant U means that the Coulomb interaction between orbitals does not depend on which orbitals are involved.)

cond-mat↗

arXiv1994

Replica Symmetry Breaking in the Critical Behaviour of the Random Ferromagnet

We study the critical properties of the weakly disordered $p$-component random Heisenberg ferromagnet. It is shown that if the specific heat critical exponent of the pure system is positive, the traditional renormalization group (RG) flows at dimensions $D=4-\e$, which are usually considered as describing the disorder-induced universal critical behavior, are {\it unstable} with respect to replica symmetry breaking (RSB) potentials as found in spin glasses. It is demonstrated that the RG flows involving RSB potentials lead to fixed points which have the structure known as the 1 step RSB, and there exists a whole spectrum of such fixed points. It is argued that spontaneous RSB can occur due to the interactions of the fluctuating fields with the local non-perturbative degrees of freedom coming from the multiple local minima solutions of the mean-field equations. However, it is not clear whether or not RSB occurs for infinitesimally weak disorder. Physical consequences of these conclusions are discussed.

cond-mat↗