Harris, A. Brooks

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2006 - 200982010 - 20125
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  • Publication
    Comment on "Ferroelectricity in Spiral Magnets"
    (2008-02-28) Kenzelmann, M.; Harris, A. Brooks
  • Publication
    Symmetry analysis for the Ruddlesden-Popper systems Ca3Mn2O7 and Ca3Ti2O7
    (2011-08-24) Harris, A. Brooks
    We perform a symmetry analysis of the zero-temperature instabilities of the tetragonal phase of Ca3Mn2O7 and Ca3Ti2O7 which is stable at high temperature.We introduce order parameters to characterize each of the possible lattice distortions to construct a Landau free energy which elucidates the proposed group-subgroup relations for structural transitions in these systems. We include the coupling between the unstable distortion modes and the macroscopic strain tensor. We also analyze the symmetry of the dominantly antiferromagnetic ordering which allows weak ferromagnetism. We show that in this phase the weak ferromagnetic moment and the spontaneous ferroelectric polarization are coupled, so that by rotating one of these orderings by applying an external electric or magnetic field one can rotate the other ordering.We discuss the number of different domains (including phase domains) which exist in each of the phases and indicate how these may be observed. First-principles calculations of Yildirim corroborate our assertion that domain walls in the nonferroelectric phase are narrow.
  • Publication
    Effect of Inversion Symmetry on the Incommensurate Order in Multiferoic RMn2O5 (R = Rare Earth)
    (2008-07-03) Harris, A. Brooks; Kenzelmann, M.; Aharony, Amnon; Entin-Wohlman, Ora
    Starting from the irreducible representations of the group of the wave vector, we construct the spin-wave functions consistent with inversion symmetry, neglected in the usual representation analysis. We obtain the relation between the basis functions of different members of the star of the wave vector. We introduce order parameters and determine their transformation properties under the operations of the space group of the paramagnetic crystal. The results are applied to construct terms in the magnetoelectric interaction, which are quadratic and quartic in the magnetic order parameters. The higher-order magnetoelectric interactions can in principle induce components of the spontaneous polarization, which are not allowed by the lowest-order magnetoelectric interaction. We also obtain the relation between the spin-wave functions of the incommensurate phase and those of the commensurate phase, which lead to analogous relations between the order parameters of these two phases.
  • Publication
    Order Parameters and Phase Diagram of Multiferroic RMn2O5
    (2008-05-30) Harris, A. Brooks; Aharony, Amnon; Entin-Wohlman, Ora
    The generic magnetic phase diagram of multiferroic RMn2O5 (with R = Y, Ho, Tb, Er, Tm), which allows different sequences of ordered magnetic structures for different R’s and different control parameters, is described using order parameters which explicitly incorporate the magnetic symmetry. A phenomenological magnetoelectric coupling is used to explain why some of these magnetic phases are also ferroelectric. Several new experiments, which can test this theory, are proposed.
  • Publication
    Charge and Spin Ordering in the Mixed-Valence Compound LuFe2O4
    (2010-04-15) Harris, A Brooks; Yildirim, Tanner
    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 LuFe2O4. 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 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.
  • Publication
    Multiple Species of Noninteracting Molecules Adsorbed on a Bethe Lattice
    (2008-10-15) Cohen, Michael; Harris, A. Brooks
    A simple method, previously used to calculate the equilibrium concentration of dimers adsorbed on a Bethe lattice as a function of the dimer activity, is generalized to solve the problem of a Bethe lattice in contact with a reservoir containing a mixture of molecules. The molecules may have arbitrary sizes and shapes consistent with the geometry of the lattice and the molecules do not interact with one another except for the hard-core restriction that two molecules cannot touch the same site. We obtain a set of simultaneous nonlinear equations, one equation for each species of molecule, which determines the equilibrium concentration of each type of molecule as a function of the (arbitrary) activities of the various species. Surprisingly, regardless of the number of species, the equilibrium concentrations are given explicitly in terms of the solution of a single equation in one unknown which can be solved numerically, if need be. Some numerical examples show that increasing the activity of one species need not necessarily decrease the equilibrium concentration of all other species. We also calculate the adsorption isotherm of an “annealed” Bethe lattice consisting of two types of sites which differently influence the activity of an adsorbed molecule. We prove that if the reservoir contains a finite number of molecular species, regions of two different polymer densities cannot simultaneously exist on the lattice. The widely used Guggenheim theory of mixtures, which can also be construed as a theory of adsorption, assumes for simplicity that the molecules in the mixture are composed of elementary units, which occupy sites of a lattice of coordination number q. Guggenheim’s analysis relies on approximate combinatorial formulas which become exact on a Bethe lattice of the same coordination number, as we show in an appendix. Our analysis involves no combinatorics and relies only on recognizing the statistical independence of certain quantities. Despite the nominal equivalence of the two approaches, the easily visualized properties of the Bethe lattice enable one to solve some apparently difficult problems by quite elementary methods.
  • Publication
    Landau Analysis of the Symmetry of the Magnetic Structure and Magnetoelectric Interaction in Multiferroics
    (2007-08-28) Harris, A. Brooks
    This paper presents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets, including Ni3V2O8, TbMnO3, MnWO4, TbMn2O5, YMn2O5, CuFeO2, and RbFe(MO4)2. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex-valued magnetic order parameters whose transformation properties are displayed. In so doing, we use the previously proposed technique to exploit inversion symmetry, since this symmetry has seemingly been universally overlooked. Inversion symmetry severely reduces the number of fitting parameters needed to describe the spin structure, usually by fixing the relative phases of the complex fitting parameters. By introducing order parameters of known symmetry to describe the magnetic ordering, we are able to construct the trilinear magnetoelectric interaction which couples incommensurate magnetic order to the uniform polarization, and thereby we treat many of the multiferroic systems so far investigated. In most cases, the symmetry of the magnetoelectric interaction determines the direction of the magnetically induced spontaneous polarization. We use the Landau description of the magnetoelectric phase transition to discuss the qualitative behavior of various susceptibilities near the phase transition. The consequences of symmetry for optical properties such as polarization induced mixing of Raman and infrared phonons and electromagnons are analyzed. The implication of this theory for microscopic models is discussed.
  • Publication
    SpinWaves in the Frustrated Kagomé Lattice Antiferromagnet KFe3(OH)6(SO4)2
    (2006-06-19) Matan, Kittiwit; Grohol, Daniel; Yildirim, Taner; Nocera, Daniel G.; Harris, A. Brooks; Lee, Seunghun H.; Nagler, Stephen E.; Lee, Young S
    The spin wave excitations of the S = 5/2 kagomé lattice antiferromagnet KFe3(OH)6(SO4)2 have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted ‘‘zero energy mode,’’ verifying a fundamental prediction for the kagomé lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin wave data. The antisymmetric Dzyaloshinskii-Moriya interaction is the primary source of anisotropy and explains the low-temperature magnetization and spin structure.
  • Publication
    Symmetry Analysis of Multiferroic Co3TeO6
    (2012-03-12) Harris, A. Brooks
    A phenomenological explanation of the magnetoelectric behavior of Co3TeO6 is developed. We explain the second harmonic generation data and the magnetic field induced spontaneous electric polarization in the magnetically ordered phase below 20 K.
  • Publication
    Landau Theory of Tilting of Oxygen Octahedra in Perovskites
    (2012-05-18) Harris, A. Brooks
    The list of possible commensurate phases obtained from the parent tetragonal phase of Ruddlesden-Popper (RP) systems, An+1BnC3n+1 for general n due to a single phase transition involving the reorienting of octahedra of C (oxygen) ions is reexamined using a Landau expansion. This expansion allows for the nonlinearity of the octahedral rotations and the rotation-strain coupling. It is found that most structures allowed by symmetry are inconsistent with the constraint of rigid octahedra, which dictates the form of the quartic terms in the Landau free energy. For A2BC4 our analysis allows only 10 of the 41 structures which satisfy the general symmetry arguments of Hatch et al. [Phys. Rev. B 39, 9282 (1989)]. The symmetry of rotations for RP systems with n > 2 is clarified. Our list of possible structures for general n excludes many structures allowed in previous studies.