## Harris, A. Brooks

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Publication Low-Frequency Response Functions of Random Magnetic Systems(1977-07-01) Harris, A. Brooks; Kirkpatrick, Scott RThe frequencies of long-wavelength spin waves in random magnets are studied through their relation to the static magnetic elastic constants A, the domain-wall stiffness, and (for antiferromagnets) χ⊥, the perpendicular susceptibility. We treat the classical limit of large spin and low temperature. In the case of random dilution A and χ⊥ are evaluated numerically as a function of magnetic concentration p for common lattices. Exact analytic results for the static susceptibility, χ(q), where q is the wave vector, are given for some models of disorder in one dimension and, for higher dimensionality, in the limit of low concentrations of vacancies. One general conclusion is that local fluctuations in the spin magnitude significantly affect χ⊥, causing it to diverge for isotropic random systems in two or fewer dimensions. If critical exponents are defined for p→pc by A~|p−pc|σ, χ⊥~|p−pc|−τ, P~|p−pc|β, and ξ~|p−pc|−ν, where pc is the percolation threshold, P is the percolation probability, and ξ is the correlation length, then our numerical results in three dimensions yield σ=1.6±0.1 and τ=0.5±0.2. A simple physical argument shows that τ≥σ−β+(2−d)ν. Our data are consistent with the possibility that this is an equality. Using mean-field-theory values for the exponents in this relation leads to a critical dimensionality dc=6. We study pc, A, and χ⊥ in diluted YIG and mixed garnets and give a detailed discussion of the regime near angular momentum compensation, where a low-frequency optical mode with both ω∝q and ω∝q2 regimes occurs. Our work contradicts the common assumption of a concentration-independent relationship between Tc and A or D, the spin-wave stiffness. We also present nonlinear calculations which allow us to study the dependence of χ⊥ on magnetic field. Our calculations agree with the experimental results on diluted KMnF3 and K2MnF4 and show that the observed nonlinearity is largely the result of local ferrimagnetic fluctuations. A novel configuration for elastic neutron scattering in the presence of a transverse magnetic field is proposed to permit direct observation of the magnitude and characteristic length scale of these fluctuations.Publication Resistance Fluctuations in Randomly Diluted Networks(1987-03-01) Blumenfeld, Raphael; Meir, Yigal; Aharony, Amnon; Harris, A. BrooksThe resistance R(x,x’) between two connected terminals in a randomly diluted resistor network is studied on a d-dimensional hypercubic lattice at the percolation threshold pc. When each individual resistor has a small random component of resistance, R(x,x’) becomes a random variable with an associated probability distribution, which contains information on the distribution of currents in the individual resistors. The noise measured between the terminals may be characterized by the cumulants Mq(x,x’) of R(x,x’). When averaged over configurations of clusters, M¯q(x,x’)~‖x-x’‖ψ̃(q). We construct low-concentration series for the generalized resistive susceptibility, χ(q), associated with M¯q, from which the critical exponents ψ̃(q) are obtained. We prove that ψ̃(q) is a convex monotonically decreasing function of q, which has the special values ψ̃(0)=DB, ψ̃(1)=ζ̃R, and ψ̃(∞)=1/ν. (DB is the fractal dimension of the backbone, ζ̃R is the usual scaling exponent for the average resistance, and ν is the correlation-length exponent.) Using the convexity property and the accepted values of these three exponents, we construct two approximant functions for ψ(q)=ψ̃(q)ν, both of which agree with the series results for all q>1 and with existing numerical simulations. These approximants enabled us to obtain explicit approximate forms for the multifractal functions α(q) and f(q) which, for a given q, characterize the scaling with size of the dominant value of the current and the number of bonds having this current. This scaling description fails for sufficiently large negative q, when the dominant (small) current decreases exponentially with size. In this case χ(q) diverges at a lower threshold p*(q), which vanishes as q→-∞.Publication Orientational Phases for M3C60(1993-10-15) Yildirim, Taner; Harris, A. Brooks; Mele, Eugene J; Hong, SuklyunThe mechanism of the orientational ordering of C60 in alkali-metal-doped fullerenes M3C60 is studied. Since the M-C60 (M=K,Rb) interactions cause the C60 molecules to assume one of two standard orientations, this model is equivalent to a generalized Ising model on a fcc lattice. The Ising interactions depend on two type of energies: (1) the direct interaction, i.e., the orientationally dependent part of interactions between nearest-neighboring C60 molecules (each carrying charge -3e), and (2) the band energy of the electrons transferred from M+ ions to the C603- ions. It is shown that the contribution to the pairwise interaction from the direct orientational interaction is ferromagnetic and dominantly nearest neighbor. However, contributions from the band (kinetic) energy of the conduction electrons are found to be antiferromagnetic for first- and third-nearest neighbors, ferromagnetic for second- and fourth-nearest neighbors, and negligible for further neighbors. The total first-neighbor interaction is probably antiferromagnetic. a non-negligible four-spin interaction is also obtained. The implication of these results for the orientational structure is discussed.Publication Series Analysis of Randomly Diluted Nonlinear Resistor Networks(1986-09-01) Meir, Yigal; Blumenfeld, Raphael; Aharony, Amnon; Harris, A. BrooksThe behavior of a randomly diluted network of nonlinear resistors, for each of which the voltage-current relationship is |V|=r|I|α, is studied with use of series expansions in the concentration p of conducting bonds on d-dimensional hypercubic lattices. The average nonlinear resistance 〈R〉 between pairs of sites separated by the percolation correlation length, scales as |p-pc|−ζ(α). The exponent ζ(α) was evaluated for 0<α<∞ and d=2, 3, 4, 5, and 6, found to decrease monotonically from the exponent describing the minimal length, at α=0, via that of the linear resistance, at α=1, to the exponent characterizing the singly connected bonds, ξ(∞)≡1. Our results agree with known results for α=0 and α=1, also with recent results for general α at d=6-ε dimensions. The second moment 〈R2〉 was found to diverge as 〈R⟩2 (for all α and d), indicating a scaling form for the probability distribution of R.Publication Possible Néel Orderings of the Kagomé Antiferromagnet(1992-02-01) Harris, A. Brooks; Kallin, Catherine; Berlinsky, A. JohnPossible Néel orderings of antiferromagnetically coupled spins on a kagomé lattice are studied using linear-spin-wave theory and high-temperature expansions. Spin-wave analysis, applied to q=0 (three spins per magnetic unit cell) and to √3 × √3 (nine spins per cell) Néel orderings yield identical excitation spectra with twofold-degenerate linear modes and a dispersionless zero-energy mode. This dispersionless mode is equivalent to an excitation localized to an arbitrary hexagon of nearest-neighbor spins. Second- (J2) and third- (J3) neighbor interactions are shown to stabilize the q=0 state for J2>J3 and the √3 × √3 state for J23. A high-temperature expansion of the spin-spin susceptibility χαβ(q) is performed to order 1/T8, for n-component, classical spins with nearest-neighbor interactions only. To order 1/T7 the largest eigenvalue of the susceptibility matrix is found to be independent of wave vector with an eigenvector that corresponds to the dispersionless mode of the ordered phase. This degeneracy is removed at order 1/T8. For n=0, the q=0 mode is favored; for n=1, the band is flat; and, for n>1, the maximum susceptibility is found for a √3 × √3 excitation. Similar results are found for the three-dimensional pyrochlore lattice. The high-temperature expansion is used to interpret experimental data for the uniform susceptibility and powder-neutron-diffraction spectrum for the kagomé-lattice system SrCr8−xGa4+xO19.Publication Magnetization Measurements of Antiferromagnetic Domains in Sr2Cu3O4Cl2(2001-03-15) Parks, Beth; Kastner, Marc A; Kim, Youngjune; Harris, A. Brooks; Chou, Fangcheng; Entin-Wohlman, Ora; Aharony, AmnonThe Cu3O4 layer in Sr2Cu3O4Cl2 is a variant of the square CuO2 lattice of the high-temperature superconductors, in which the center of every second plaquette contains an extra Cu2+ ion. Whereas the ordering of the spins in the ground-state and the spin-wave excitations of this frustrated spin system are both well understood, we find peculiar behavior resulting from antiferromagnetic domain walls. Pseudodipolar coupling between the two sets of Cu2+ ions results in a ferromagnetic moment, the direction of which reflects the direction of the antiferromagnetic staggered moment, allowing us to probe the antiferromagnetic domain structure. After an excursion to the high fields (>1 T), as the field is lowered, we observe the growth of domains with ferromagnetic moment perpendicular to the field. This gives rise to a finite domain wall susceptibility at small fields, which diverges near 100 K, indicating a phase transition. We also find that the shape of the sample influences the domain-wall behavior.Publication Direct Transition From a Disordered to a Multiferroic Phase on a Triangular Lattice(2007-06-29) Kenzelmann, Michel; Lawes, Gavin J; Harris, A. Brooks; Gašparović, Goran; Broholm, Collin L; Ramirez, Arthur P; Jorge, Guillermo A; Jaime, Marcelo; Park, Sungil; Huang, Qingzhen; Shapiro, Alex Ya; Demianets, L. AWe report the first direct transition from a paramagnetic and paraelectric phase to an incommensurate multiferroic in the triangular lattice antiferromagnet RbFe(MoO4)2. Ferroelectricity is observed only when the magnetic structure has chirality and breaks inversion symmetry. A Landau expansion of symmetry-allowed terms in the free energy demonstrates that chiral magnetic order can give rise to a pseudoelectric field, whose temperature dependence agrees with experiment.Publication Distribution of the Logarithms of Currents in Percolating Resistor Networks. I. Theory(1993-03-01) Aharony, Amnon; Blumenfeld, Raphael; Harris, A. BrooksThe distribution of currents, ib, in the bonds b of a randomly diluted resistor network at the percolation threshold is investigated through a study of the moments of the distribution P^(i2) and the moments of the distribution P(y), where y=-lnib2. For q>qc the qth moment of P^(i2), Mq (i.e., the average of i2q), scales as a power law of the system size L, with a multifractal (noise) exponent ψ̃(q)-ψ̃(0). Numerical data indicate that qc is negative, but becomes small for large L. Assuming that all derivatives ψ̃(q) exist at q=0+, we show that for positive integer k the kth moment, μk, of P(y) is given by μk=(α0 lnL)k{1+[kC1+1/2k(k-1)D1] (lnL)−1+O[(lnL)−2]}, where α0 and D1 (but not C1) are universal constants obtained from ψ̃(q). A second independent argument, requiring an assumed analyticity property of the asymptotic multifractal function, f(α), leads to the same equation for all k. This latter argument allows us to include finite-size corrections to f(α), which are of order (lnL)−1. These corrections must be taken into account in interpreting numerical studies of P(y). We note that data for P(-lni2) seem to show power-law behavior as a function of i2 for small i. Values of the exponents are directly related to the values of qc, and the numerical data in two dimensions indicate it to be small (but probably nonzero). We suggest, in view of the nature of the finite-size corrections in the expression for μk, that the asymptotic regime may not have been reached in the numerical work. For d=6 we find that Mq(L)~(lnL)θ(q), where θ(q)→∞ for q→qc=-1/2.Publication Spin-Wave Excitations and Perpendicular Susceptibility of a Diluted Antiferromagnet Near Percolation Threshold(1985-09-01) Kumar, Deepak; Harris, A. BrooksThe long-wavelength excitations of a diluted antiferromagnet near the percolation threshold pc are studied. Within the hydrodynamic theory, the excitation frequency depends on two parameters, A and χt. A is the stiffness associated with the spatial variation in the staggered magnetization and χt is the perpendicular susceptibility in the ordered state of the antiferromagnet. The critical behavior of A near pc is known. We develop a field-theoretic formalism to calculate χt. We explicitly calculate χt in the mean-field approximation and find that it diverges as |ln(p-pc)|, as the concentration p approaches pc. Some further scaling arguments yield a scaling relation relating the divergence exponent of χt with other known exponents at the percolation critical point.Publication Symmetry Analysis of Multiferroic Co3TeO6(2012-03-12) Harris, A. BrooksA 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.