DOMAIN WALLS IN THE QUANTUM TRANSVERSE ISING MODEL

We discuss several problems concerning domain walls in the spin $S$ Ising model at zero temperature in a magnetic field, $H/(2S)$, applied in the $x$ direction. Some results are also given for the planar ($y$-$z$) model in a transverse field. We treat the quantum problem in one dimension by perturbation theory at small $H$ and numerically over a large range of $H$. We obtain the spin density profile by fixing the spins at opposite ends of the chain to have opposite signs of $S_z$. One dimension is special in that there the quantum width of the wall is proportional to the size $L$ of the system. We also study the quantitative features of the `particle' band which extends up to energies of order $H$ above the ground state. Except for the planar limit, this particle band is well separated from excitations having energy $J/S$ involving creation of more walls. At large $S$ this particle band develops energy gaps and the lowest sub-band has tunnel splittings of order $H2^{1-2S}$. This scale of energy gives rise to anomalous scaling with respect to a) finite size, b) temperature, or c) random potentials. The intrinsic width of the domain wall and the pinning energy are also defined and calculated in certain limiting cases. The general conclusion is that quantum effects prevent the wall from being sharp and in higher dimension would prevent sudden excursions in the configuration of the wall.Comment: 40 pages and 13 figures, Phys. Rev. B, to be publishe

Longitudinal Dynamical Susceptibility of the Heisenberg Ferromagnet at Short Wavelengths and Low Temperatures

The longitudinal dynamical susceptibility of the Heisenberg ferromagnet is studied at short wavelengths and low temperatures. It is shown that identical results to order 1/S are obtained using (a) a spin decoupling technique, (b) a diagrammatic method using the Holstein-Primakoff transformation, and (c) a diagrammatic method using the Dyson-Maleev transformation. We thus conclude that there are no significant kinematic effects at low temperatures. Using the random-phase approximation, we find that the Dyson-Maleev interactions between magnons are too weak to support the existence of a zero-sound mode. Both these conclusions disagree with the recent results of other authors

Low‐Temperature Properties of a Heisenberg Antiferromagnet

It is shown how the propagator formalism can be used to obtain the low‐temperature expansion of the free energy of an isotropic Heisenberg antiferromagnet. The lowest‐order terms in such an expansion can be calculated using the proper self‐energy evaluated at zero temperature. The analytic properties of this quantity are investigated by expressing it in terms of time ordered diagrams. The low‐temperature expansion of the free energy is shown to be of the form AT 4+BT 4+CT 8, where A, B, and C are given by Oguchi correctly to order 1/S. For spin ½ the term in 1/S 2 gives a 2% reduction in A for a body‐centered lattice

Ferroelectricity Induced by Incommensurate Magnetism (Invited)

Ferroelectricity has been found to occur in several insulating systems, such as TbMnO3 and Ni3V2O8 which have more than one phase with incommensurately modulated long-range magnetic order. Here we give a phenomenological model which relates the symmetries of the magnetic structure as obtained from neutron diffraction to the development and orientation of a spontaneous ferroelectric moment induced by the magnetic ordering. This model leads directly to the formulation of a microscopic spin-phonon interaction which explains the observed phenomena. The results are given in terms of gradients of the exchange tensor with respect to generalized displacements for the specific example of NVO. It is assumed that these gradients will now be the target of first-principles calculations using the LDA+U or related scheme

Scaling of the Negative Moments of the Harmonic Measure in Diffusion-Limited Aggregates

It is shown that, unlike the case of the distribution of currents in a random resistor network, all negative moments of the harmonic measure in diffusion-limited aggregates exhibit power-law scaling with sample size

Phase Locking in the Heisenberg Helimagnet

The commensurability energy ΔE is calculated for a Heisenberg helimagnet whose wavelength is three lattice constants at zero temperature with a small but nonzero uniform field applied in the plane of polarization of the spins. It is shown that ΔE=0 for classical spins but ΔE≠0 for quantum spins when spin‐wave interactions are considered

Effect of Dipolar Interactions on the Spin-Wave Spectrum of a Cubic Antiferromagnet

The effect of dipolar interactions on the spin-wave spectrum of a cubic antiferromagnet is studied. The spin-wave spectrum is found to consist of two branches whose frequencies are (ℏω)2=(gβ)2[HA+HEa2k2][HA+HE(2−a2k2)−8πM/3+8πM sin2∂k] and (ℏω)2=(gβ)2[HA+HEa2k2][HA+HE(2−a2k2)−8πM/3]. Here a is the lattice constant, M the magnetic moment per unit volume, k the wave vector, θk the angle between the magnetization and the wave vector, and HA and HE the anisotropy and exchange fields. The reasons for discrepancies between these formulas and those given previously by other authors are discussed

Exact Solution of a Model of Localization

The exact solution is presented for the susceptibility, χ (the number of sites covered by the maximally extended eigenfunction), for the zero-energy solutions of a hopping model on a randomly dilute Cayley tree. If p is the concentration, then χ~(p*−p)−1 with p*~pce1/ξ1, where pc is the critical percolation concentration and ξ1 the one-dimensional localization length. This result is argued to hold for the dilute quantum Heisenberg antiferromagnet at zero temperature

Field-Theoretic Formulation of the Randomly Diluted Nonlinear Resistor Network

A field-theoretic formulation is used to describe the resistive properties of a randomly diluted network consisting of nonlinear conductances for which V~Ir. The nonlinear resistance R(x,x’) between sites x and x’ is expressed in terms of an analytic continuation in an associated crossover field. The renormalization-group recursion relations are analyzed within this analytic continuation to order ε=6-d, where d is the spatial dimension. For r near unity a perturbative calculation to first order in (r-1) agrees with both the result obtained here for general r and with the approximate relation proposed by de Arcangelis et al. between the nonlinear conductivity and the noise characteristics of a linear network. For arbitrary r and d a generalization of this perturbative treatment gives (r+1)dφ(r)/dr=∂ψ(q,r)/∂q‖q=1, where φ(r) is the resistance crossover exponent and ψ(q,r) a generalized noise crossover exponent associated with ‖∂R/∂σb‖q, both quantities referred to the nonlinear system, where σb is the conductance of an individual bond. For r not near unity our results to first order in ε for φ(r) and ψ(q,r) satisfy the above relation but not that of de Arcangelis et al. For q=0, ψ(q,r)/νp is the fractal dimension of the backbone, where νp is the correlation length exponent for percolation. As is known, φ(0)/νp is an exponent associated with the chemical length, for which our result agrees with that given by Cardy and Grassberger and by Janssen

Relaxation in Antiferromagnets Due to Spin‐Wave Interactions

For an antiferromagnet it is shown that within perturbation theory the Holstein‐Primakoff and Dyson‐Maleev transformations do not lead to identical results for either the static or dynamic properties. By examining the spin Green\u27s functions we justify the use of the Dyson‐Maleev transformation when there are few spin waves present. Using second‐order perturbation theory we find the antiferromagnetic resonance line-width to be Δω0=(64ωAω0/π3S2ωE)(kT/ℏωE)2exp(−ℏω0/kT)  for  kT≪ℏω0 and Δω0=[40ωAζ(3)/π3S2](kT/ℏωE)3  for  ℏω0≪kT≪ℏωE, in qualitative agreement with the experimental results for MnF2