Measurement of the ${\mathit{A}}_1$(TO) soft-polariton mode in ${\mathrm{KTa}}_{0.93}$${\mathrm{Nb}}_{0.07}$${\mathrm{O}}_3$ has been made as a function of wave vector and temperature by means of a time-resolved third-order optical susceptibility technique. With the use of a polariton model calculation, the ${\mathit{A}}_1$(TO) soft-phonon mode self-energy wave-vector dependence, the Raman tensor, and the electro-optic tensor are inferred. The results indicate the particularity of the soft-phonon mode dynamics in the polariton region. The soft-phonon self-energy shows the presence of a four-particle interaction relaxation process and of an additional relaxation process associated with the intercluster dynamics, while the Raman and electro-optic tensor behavior as a function of temperature indicates the predominance of the electromagnetic interaction in the soft-phonon mode dynamics close to ${\mathit{T}}_{\mathit{c}}$.

Results obtained from optical absorption measurements on ${\mathrm{Nd}}^{3+}$:${\mathrm{Y}}_3$${\mathrm{Al}}_5$${\mathrm{O}}_{12}$ (Nd:YAG) at 10 and 29 K are reported and analyzed. The low-temperature (10 K) absorption spectrum shows transitions from the lowest Stark component of the ${}_{}{}^4{}_{}{}^{}$${\mathit{I}}_{9/2}$ (ground) multiplet to 133 of the 155 crystal-field (Stark) levels predicted to be located between 3900 and 40 000 ${\mathrm{cm}}^{\mathrm{-}1}$, spanning 35 excited multiplet manifolds of ${\mathrm{Nd}}^{3+}$(4${\mathit{f}}^3$). Among the 133 transitions observed in the 10-K absorption spectrum, 97 are sufficiently well resolved to permit quantitative determination of transition line strengths. Energy levels for the ${}_{}{}^4{}_{}{}^{}$${\mathit{I}}_{9/2}$ and ${}_{}{}^4{}_{}{}^{}$${\mathit{I}}_{11/2}$ multiplets are taken from previously obtained optical emission measurements, and the resulting 144-level data set is analyzed in terms of a model Hamiltonian that assumes ${\mathrm{D}}_2$ site symmetry for the ${\mathrm{Nd}}^{3+}$ ions in Nd:YAG. Inclusion of two-electron correlation crystal-field (CCF) interaction terms in the model Hamiltonian explains the crystal-field splittings of several anomalous multiplets, and reduces the rms deviation between calculated and observed energies (for 144 levels) from 28 to 14 ${\mathrm{cm}}^{\mathrm{-}1}$. The optical line-strength data obtained in this study are analyzed in terms of an f-f transition intensity model developed by us in previous work. This model has broad applicability in analyses of f-f intensity data for transitions between Stark levels. Emission branching ratios for transitions from the ${}_{}{}^4{}_{}{}^{}$${\mathit{F}}_{3/2}$ multiplet are calculated and compared with literature values.

The effect of hydrostatic as well as uniaxial pressure upon proper ferroelastic (martensitic) phase transitions in cubic crystals is considered. The volumetric strain is considered to be the secondary order parameter conjugated to the symmetrized shear strain that governs the reduction of point symmetry to a tetragonal one. Corresponding terms in the Ginzburg-Landau expansion of the Gibbs free energy are analyzed for transitions of the first as well as of the second order. The pressure effect on the transition temperature as well as on the anomalies of isothermal compressibility and the linear thermal-expansion coefficient are studied and recent experimental data on thermal expansion anomalies in ${\mathrm{V}}_3$Si, In-Tl, and Ni-Al are discussed. The nonlinearity of thermal expansion is found to imply a special relation between the shear strain and volume change that can lead to the transformation from a fcc lattice to a bcc one, as observed in the iron alloys.

The procedure for the estimation of the defect-interaction parameters for solids is suggested. The vacancy-type defect (VTD) effective interaction is described by the mixing potential. The sign of this potential determines the solubility in the VTD-atom solid solution. The VTD thermodynamic parameters are evaluated by fitting to the temperature dependence of the self-diffusion coefficient. For the example of Nb, we illustrate the ability of the suggested approach to describe the stability of the VTD-atom ‘‘alloy.’’

This paper reports an extensive study of the static (spontaneous polarization, ${\mathit{P}}_{\mathit{s}}$, tilt angle θ, and pitch) and dynamic properties of a ferroelectric liquid-crystalline polymer. It is shown that a ferroelectric liquid-crystalline polymer (diluted polysiloxane) exhibits physical behavior similar to that of a low-molar-mass liquid crystal in terms of contrast ratio, pitch of the helix, and relationship between ${\mathit{P}}_{\mathit{s}}$ and θ. The degenerated collective modes for the director rotation are shown to split into two modes at the Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ phase transition temperature using dielectric spectroscopy. Both frequency and the inverse dielectric strength show critical slowing down behavior in the vicinity of the Sm-A–Sm-${\mathit{C}}^{\mathrm{*}}$ phase transition temperature. The dynamical behavior and the relative dependence of the dielectric strength on temperature for the soft mode in Sm-${\mathit{C}}^{\mathrm{*}}$ and Sm-A phase is consistent with the influence of a significant biquadratic coupling compared to its linear coupling between ${\mathit{P}}_{\mathit{s}}$ and θ. The material parameters of the generalized Landau model for the diluted polysiloxane liquid-crystalline polymer have been found by fitting the experimental data to the mean-field theory.

We have calculated the z-average static structure factor [S(q${)}_{\mathit{z}}$], z-average radius of gyration (${\mathit{R}}_{\mathit{g}\mathit{z}}$), and the weight average aggregation number (${\mathit{m}}_{\mathit{w}}$) of fractal aggregates with an aggregate number distribution given by N(m)∝${\mathit{m}}^{\mathrm{-}\mathrm{\tau }}$f(m/${\mathit{m}}^{\mathrm{*}}$). Here, q is the scattering wave vector and for the cutoff function f(m/${\mathit{m}}^{\mathrm{*}}$) at a characteristic aggregation number ${\mathit{m}}^{\mathrm{*}}$ we have chosen a stretched exponential function. We derive expressions for the prefactors of the scaling relations ${\mathit{m}}_{\mathit{w}}$∝${\mathit{R}}_{\mathit{g}\mathit{z}}^{\mathit{d}\mathit{f}\mathrm{*}}$ and S(q${)}_{\mathit{z}}$∝(${\mathit{qR}}_{\mathit{g}\mathit{z}}$${)}^{\mathrm{-}\mathit{d}\mathit{f}\mathrm{*}}$ and make explicit the conditions for their validity at finite values of ${\mathit{m}}_{\mathit{w}}$ and ${\mathit{qR}}_{\mathit{g}\mathit{z}}$. For values of τ close to two these conditions are shown to be very difficult to meet in practice. For the case of aggregates formed by a percolation process where τ=2.2 it is shown that attempts to measure ${\mathit{df}}^{\mathrm{*}}$ directly from the slope of ${\log }_{10}$(${\mathit{m}}_{\mathit{w}}$) vs ${\log }_{10}$(${\mathit{R}}_{\mathit{g}\mathit{z}}$) or ${\log }_{10}$(S(q${)}_{\mathit{z}}$) vs ${\log }_{10}$(q) are biased by the effect of the internal and/or external cutoff of the fractal regime.

General properties of a stochastic interaction between acoustic waves with a gapless spectrum and optic waves, the spectrum of which has a gap, are investigated in the region where their dispersion curves cross. The coupling parameter of these waves is considered as a random spatial zero-mean-value function with root-mean-square value λ and correlation radius ${\mathit{r}}_{\mathit{c}}$. This model only admits an interaction between the coherent waves and their scattered counterparts. It is shown that stochastic interaction leads to both dynamic and relaxation effects. The former are proportional to λ and promote degeneration removal and repulsion of the dispersion curves Δ at the crossing point, while the latter are proportional to ${\mathit{r}}_{\mathit{c}}^{\mathrm{-}1}$ and hinder this phenomenon. The values of Δ are different for the cases of coherent acoustic and optic waves. In the vicinity of the resonance point the relative stabilization of the fluctuation waves takes place due to the formation of long-living coupled states of the coherent and scattered waves.

We investigate the small-polaron mechanism as a possible explanation of electrical-conduction and electrical-noise properties of the linear chain material ${\mathrm{Mo}}_2$${\mathrm{S}}_3$. Experimental conductivity and noise data obtained in earlier papers [Phys. Rev. B 38, 3973 (1988); Phys. Rev. B 39, 5139 (1989)] are analyzed in terms of a small-polaron mechanism and a double-well potential model. We interpret the observed electronic properties in terms of kinetic equations describing the interaction of free carriers with fluctuations of density of the lattice. Appropriate kinetics equations to describe this interaction, which leads to small-polaron formation, are derived. These equations are found to explain quantitatively both the nonequilibrium electronic properties and electrical noise in ${\mathrm{Mo}}_2$${\mathrm{S}}_3$.

The moment-expansion technique for the calculation of spectral functions is applied to a realistic model of argon for which molecular-dynamics results have previously been obtained. The first five even moments, ${\mathrm{\mu }}_0$ to ${\mathrm{\mu }}_8$, are calculated in a classical Monte Carlo simulation. Various methods of terminating the continued fraction expansion for the spectral function are tested. When a Gaussian model spectrum is used to supplement the calculated moments, the peak center is accurately located and the height and width of the peak are given to about 20% accuracy.

The analogy between electrical conductivity and matter transport holds only in simple cases, where the point defect which is responsible for the diffusion does not alter the shape of the percolating cluster. In the five variants of a model of matter transport by a dumbbell interstitial defect mechanism in fcc alloys, the point defect migrates on a sublattice of coordinance 8 and has only two jump frequencies at its disposal. When the disparity between these frequencies tends to infinity, a percolative regime of diffusion is observed, but the critical threshold arising in the diffusion problem can be identified with a standard percolation one only under restrictive conditions. The present paper evaluates the site percolation threshold ${\mathit{p}}_{\mathit{c}}$ corresponding to one of the five variants by the usual series method. Extensive computer enumeration yields perimeter polynomials for clusters containing up to 14 sites. A classical analysis by Dlog-Padé approximants to the first two moments of the cluster density function n(s) yields the two critical exponents β(${\mathit{p}}_{\mathit{c}}$) and γ(${\mathit{p}}_{\mathit{c}}$) associated to the percolation probability and the mean cluster size, respectively, as functions of the (unknown) threshold ${\mathit{p}}_{\mathit{c}}$. It is shown further that, using the higher-order moments of the cluster density function n(s), a very tight range for ${\mathit{p}}_{\mathit{c}}$ can be proposed (0.2775<${\mathit{p}}_{\mathit{c}}$<0.2782), and that the corresponding values β(${\mathit{p}}_{\mathit{c}}$) and γ(${\mathit{p}}_{\mathit{c}}$) are in close agreement with the recent and most commonly adopted values for both of these exponents.

From a series of total energy calculations by the full-potential linear muffin-tin orbital method, the total energy hypersurface as a function of atomic displacements from equilibrium positions has been fitted for different Γ phonon modes in orthorhombic ${\mathrm{KNbO}}_3$. Frequencies and eigenvectors of all transverse optical Γ phonons have been calculated in the harmonic approximation, and in the quantum oscillator scheme, for ${\mathit{A}}_2$ and ${\mathit{B}}_2$ modes. The microscopic structure of the orthorhombic phase has been analyzed in a series of supercell calculations for different patterns of Nb displacements, providing indications in favor of the chain structure with oppositely directed neighboring chains.

The interplay between the Mn interlayer coupling constant ${\mathit{n}}_{\mathrm{Mn}\mathrm{-}\mathrm{Mn}}$ and the thermal expansion has been investigated by means of thermal-expansion, specific-heat, and magnetization measurements. A linear relation between ${\mathit{n}}_{\mathrm{Mn}\mathrm{-}\mathrm{Mn}}$ and the thermal expansion was established. This linear relation is used in the formulation of a quantitative model for temperature-induced metamagnetic transitions in R${\mathrm{Mn}}_2$${\mathrm{Ge}}_2$ compounds. The observed relation between the unit-cell dimensions and the transition temperatures is interpreted in terms of this model. For polycrystalline ${\mathrm{Sm}}_{0.9}$${\mathrm{Y}}_{0.1}$${\mathrm{Mn}}_2$${\mathrm{Ge}}_2$, the relation between the metamagnetic transitions and anomalies in the electrical resistivity was investigated. A magnetic-field-induced change of the resistance of 10% was observed at 185 K. It appears likely that magnetovolume effects are responsible for the anomalous resistance behavior.

The influence of the spin-phonon coupling on soliton characteristics and the soliton response on the lattice subsystem in a quasi-one-dimensional magnetic chain is examined. It was found that, in the case of the ferromagnetic coupling, these correlations may induce reduction of the effective exchange integral which, in the temperature range where one-dimensional ordering prevails, may be maximally about 1%. Consequently the soliton energy and width suffer the negligible modification, too. On the other hand, the magnetic subsystem may have a certain impact on elastic subsystem characteristics, the speed of sound in particular. The character of these changes depends strongly on the type of the excitations of the magnetic subsystem—solitons or magnons.

We have investigated the magnetic response of ultrathin paramagnetic Co/Cu(001) films in an applied field using the magneto-optic Kerr effect. We find that the paramagnetic susceptibility χ increases sharply upon Co deposition within a narrow thickness range close to the critical thickness at which the onset of ferromagnetism occurs. We attribute the observed behavior to a geometrical, or percolation phase transition, since the corresponding critical exponent γ=43/18=2.39 agrees well with the experimentally determined value of 2.40±0.07.

We investigate static properties of the two-dimensional quantum Heisenberg antiferromagnet in the framework of the 1/N expansion of the ${\mathit{CP}}^{\mathit{N}\mathrm{-}1}$ model. The calculations are done in the renormalized-classical region. The logarithmic corrections to the spin-correlation length are found to change the temperature dependence of its prefactor. The renormalized staggered susceptibility is completely determined by the renormalization of the spin-correlation length. The results we obtain are in agreement with the renormalization-group and 1/N studies of the O(N) nonlinear σ model.

Neutron-scattering measurements characterizing the magnetic behavior of single-crystal ${\mathrm{Cr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ (x=0.007) are reported. Four distinct phases are observed: paramagnetic, commensurate spin density wave (SDW), transversely polarized incommensurate SDW, and longitudinally polarized incommensurate SDW. Transitions between these phases occur at ${\mathit{T}}_{\mathit{N}}$=455 K, ${\mathit{T}}_{\mathrm{IC}}$=182 K, and ${\mathit{T}}_{\mathrm{SF}}$=85 K, respectively. A revised phase diagram for the ${\mathrm{Cr}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$ alloy system is presented in light of these data.

We study zero-temperature properties of the three-dimensional Edwards-Anderson Ising spin glass on finite lattices up to size ${12}^3$. Using multicanonical sampling we generate large numbers of ground-state configurations in thermal equilibrium. Finite-size scaling fits of the data are carried out for two hypothetical scenarios: Parisi mean-field theory versus a droplet scaling ansatz. With a zero-temperature scaling exponent y=0.72±0.12 the data are well described by the droplet scaling ansatz. Alternatively, a description in terms of the Parisi mean-field behavior is still possible. The two scenarios give significantly different predictions on lattices of size ≥${12}^3$.

We study by extensive histogram Monte Carlo simulations the phase transition in the antiferromagnetic stacked triangular lattices with classical Heisenberg spins. It is shown that in a range of the antiferromagnetic next-nearest-neighbor interaction ${\mathit{J}}_2$, the transition is clearly of first order. We also reconsider the controversial question concerning the nature of the phase transition when ${\mathit{J}}_2$=0: we show that the critical exponents obtained, in agreement with previous simulations, exclude the possibility of the O(4) class predicted by a nonlinear σ model in a 2+ɛ renormalization-group calculation. The phase diagram in the (${\mathit{J}}_2$,T) space (T: temperature) is shown and discussed. For comparison, the phase diagram obtained by a Green-function method in the case of quantum Heisenberg spins is also shown.

The π-electron ring current magnetic susceptibilities and endohedral chemical shifts of the fullerenes are calculated with the London theory. The diamagnetism calculated for the fullerenes that have been characterized to date does not show a monotonic increase toward the graphite value. By carrying out calculations on high-symmetry giant fullerenes (${\mathrm{C}}_{\mathit{n}}$) in the size regime 100<n<1000, we are able to demonstrate the beginnings of such a trend. In particular ${\mathrm{C}}_{540}$ is calculated to exhibit more than 10% of the π-electron ring current magnetic susceptibility of graphite on a per carbon basis. Endohedral chemical shifts are predicted to be invariant to cluster size, but subject to the quantum size effects seen in smaller fullerenes and metallic clusters. The fullerenes are different from the metallic clusters because the finite band gap in conjugated carbon compounds allows the diamagnetic term to dominate at large cluster size. The experimentally observed decrease in nanotube material diamagnetism with temperature is attributed to the increased importance of the Van Vleck term due to finite-temperature effects.

A magnetization step due to isolated ${\mathrm{Co}}^{2+}$ spins in ${\mathrm{Cd}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$S was observed at 30 mK. The magnetic field at this step gave 2D=1.32±0.04 ${\mathrm{cm}}^{\mathrm{-}1}$ for the single-ion axial anisotropy constant of ${\mathrm{Co}}^{2+}$. This value is close to those obtained by other methods. EPR experiments at 96 GHz gave 2D=1.28±0.04 ${\mathrm{cm}}^{\mathrm{-}1}$. The EPR data suggest the existence of a Koster-Statz term in the spin Hamiltonian.