EPR and NMR line shapes in disordered ferroelectric crystals

A theory is developed for the magnetic resonance line shape in disordered ferroelectric crystals. In a study of the random fields responsible for inhomogeneous line broadening, nonlinear and spatial correlation effects are taken into account. It is shown that homogeneous broadening depends on the temperature and on the magnitude and orientation of the external magnetic field, as well as on the nonlinearity parameters of the ferroelectric material. The resonance line shape is calculated as the envelope of homogeneously broadened Lorentzian spin packets. Analytic expressions for I ₂(ω) and I ₃(ω) are introduced to account for nonlinearity and correlation effects of second and third order, respectively. Calculations are done for centrally symmetric crystals, as well as for those without a center of symmetry. It is shown that homogeneous broadening is important near the line peak, while the wings are determined mainly by inhomogeneous broadening. Manifestations of the predicted effects in the spectrum lines of disordered ferroelectric crystals are discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 340–347 (February 1998)     

Self-localized carrier states in disordered ferroelectrics

A theory of self-localized states of free carriers near polarization fluctuations (fluctuons) in disordered ferroelectrics is developed. Calculations are carried out for the model disordered ferroelectric K_{1− x} Li_xTaO₃ (x≪0.05). The basic characteristics of the fluctuon — the energy and radius of the fluctuon state — are calculated as functions of the impurity dipole concentration and temperature. The theory predicts the appearence of stable fluctuon states in both the mixed ferroelectric-dipole-glass phase (a dipole glass is the electric analog of a spin glass) and the dipole-glass state of disordered ferroelectrics. The possible role of fluctuons in kinetic phenomena such as conductivity in these substances is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 5, 425–429 (10 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Metal-insulator transition in amorphous Si1−c Mnc obtained by ion implantation

A metal-insulator transition (MIT) induced by a change in the impurity Mn concentration in a material with topological disorder — amorphous Si_1−c Mn_c — is investigated. It is found that near the critical point the localization radius, permittivity, and conductivity vary according to a power law in accordance with the scaling theory of localization. The critical exponents are determined. It is concluded that the basic mechanisms of the MIT in disordered systems do not depend on the type of disorder and are universal. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 333–337 (25 February 1997)     

Fluctuation states and optical spectra of solid solutions with a strong isoelectronic perturbation

We propose an approach to describing the density of fluctuation states in a disordered solid solution with a strong perturbation introduced by isoelectronic substitution in the range of attraction-center concentrations below the threshold of percolation along the sites of a disordered sublattice. To estimate the number of localized states we use the results of lattice percolation theory. We describe a method for distinguishing, within the continuum percolation theory, among the various “radiating” states of the fluctuation-induced tail, states that form the luminescence band at weak excitation. We also establish the position of the band of radiating states in relation to the absorption band of the excitonic ground state and the mobility edge of the system. The approach is used to describe the optical spectra of the solid solution ZnSe_1−c Te_c, which at low Te concentrations can be interpreted as a system with strong scattering. We take into account the exciton-phonon interaction and show that the calculated and observed luminescence spectra of localized excitons are in good agreement with each other. Zh. éksp. Teor. Fiz. 115, 1039–1062 (March 1999)     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Nonequilibrium properties of re-entrant spin glasses in a magnetic field

In this paper the authors discuss how the re-entrant spin-glass state arises in the disordered alloys Ni_100−x Mn_x (x=19, 21, 23), along with the nonequilibrium magnetic properties of these alloys. It is shown that near the Gabay-Toulouse phase line the time it takes the system to reach equilibrium is comparable to times required to perform static experiments (10¹–10⁴ s); cooling the sample into the region of crossover with the de Almeida-Thouless line causes these times to increase to astronomical values of more than 10¹⁶ s. A method is proposed for constructing magnetic phase diagrams of systems of this type in “magnetic field-temperature” coordinates. Fiz. Tverd. Tela (St. Petersburg) 41, 2028–2033 (November 1999)     

Intrinsic luminescence of amorphous and disordered crystalline systems

A unified method is developed for describing the steady-state luminescence of exciton fluctuation states for weak excitation in different disordered systems. The phononless luminescence band is found to be formed by “radiative” states of the fluctuation tail in the density of states, i.e., by states for which nonradiative states are either nonexistent or have a low probability. The shape of the emission spectra calculated including the phonon interaction is in good agreement with experimental luminescence spectra of α Si:H and of solid solutions of ZnSe_(1−c)Te_c and CdS_(1−c)Se_c. Fiz. Tverd. Tela (St. Petersburg) 40, 890–891 (May 1998)     

Zero-Temperature Dynamics of ±J Spin Glasses¶and Related Models

We study zero-temperature, stochastic Ising models σ ^t on Z ^d with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every x in Z ^d , σ _x ^t flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”. For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ _J +(1-α)δ_{- J} ) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem. Received: 3 November 1999 / Accepted: 10 April 2000     

The shape of inhomogeneously broadened resonant lines due to nonlinear contributions

A theory of the shape of inhomogeneously broadened resonant lines is developed for the case where the shifts of the spin-packet resonance frequencies are determined by nonlinear (in particular, quadratic) random-field contributions. It is shown that the line shape I(ω) is described by a narrow δ-type curve with broad wings. Homogeneous broadening reduces the intensity I _max(ω) and broadens the line. A comparison is made of the calculated and measured 93Nb NMR line shapes for PbMg_1/3Nb_2/3O₃ (PMN) at T=430 K and KTa_0.988Nb_0.012O₃ (KTN). The theory describes well the observed resonant-line shape anomalies. Specific features in the structure of the disordered ferroelectrics PMN and KTN are discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 1313–1320 (July 1998)     

Magnetoelectric effect and toroidal ordering in Ga2−x FexO3

The field dependence of the magnetoelectric effect and longitudinal magnetostriction of Ga_2−x Fe_xO₃ single crystals is studied in magnetic fields up to 200 kOe in the temperature range from 4.2 to 300 K. It is shown that the magnetoelectric effect in these materials is determined mainly by the toroidal moment T and is not related to magnetostriction, as was previously theorized. A new method for determining the toroidal moment by measuring the electric polarization in a strong magnetic field is proposed. The value of the toroidal moment of the unit cell in Ga_1.15Fe_0.85O₃ is calculated: T=(T _a ,0,0), where T _a =24.155μ _B Å per unit cell. Experimental data are analyzed using a theory of toroidal spin ordering, which gives good agreement with experiment. Zh. éksp. Teor. Fiz. 114, 263–272 (July 1998) Deceased.     

Dependence of the resistivity of nonstoichiometric titanium carbide TiCy on the density and distribution of carbon vacancies

The influence of temperature and of the density and distribution of structural vacancies in the carbon sublattice on the resistivity of nonstoichiometric titanium carbide TiC_y(0.5⩽y⩽0.98) is studied. It is shown that in titanium carbide TiC_y with y<0.7 reversible disorder-order structural phase transitions occur at temperatures below 1000 K. The temperatures of order-disorder phase transformations are determined. The dependence of the residual resistivity on the composition of the disordered titanium carbide is explained by the change in the carrier density in the region of homogeneity of the carbide TiC_y, on the one hand, and the atom-vacancy interaction, on the other. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 284–289 (25 August 1999)     

Dielectric relaxation in the weak ferroelectric Li2Ge7O15 near the ferroelectric phase transition

The dielectric permittivity of Ni-doped Li₂Ge₇O₁₅ crystals was studied in the vicinity of the ferroelectric phase transition. Introduction of Ni has been shown to suppress the dielectric anomaly and to reduce substantially the transition temperature. A temperature hysteresis in ɛ (T) has been observed in nominally pure and Ni-doped Li₂Ge₇O₁₅ crystals near the transition point. Measurements performed under cooling from the paraphase reveal dispersion of dielectric permittivity at Debye relaxation frequencies of the order of 10⁴–10⁵ Hz at T _c . It is proposed that the hysteresis phenomena and the low-frequency dispersion are caused by residual defects (of the type of random local fields), which become polarized in the ferroelectric phase and become disordered above T _c . Fiz. Tverd. Tela (St. Petersburg) 40, 2198–2201 (December 1998)     

Macroscopic quantum tunneling in small magnetic particles

Macroscopic quantum tunneling of magnetization in small antiferromagnetic clusters is studied for the spin-1/2 anisotropic (J _z ≡ J, J _x =J _y ≡J _xy ) Heisenberg model with the use of both perturbation theory and an exact numerical diagonalization technique. Splitting of the two lowest levels due to the lifting of the degeneracy between them (in the case J _xy =0) by the in-plane exchange (J _xy ≠ 0) is found to occur in the N/2th order of perturbation theory. Tunneling is absent in systems with an odd number of sites, in which the levels are doubly degenerate in zero magnetic field. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 688–693 (10 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Mean-Field Driven First-Order Phase Transitions in Systems with Long-Range Interactions

We consider a class of spin systems on ℤ ^d with vector valued spins (S _x ) that interact via the pair-potentials J _x,y S _x ⋅S _y . The interactions are generally spread-out in the sense that the J _x,y 's exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions d≥3, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions d = 1,2 for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique “state,” then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.     

Liouville theory on a Z N Riemann surface

Liouville field theory on a Z _N curve is studied. It is shown that the partition function on such surfaces reduces to Liouville correlation functions on a sphere and to a free scalar theory with Ramond boundary conditions. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 2, 85–90 (25 July 1997)     

Electron states in quantum-dot and antidot arrays placed in a strong magnetic field

Quantum electronic states in a dot (antidot) array in the presence of a dc magnetic field are studied. A new method of numerical calculation of the electron spectrum and wave functions in a two-dimensional periodic potential and perpendicular magnetic field is proposed. The magnetic-subband energies, density of electron states, and electron density |ψ(x,y)|², as well as the amplitude of the potential, and lattice period and degree of anisotropy for different magnetic fields have been found. The calculations were performed for quantum dots in the In_0.2Ga_0.8As-GaAs and GaAs-Al_0.3Ga_0,7As systems. The rearrangement of the spectrum with variation of magnetic field and with transition from the tight-binding to weak-binding approximation is studied (ω _c is the cyclotron frequency, and V ₀ is the periodic-potential amplitude). The calculations show that the two-dimensional lattices epitaxially grown presently on semiconductor surfaces permit observation of quantum effects associated with rearrangement of the spectrum (electron transport and optical absorption) in magnetic fields H⩽1 MG. Fiz. Tverd. Tela (St. Petersburg) 40, 1134–1139 (June 1998)     

Dynamic and stimulated rf echo in high-Tc superconducting powders

Two-pulse and three-pulse echoes in powdered yttrium and bismuth high-T _c superconductors are investigated to determine the dependence of the signal amplitude on the magnetic field, the temperature, and the gas pressure. The temperature is measured as a function of the relaxation time of the echo signal. The properties of the long-lived rf echo are studied in detail; it exhibits a persistent (lasting more than several hours) memory of a time series of write pulses and a cumulative storage effect. The experimental results can be explained qualitatively within the framework of the theory proposed by Asadullin [Sverkhprovodimost’ 6, 545 (1993)] to account for the nonlinear motion of vortices associated with sample defects. Zh. éksp. Teor. Fiz. 111, 1032–1046 (March 1997)     

Paramagnetic labeling as a method for the soft spectroscopy of electronic states

A self-consistent microscopic theory of the relaxation of the crystal-field levels of an impurity ion in a state with an integer valence implanted in a normal metal is devised. A microscopic approach based on the Coqblin-Schrieffer-Cooper approach, rather than the formal model of the sf exchange interaction, makes it possible to take into account the specific details of both the crystal-field states of the impurity ion and the electronic band spectrum of the metal. A new method for the soft spectroscopy of electronic states based on measurements of the temperature dependence of the width Γ_MM′(T) of transitions between the crystal-field states |M〉 of a paramagnetic ion implanted in the compound being studied is proposed. To make specific use of this method in neutron and optical spectroscopy, a classification of the types of temperature dependence of the natural relaxation width γ _M (T) of the levels is devised, and procedures for possible experimental methods are proposed. A nonzero value of the natural relaxation width γ _G (T) of the crystal-field ground state | G〉 of an impurity ion at zero temperature is obtained within the proposed self-consistent model, but is beyond the scope of perturbation theory. It is shown that the widely accepted estimate of the characteristic temperature of Kondo systems T*=Γ _G(T=0)/2 from the quasielastic scattering width at zero temperature Γ _G (T=0)/2 is incorrect in the case of strong relaxation in a system with soft crystal fields. The proposed model is applied to the quantitative analysis of the relaxation of the crystal-field levels of paramagnetic Pr³⁺ ions implanted in CeAl₃ and LaAl₃. The results of the calculations are in quantitative agreement with the experimental data. Zh. éksp. Teor. Fiz. 113, 1843–1865 (May 1998)     

Thermoelectric power in quasi-two-dimensional systems with scattering of current carriers by phonons

The thermopower α in electron systems with a quasi-two-dimensional energy spectrum is investigated in the relaxation-time tensor approximation. The longitudinal and transverse components of the thermopower are calculated for scattering of the current carriers by different types of phonons. It is shown that the anisotropy of the thermopower in such systems is substantial. The dependence of a on the ratio of the Fermi level ɛ _F to the half-width ɛ ₀ of the one-dimensional conduction band is considered. For scattering by acoustical and nonpolar optical phonons, the thermopower changes sign: α becomes positive for ɛ _F<ɛ ₀. Comparison of the theory with published experimental data demonstrates good qualitative agreement. Fiz. Tverd. Tela (St. Petersburg) 39, 1857–1858 (October 1997)     

Critical quantum chaos in 2D disordered systems with spin-orbit coupling

We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic models. Received 1 September 1999