AbstractThe conductivity law derived by Efros and Shklovskii for variable‐range hopping (VRH) in the presence of long‐range Coulomb interaction is modified to take into account new numerical results for the density of single‐particle states (DOS) within the Coulomb gap. The characteristic temperatures appearing in this modified VRH law, including limiting temperatures for the applicability of VRH, are expressed in terms of DOS parameters, localization length and dielectric constant. The results are compared with experimental studies in crystalline and amorphous semiconductors.

physica status solidi (b)Volume 135, Issue 2 p. K153-K158 Short Note Electrical resistivity and thermoelectric power of Fe50Co50 F. Goedsche, F. Goedsche Zentralinstitut für Festkörperphysik und Werkstofforschung der Akademie der Wissenschaften der DDR, Dresden Search for more papers by this author F. Goedsche, F. Goedsche Zentralinstitut für Festkörperphysik und Werkstofforschung der Akademie der Wissenschaften der DDR, Dresden Search for more papers by this author First published: 1 June 1986 https://doi.org/10.1002/pssb.2221350258 Berzdorfer Str. 2, DDR-8036 Dresden, GDR AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume135, Issue21 June 1986Pages K153-K158 RelatedInformation

AbstractThe spin‐disorder model is adopted to calculate the electrical resistivity and thermoelectric power of ferromagnetic metallic galsses within the molecular field approximation. The resistivity expression interpolates correctly between the low (T = 0 K) and the high temperature (T ≧ TC) results derived previously. Using Mott's formula a magnetic contribution Sm(T) to the thermopower is calculated which exhibits a nonlinear temperature dependence. Both, sign and curvature of Sm(T) are correlated with the actual position of 2kF in the structure factor. For a combined spin and potential scattering the total thermopower is evaluated according to the Nordheim‐Gorte rule. The results reproduce qualitatively sign and curvature of the thermopower observed experimentally in ferromagnetic metallic glasses.

AbstractA general relation between the electrical resistivity and the dynamical susceptibility of the scattering system, valid in the weak scattering limit and for arbitrary temperatures, is extended to disordered spin systems including elastic spin‐conserving as well as inelastic spin‐flip scattering. Averaging procedures for the position‐dependent susceptibilities are discussed. As an application, the low‐temperature resistivity R is calculated for the Heisenberg‐Mattis model as a site‐random magnet with ferro‐antiferromagnetic exchange disorder. The superposition of the spin‐dependent elastic scattering contributions to R and the contributions due to inelastic scattering by quasipropagating excitations with linear dispersion and quadratic disorder damping yields a weak resistivity minimum. Comparisons with other theoretical papers are made, and the relevance of the results for the interpretation of experimental data is discussed.

AbstractA general linear response theory of the thermoelectric transport is developed on the basis of Zubarev's approach to non‐equilibrium statistical thermodynamics. In the weak‐scattering limit electrical resistivity and thermopower are related to generalized dynamical susceptibilities. It is shown that the Mott formula for the thermopower is approximately correct in two cases, first in the case of elastic scattering, and furthermore, in the presence of inelastic scatterers at high temperatures. At low temperatures Mott's formula is shown to be no longer valid. The correction terms due to the inelasticity of the scattering are derived systematically and estimated for a Debye model of electron‐phonon scattering. For the same reason the Nordheim‐Gorter rule must be generalized at low temperatures. The theory is extended to homogeneously disordered systems. The phonon drag is briefly discussed.

AbstractThe method of the functional integral is applied to a doubly degenerate Hubbard model with arbitrarily filled bands. The relation between the number of electrons per atom n, and the chemical potential μ, the local moments, and the static susceptibilities corresponding to the magnetic, orbital, and charge‐ordered states are studied. At zero temperature a phase diagram is obtained in dependence on the electron concentration n, correlation energy U, intra‐atomic exchange energy I, and half bandwidth Δ. The exchange energy is important for the stability of the ferromagnetic state. Additionally to magnetic long‐range ordering an ordering of the orbital states within the ferromagnetic region is possible.

The d.c. electrical resistivity is considered for a general solid state model characterized by local interactions of the charge carriers with a system of scatterers which may be e.g. quasiparticles, spins or impurities. A basic relationship - valid over the full temperature range - between the electrical resistivity of the charge carrier system (without magnetic field) and the generalized dynamical susceptibility of the scattering system is derived in the weak scattering limit. The equivalence of the following methods is shown: Boltzmann equation approach (variation procedure), Mori formalism, force-force correlation function method (for the total forces on the charge carriers), and the method of the transformed Liouville equation; herewith the equivalence with the Kubo or Green function method, the Zubarev formalism, the information-theoretical method and the Zwanzig formalism is also given. As a specific example, the s-d exchange model for the scattering of conduction electrons by localized spins is discussed including the corresponding electron-magnon system as a low-temperature approximation.

AbstractThe electrical resistivity of a disordered ferromagnetic alloy is estimated in terms of the two‐current model. Besides the residual resistivity due to spin dependent potential scattering a spin‐disorder residual resistivity is obtained. A significantT3/2term associated with incoherent electron magnon collisions and representing large deviations from Matthiessen's rule dominates the temperature dependence of the resistivity below about 10 K. Deviations from Matthiessen's rule arising from the two‐current conduction are discussed.

AbstractThe spin‐disorder resistivity of amorphous ferromagnets is investigated in the temperature regimes 0 ≦ T ≫ TC and T ≫ TC. The resistivity is calculated within the force–force correlation function method up to the second order in the sd‐exchange constant. A simple structural model for a structurally disordered Heisenberg ferromagnet is presented. At lowest temperatures the spin‐disorder resistivity varies as T3/2 for a sufficient high degree of disorder. It is concluded that the experimentally observed T2‐dependence at these temperatures is of non magnetic origin. This dependence can be qualitatively understood if the thermal smearing of the structure factor is taken into account.

AbstractThe method of the force‐force correlation functions is used to derive, beyond the weak scattering approximation, a tractable approximative formula for the electrical resistivity of disordered binary alloys. The starting point is a one‐particle expression for the resistivity formulated in terms of the total scattering operator T. The local approximation is introduced by replacing the T operator by the atomic t matrices in order to treat transition metal alloys described by muffin‐tin single‐particle Hamiltonians. Short‐range multiple‐scattering corrections to the local approximation are evaluated using a non‐selfconsistent single‐site average‐t‐matrix approximation. Explicit results are given and discussed for the resistivity of a one‐dimensional muffin‐tin model for transition‐metal‐like alloys with resonant states.

AbstractThe electrical resistivity of iron is measured between 2 and 30 K. The results can be extremely well explained by fitting the data to a simple two‐current model including electron–magnon, electron–phonon, and electron–impurity scattering. Below 10 K large deviations from Matthiessen's rule are observed arising from the two‐current character of the conduction.

AbstractThe method of the functional integral is applied to the conventional Hubbard model with an arbitrary filled band. A relation between the number of electrons per atom, n, and the chemical potential μ at T = 0 is calculated. The static magnetic susceptibility and the local magnetic moments are studied. Looking for the dependence of magnetic properties on the electron correlation U and the number of electrons per atom n, a phase diagram is obtained at zero temperature. Besides the paramagnetic phase ferromagnetic and antiferromagnetic phases exist within this diagram.

AbstractThe dc electrical resistivity is calculated for a b.c.c. based random binary substitutional magnetic alloy with partial long‐range order for a single‐band tight‐binding model with diagonal disorder, two kinds of localized spins, arbitrary concentrations and arbitrary order parameter. The spin‐disorder contribution to the resistivity is treated by means of the sd exchange model. Within the framework of the CPA up to second order in the scattering potential a general closed resistivity formula is given in terms of alloy parameters and spin parameters. The resitivity is discussed for various special cases in dependence on the long‐range order parameter.

AbstractWithin the framework of the coherent potential approximation the de electrical resistivity is calculted for random ternary substitutional magnetic alloys with partial atomic long‐range order. The special case of nonmagnetic alloys with potential scattering only is included. The case of a two sublattice system with two long‐range order parameters is studied. The spin‐disorder contribution to the resistivity is treated using the s–d exchange model. The calculations are done for a single‐band tight‐binding model with diagonal disorder, three kinds of localized spins, arbitrary concentrations, and arbitrary order parameters. A general closed resistivity formula in terms of alloy, spin, and order parameters is given in second order of the scattering potential and is discussed for a number of special cases including antiferromagnetic ordering.

AbstractThe multiple‐scattering theory is applied to determine the electronic spectrum of a one‐dimensional binary alloy of spatially non‐overlapping randomly distributed scatterers. A general expression is derived for the alloy density of states using the average‐T‐matrix approximation (ATA). Within the framework of the ATA both the complex energy bands and the electronic density of states are calculated numerically for a transition metal like alloy.

physica status solidi (b)Volume 85, Issue 2 p. K81-K84 Short Note Spin-disorder resistivity of ternary alloys in the CPA weak scattering limit F. Goedsche, F. Goedsche Zentralinstitut für Festkörperphysik und Werkstofforschung der Akademie der Wissenschaften der DDR, Dresden Search for more papers by this authorG. Vojta, G. Vojta Zentralinstitut für Festkörperphysik und Werkstofforschung der Akademie der Wissenschaften der DDR, Dresden Search for more papers by this author F. Goedsche, F. Goedsche Zentralinstitut für Festkörperphysik und Werkstofforschung der Akademie der Wissenschaften der DDR, Dresden Search for more papers by this authorG. Vojta, G. Vojta Zentralinstitut für Festkörperphysik und Werkstofforschung der Akademie der Wissenschaften der DDR, Dresden Search for more papers by this author First published: 1 February 1978 https://doi.org/10.1002/pssb.2220850249Citations: 4 DDR-8027, Dresden, Helmholtzstr. 20, DDR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1 L. M. Scarfone, Phys. Rev. B 7, 4435 (1973). 2 L. M. Scarfone and J. D. Chlipala, Phys. Rev. B 11, 4960 (1975). 3 T. Jo, H. Hasegawa, and J. Kanamori, J. Phys. Soc. Japan 35, 57 (1973). 4 K. I. Wysokiński, phys. stat. sol. (b) 77, K139 (1976). 5 K. I. Wysokiński and M. Pilat, J. Phys C 9, 4271 (1976). 6 F. Goedsche, R. Richter, and A. Richter, phys. stat. sol. (b) 69, 213 (1975). Citing Literature Volume85, Issue21 February 1978Pages K81-K84 ReferencesRelatedInformation

AbstractThe CPA‐conductivity theory is applied to the s–d exchange model to calculate the spin contribution to the electrical resistivity of disordered binary alloys containing two kinds of localized spins. The second‐order resistivity is expressed in terms of alloy magnetization, spin‐pair correlation functions, atomic spin difference, and mean spin value. Striking deviations from a Nordheim‐like behaviour of the spin‐disorder residual resistivity are obtained, if the magnitude of the atomic spins depends on alloy composition and local environment.

Spin-wave-modes inside a ferromagnetic particle (imbedded in a paramagnetic matrix) are deduced by means of phenomenological spin-wave-theory for a spherical and a square-shaped particle (including a thin film). Surface-anisotropy is included, magnetostatic effects are excluded. The conditions for the occurrence of surface-exchange-modes are given. It is shown that these surface modes also follow from an exact quantummechanical treatment of localized spins in a square-shaped particle. Some thermodynamic consequences of such surface modes are pointed out.