Landauer resistance in the case of multichannel scattering

The Landauer resistance ρ _N ^L has been generalized to the case of multichannel scattering of a particle by the system of N nonoverlapping random potentials that are localized at the points x _i (i = 1, 2,..., N) and depend on x − x _i and y. It has been shown that, in this case, a new resistance ρ _N ^L appears, which is an exponential function of N. The recurrence equation for determining the Landauer resistance ρ _N ^L has been derived and its solution in the general case has been obtained.     

Magnetic, electrical, and optical properties of Ca1 ? x Ce x MnO3 ( x ≤ 0.12) single crystals

The magnetic, electrical, and optical properties of Ca_{1 − x} Ce _x MnO₃ (x≤0.12) manganite single crystals are investigated with the aim of revealing the specific features of the multiphase electronic and magnetic state as a function of the cerium concentration and the atmosphere used for growing single crystals. It is found that the concentration dependence of the low-temperature magnetization M(x) of the single crystals is shifted toward the high-concentration range as compared to the corresponding dependence of the polycrystals, which is explained by the predominant cation deficiency. The electrical resistivity and the reflection spectra of the single crystals in the infrared spectral range indicate that charge carriers exhibit a band nature at temperatures close to room temperature. The temperature dependence of the electrical resistivity of the single crystal with x = 0.08, which has the maximum magnetization in the studied series of Ca_{1 − x} Ce _x MnO₃ compounds, unlike polycrystals, exhibits a metallic behavior over the entire temperature range. The G-type antiferromagnetic phase with the Néel and Curie temperatures T _N(G) = T _C = 100 K is characterized by maxima of the electrical resistivity ρ and the magnetoresistance Δρ/ρ = |(ρ₀ − ρ _H )/ρ₀| = 38% in the magnetic field H = 90 kOe. The magnetoresistance Δρ/ρ of the single crystals at cerium concentrations x = 0.10 and 0.12 with variations in temperature exhibit three specific features: near the temperature of charge ordering T _co, near the temperature of the magnetic phase transition to the C-type antiferromagnetic phase T _N(C), and near the temperature of the phase transition to the magnetic charge-ordered phase T _N(MCO). An anomalous temperature dependence of the magnetization is revealed for a single crystal with x = 0.10 grown in oxygen at a pressure of 5 atm, which is explained by the presence of regions with hole conductivity due to cation deficiency. The inhomogeneous electronic and magnetic state is associated with the interrelation of the charge, orbital, and spin orderings. Original Russian Text ? N.N. Loshkareva, A.V. Korolev, N.I. Solin, E.V. Mostovshchikova, S.V. Naumov, N.V. Kostromitina, A.M. Balbashov, 2009, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 135, No. 1, pp. 98–107.     

Metal-insulator transition in electron-doped Ba1−x La x MnO3 compounds

Electron-doped (Ba_1−x La _x )MnO₃ compounds were prepared for x=0−0.5. Measurements of X-ray diffraction (XRD) at room temperature and temperature variation of dc electrical resistivity down to 20 K were carried out. Samples with x=0.2–0.5 exhibit metal-insulator (M-I) transition. The maximum M-I transition temperature (T _c) of 289 K was observed for 30% of La doping (x=0.3). XRD patterns of these samples (x=0.2−0.5) were analyzed using Rietveld refinement. These samples are found to be mostly in single-phase form with orthorhombic symmetry (space group Pbnm). We have found strong correlation between Mn-O-Mn bond angles and T _c of M-I transition. The resistivity data below T _c could be fitted to the expression ρ=ρ ₁+ρ ₂ T ² and this shows that double exchange interaction plays a major role even in Mn⁴⁺-rich compound. Above T _c the resistivity data were fitted to variable range hopping and small polaron models.     

Magnetically two-phase state in Eu1−x AxMnO3 (A=Ca, Sr)

It is observed that low-temperature magnetic properties (dependence of the magnetization on the cooling conditions and the presence of a maximum in the initial magnetic susceptibility) of Eu_{1− x} A_xMnO₃ (A=Ca, Sr; x=0,0.3) samples are similar to those of spin glasses. However, there are also substantial differences: The magnetization depends on the cooling conditions right up to the maximum measurement fields H=45 kOe, and the temperature of T _N of the maximum of the initial magnetic susceptibility is independent of the frequency of the ac magnetic field in which the susceptibility is measured. The magnetization isotherms for T<T _N are a superposition of a linear part, characteristic for an antiferromagnet, and a small spontaneous part. For compositions containing Sr a maximum of the resistivity ρ (ρ_max∼10⁸ Ω ·cm) is observed near T _N; in a 120 kOe magnetic field this maximum is lowered by four orders of magnitude and the temperature of the maximum is two times higher. In compositions with x=0.3 the paramagnetic Curie point is much higher than for the composition with x=0: θ=110 K (A=Ca), 175 K (A=Sr), and −100 K (x=0). These characteristic features of the magnetic and electric properties are explained by the existence of a magnetically two-phase state in this system, consisting of ferromagnetic clusters, in which the charge carriers are concentrated, embedded in an insulating antiferromagnetic matrix. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 5, 375–380 (10 March 1999)     

Influence of grain boundaries on resistivity of manganites La1 − x K x MnO3

Results of investigation of resistivity and magnetoresistance of manganites La_{1 − x} K _x MnO₃ (x = 0.050–0.175) are presented. Behavior of resistivity ρ(T) in the paramagnetic and ferromagnetic phases has been described. To describe ρ(T) near the phase-transition temperature, notions of the percolation theory have been used. Two maxima have been found in the dependence ρ(T); their appearance has been attributed to the ceramic nature of the studied samples. The observed increase in magnetoresistance with a decrease in temperature is caused by intergranular spin-polarized tunneling of charge carriers.     

Analysis of the dc-resistivity of YBa2Cu3Ox: Deduction of the intragrain resistivity

The resistivity (100 K) scatters very much for YBa₂Cu₃O_x prepared as single crystals, epitaxial films or bulk samples which consist of grains of 1 to 10 m diameter. An analysis of (T) for granular bulk samples is presented indicating the existence of a low intrinsic resistivity ⁱ (T)= _0L ⁱ + ⁱ T with _0L ⁱ 0 and ⁱ 0.5µcm/K. The large grain boundary resistivity _b between the grains (>1 m) yield a macroscopic percolative conduction path lengtheningL/L ₀>1 with a reduced effective cross sectionC<C ₀ and thus, (T)= _b +(LC ₀/L ₀ C)· ⁱ (T). Evidence is presented for weak links inside single crystals and grains.     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Electrical-optical analysis of a GaN/sapphire LED chip by considering the resistivity of the current-spreading layer

The effects of current distribution in LED chips on the electrical potential and optical light extraction efficiency are investigated by a numerical simulation. The results show that when the resistivity of the current-spreading layer is decreased there is current-crowding near the n-contact. On the other hand, when the resistivity in the current-spreading layer increases, there is current-crowding near the p-contact. When the current is crowded near the n-contact due to less resistivity of the current-spreading layer, the input power is lower because of the smaller series resistance in the chip, and the light extraction efficiency is higher since the shadowing effect of the p-contact can be avoided. For L _p = 50 μm in this study, the light extraction efficiency at ρ _ITO = 0.1 × 10⁻³ Ω·cm is 1.4 times better than that when L _p = 100 μm, even though the driving voltage is raised 1.02 times.     

Magnetic susceptibility and inelastic electrical resistivity of GdZnxCu1−x alloys

The deviation from the Nordheim-Kurnakov rule and the anomalous behavior of spin-disordered electrical resistivity in quasi-binary GdZn (T _C =268 K)-GdCu (T _N =142 K) solid solutions is explained in effective medium approximation within percolation theory for the case of three phases, viz., ferro-, antiferro-, and paramagnetic. The strong increase of ρ at zinc concentrations x∼0.45 is attributed to the closeness of the system to the percolation threshold. The phase volumes calculated for the random-distribution case fit well to the concentration dependence of magnetic susceptibility. Fiz. Tverd. Tela (St. Petersburg) 40, 974–979 (June 1998)     

Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory

Motivated by the study of multivortices in the Electroweak Theory of Glashow–Salam–Weinberg [33], we obtain a concentration-compactness principle for the following class of mean field equations: on M, where (M,g) is a compact 2-manifold without boundary, 0 < a≤K(x)≤b, x∈M and λ > 0. We take with α _i > 0, δ _{p i} the Dirac measure with pole at point p _i ∈M, i= 1,…,m and ψ∈L ^∞(M) satisfying the necessary integrability condition for the solvability of (1)_λ. We provide an accurate analysis for solution sequences of (1)_λ, which admit a “blow up” point at a pole p _i of the Dirac measure, in the same spirit of the work of Brezis–Merle [11] and Li–Shafrir [35]. As a consequence, we are able to extend the work of Struwe–Tarantello [49] and Ding–Jost–Li–Wang [21] and derive necessary and sufficient conditions for the existence of periodic N-vortices in the Electroweak Theory. Our result is sharp for N= 1, 2, 3, 4 and was motivated by the work of Spruck–Yang [46], who established an analogous sharp result for N= 1, 2. Received: 24 September 2001 / Accepted: 7 December 2001     

Anisotropy of the superconducting properties of YBa2Cu3O7−x single crystals with reduced oxygen content

In an investigation of the resistivity anisotropy of YBa₂Cu₃O_7−x single crystals with suboptimal oxygen content it is observed that the superconducting transition for the component ρc of the resistivity tensor is shifted to lower temperatures with respect to the transition for the component ρab. A similar shift is also observed for the transition in the temperature dependence of the dynamic magnetic susceptibility. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 309–313 (25 August 1998)     

Quantum oscillations of the resistivity and hall coefficient and the quantum limit in Bi<Subscript>0.93</Subscript>Sb<Subscript>0.07</Subscript> alloys in a magnetic field along the trigonal axis

The dependences of the electrical resistivity ρ and the Hall coefficient R on the magnetic field have been measured for single-crystal samples of the n-Bi_0.93Sb_0.07 semiconductor alloys with electron concentrations in the range 1 × 10¹⁶ cm⁻³ < n < 2 × 10¹⁸ cm⁻³. It has been found that the measured dependences exhibit Shubnikov-de Haas quantum oscillations. The magnetic fields corresponding to the maxima of the quantum oscillations of the electrical resistivity are in good agreement with the calculated values of the magnetic fields in which the Landau quantum level with the number N intersects the Fermi level. The quantum oscillations of the Hall coefficient with small numbers are characterized by a significant spin splitting. In a magnetic field directed along the trigonal axis, the quantum oscillations of the resistivity ρ and the Hall coefficient R are associated with electrons of the three-valley semiconductor and are in phase with the magnetic field. In the case of a magnetic field directed parallel to the binary axis, the quantum oscillations associated both with electrons of the secondary ellipsoids in weaker magnetic fields and with electrons of the main ellipsoid in strong magnetic fields (after the overflow of electrons from the secondary ellipsoids to the main ellipsoid) are also in phase. In magnetic fields of the quantum limit ħω _c /2 ≥ E _F, the electrical conductivity increases with an increase in the magnetic field: σ₂₂(H) ∼ H ^k . A theoretical evaluation of the exponent in this expression for a nonparabolic semiconductor leads to values of k close to the experimental values in the range 4 ≤ k ≤ 4.6, which were obtained for samples of the semiconductor alloys with different electron concentrations. A further increase in the magnetic field results in a decrease of the exponent k and in the transition to the inequality σ₂₂(H) ≤ σ₂₁(H).     

Bistability of quantum magnetotransport in a multilayer Ge/p-Ge1−x Six heterostructure with wide potential wells

Two metastable states of a multilayer Ge/p-Ge_1−x Si_x heterosystem with wide (∼ 35 nm) potential wells (Ge) are observed in strong magnetic fields B at low temperatures. In the first state, the Hall resistivity exhibits an inflection near the value ρ_xy=h/e ² scaled to one Ge layer. The longitudinal magnetoresistivity ρ_xx(B) possesses a minimum in the range of fields where this inflection occurs. The temperature evolution of the inflection in ρ_xy(B), the minimum of ρ _xx(B), and the value of ρ_xy at the inflection indicates a weakly expressed state of the quantum Hall effect with a uniform current distribution over the layers. In the second metastable state, an unusually wide plateau near h/2e ² with a very weak field dependence is observed in ρ_xy(B). Estimates show that in these samples the Fermi level lies below but close to the top of the inflection in the bottom of the well. For this reason, the second state can be explained by separation of a hole gas in the Ge layers into two sublayers, and the saturation of ρ_xy(B) near h/2e ² can be explained by the formation of a quantum Hall insulator state. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 290–297 (25 August 1999)     

Investigation of low-temperature electrical conduction mechanisms in highly resistive GaN bulk layers extracted with Simple Parallel Conduction Extraction Method

The electrical conduction mechanisms in various highly resistive GaN layers of Al _x Ga_1−x N/AlN/GaN/AlN heterostructures are investigated in a temperature range between T=40 K and 185 K. Temperature-dependent conductivities of the bulk GaN layers are extracted from Hall measurements with implementing simple parallel conduction extraction method (SPCEM). It is observed that the resistivity (ρ) increases with decreasing carrier density in the insulating side of the metal–insulator transition for highly resistive GaN layers. Then the conduction mechanism of highly resistive GaN layers changes from an activated conduction to variable range hopping conduction (VRH). In the studied temperature range, ln (ρ) is proportional to T ^−1/4 for the insulating sample and proportional to T ^−1/2 for the more highly insulating sample, indicating that the transport mechanism is due to VRH.     

Transport and magnetic properties of Pr1-xCaxCrO3 (x = 0.0–0.5): effect of t2g orbital degeneracy on the thermoelectric power

We report on the resistivity (ρ), thermoelectric power (S for Seebeck) and magnetic measurements of the series Pr_1-xCa_xCrO₃ (x=0.0–0.5). These orthochromites exhibit a T independent, large and positive S, from 100 K to 700 K which follows the Cr⁴⁺ concentration. Upon Ca²⁺ for Pr³⁺ substitution, a concomitant decrease of the resistivity and S values is found. The evolution of S as a function of hole concentration (Cr⁴⁺) can be nicely fitted by the modified Heikes formula which takes into account the orbital degeneracy associated to Cr³⁺/Cr⁴⁺. This is in good agreement with the model previously calculated by Marsh and Parris, in the case of weak magnetic coupling [Phys. Rev. B 54, 7720 (1996)]. The magnetic susceptibility measurements support the assumption of a weak magnetic coupling since the antiferromagnetic ordering T_N values are found to be lower than 250 K. For Pr_0.7Ca_0.3CrO₃, the power factor PF= S²/ρ measured at 700 K is equal to 1.9×10^-4 W m^-1K^-2. The present system, chemically stable in air up to T > 1000 °C, is promising for thermoelectric application at very high temperature.     

Anomalous Hall effect in granular Fe/SiO2 films in the tunneling-conduction regime

It is established that the Hall effect in Fe/SiO₂ nanocomposite films in the activational tunneling conduction range is anomalous, i.e., the Hall resistivity ρ_h is proportional to the magnetization and is due to the spin-orbit interaction. The parametric coupling of the Hall and longitudinal (ρ_xx) resistances ρ_h ∝ ρ _xx ^m (with temperature as the parameter) is characterized by a much lower value of the exponent m than in a uniform ferromagnetic metal. This circumstance is attributed to the characteristic features of the Hall effect mechanism in the hopping regime — in our case, the interference of the amplitudes of tunneling transitions in a set of three granules. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 87–92 (25 July 1999)     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)