On the phase transitions for the electronic excitations in semiconductors

A model Hamiltonian for a system of interacting electrons, holes and Wannier excitons is derived. This system of electronic excitations is assumed to be in a quasi-equilibrium state. With the aid of Bogolubov's variational principal the thermodynamic potential is calculated. Using the most general mean-field Hamiltonian as a trial Hamiltonian, a set of coupled integral equations is obtained for the self-energies. These equations are solved numerically for equal effective masses of the electrons and holes. Below a critical temperature ofk _B T _c0.65E _ex ^b whereE _ex ^b is the exciton binding energy, we find a first order phase transition from an exciton rich phase into a degenerate electron-hole phase. The mechanical and thermal stability of both phases is proven. Below a critical temperaturek _B T _c0.11E _ex ^b the exciton system becomes degenerate (Bose-Einstein condensation). A complete phase diagram of these three phases is given.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Mean field kinetic theory of a classical electron gas in a periodic potential. III. The high-temperature limit in two dimensions

The Vlasov-like mean field kinetic equation for a classical electron plasma in the periodic field of an ionic lattice is solved in the high-temperature limit in two dimensions. The predictions for the one-electron density, the static structure factor, and the long-wavelength charge fluctuation spectrum are compared to the results of extensive molecular dynamics simulations. The predicted shift and damping of the plasma oscillation mode are in reasonable agreement with the simulation data at intermediate couplings (=e ²/k _B T1), but the agreement deteriorates as the temperature or the density is lowered, because mean field theory does not lead to the expected Kosterlitz-Thouless transition to the dielectric phase where electrons are localized.     

Three-particle recombination coefficient of a weakly nonideal ultracold plasma in a high magnetic field

An expression for the recombination coefficient α _B in a weakly nonideal ultracold plasma in a high magnetic field has been proposed. According to this expression, α _B ∼ T _e ^−1.5 B ⁻², where T _e is the temperature of electrons and B is the strength of the magnetic field. Comparison of calculated values with experimental data including the results of the recent experiments on recombination in antihydrogen confirms the theoretical dependence.     

Energy relaxation of two-dimensional electrons in the quantum Hall effect regime

The mm-wave spectroscopy with high temporal resolution is used to measure the energy relaxation times τ_e of 2D electrons in GaAs/AlGaAs heterostructures in magnetic fields B=0–4 T under quasi-equilibrium conditions at T=4.2 K. With increasing B, a considerable increase in τe from 0.9 to 25 ns is observed. For high B and low values of the filling factor ν, the energy relaxation rate τ _e ^?1 oscillates. The depth of these oscillations and the positions of maxima depend on the filling factor ν. For ν>5, the relaxation rate τ _e ^?1 is maximum when the Fermi level lies in the region of the localized states between the Landau levels. For lower values of ν, the relaxation rate is maximum at half-integer values of τ _e ^?1 when the Fermi level is coincident with the Landau level. The characteristic features of the dependence τ _e ^?1 (B) are explained by different contributions of the intralevel and interlevel electron-phonon transitions to the process of the energy relaxation of 2D electrons.     

A Mathematical Representation of Quantizing the Motion of Relativistic Electrons in a Magnetic Field

It is shown that the quadratic component of the kinetic energy of continuous longitudinal motion of relativistic electrons in the external magnetic field is varied continuously between 0 and 2(2m _e c ²_B H) within each Landau energy level, undergoing an abrupt change at the boundaries of the levels. This results in the fact that in the quantum limit of a superstrong magnetic field where all electrons are at the zero Landau level, the maximum quadratic component of the kinetic energy of free longitudinal electron motion along the direction of the magnetic field is twice as high as the maximum quadratic component of the kinetic energy of its bound transverse motion.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Effects of the blackbody radiation on the harmonically bound electron-energy level shifts and consistency conditions

The influence of the vacuum radiation field on the harmonically bound electron (frequency ₀) is considered. The electron is minimally coupled to the blackbody radiation field. The dynamics of the system is exactly solvable. The high (k _B T₀) and low (k _B T₀) temperature expansions of the kinetic and potential energy are given. In the high temperature regime theT ²-dependent dynamic Stark shift is found whereas in the low temperature regime there is no temperature dependent shift. The position correlation function of the electron shows in the low temperature regime a unclassical algebraic decay (t ^–4,t/k _B T).     

Study of magnetic interactions of the Fe2+ ions and the protons of crystallization water in FeSO4.n H2O hydrates

The paper deals with a study of interactions of protons in crystallization water of paramagnetic hydrates FeSO₄.n H₂O (wheren=1, 4, 5 and 7). The interaction of protons and paramagnetic ions Fe²⁺ and the nuclear dipole-dipole interaction of protons have been studied by means of the parameters expressing the dependence of the second moment of the proton nuclear magnetic resonance (NMR) spectrum on the external magnetic field, by means of the volume magnetic susceptibilities and the relaxation timesT ₁ of the investigated series of hydrates.We are grateful to Prof. Dr. hab. Z.Pajak, director of Department of Radiospectroscopy IF UAM in Poznan, and to his coworkers Dr. J.Kapturczak, Dr. K.Jurga, Dr. S.Glowinkowski and Mgr. F.Brych for facilitating our measurements mentioned in the paper as well as for a valuable discussion.     

Utilization of rotational and vibrational temperatures for plasma diagnostics of high-pressure discharges

In the spectra of high-pressure discharges excited in molecular gases, very intensive molecular spectral bands may usually be observed. We may determine the rotational and vibrational temperatures without difficulty, however, the rotational and vibrational temperatures (T _r, T_v) do not offen equal to the temperature of neutral gas (T ₀) or to that of electrons (T _e). If the collision cross sections of electronic, atomic, and molecular excitation (deexcitation) are known, we may then calculate the dependence of the rotational and vibrational temperatures onT _e,T ₀,N _e and the pressure of the gas. The calculations have been performed for pure N₂ and for an Ar-N₂ mixture at atmospheric pressure. The computed graphs make it possible to determine some of the values 4T _e,T ₀,N _e if the temperaturesT _r andT _v are known.The author wishes to extend his thanks to Prof. V. Truneek for valuable comments and to Mr. A. Struka for the preparation of the diagrams.     

Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

Mössbauer study of iron-doped lithium niobate

From Mössbauer spectra of LiNbO₃⁵⁷Fe(III) single crystals under external fields of 4.92 and 6.2 T, the crystal field and hyperfine parameters are determined. Transmission integral fits indicate a Boltzmann population of the Fe(III) electronic levels with a spin temperature equal to the sample temperature. Spectra at external fields of 0 T and 19 mT can be satisfactorily simulated using an effective spin 1/2,g-factors calculated from spin-expectation values and an internal averaged dipole field of 5.5 mT inclined 20 to thec-axis. The simulations indicate cross-relaxation between Nb and Li nuclear spins and the Fe(III) electronic spin.     

Temperature dependence of the electronic spin relaxation of DCNQI salts

For the elucidation of the charge and spin dynamics of the radical anion salts of DCNQI with metallic counterions we have performed cw- and pulsed ESR experiments (βB _pp,T _1e ^?1 andT _2e ^?1 ) between 300 and 4 K at nine salts differing in counterions and sidegroups, respectively. We can explain the relaxation rates by dipolar electron-electron interaction and spin-orbit contribution. In the high temperature range we have a gradual decrease in the number of charge carriers by interband transitions without a slowing down of the mobility. With complete localization of the electron spins (no mobile electrons anymore) exchange interaction governs the spectral density, becoming strongly temperature dependent due to effective spin exchangeJ _eff(T), explained by an extended REHAC-model. This effective spin exchangeJ _eff(T) includes for the first time a contribution by the metallic counterions. For spin-orbit interaction we developed a model based on F. Adrian [1] not depending on the mixture of Bloch and spin states as given by Elliott [2]. This is achieved by the inclusion of the electronic probability on atoms with higher atomic numbers, modulated by phonons. This model explains the drastic changes in the ESR linewidth of different radical ion salts of DCNQI and allows inductively the prediction of the electronic properties of new radical ion systems of which just the molecular and crystal structure is known.     

Two successive magnetic transitions in Y2Cu2O5 studied by μSR

Zero field muon spin rotation and magnetic susceptibility experiments on investigation of magnetic properties of cuprateY ₂Cu₂O₅ have been performed in the temperature range 4.2–30 K. Transverse fieldSR-experiments have been also carried out in order to obtain accurate information about transition temperature and to study the influence of the external magnetic field. Our data show that two magnetic phase transitions occur inY ₂Cu₂O₅ with lowering temperature. Upper Neel temperatureT _N=13 K is consistent with previous experimental data. We obtained the temperature dependence of the local magnetic field on the muonB (T) in the antiferromagnetic phase.B (T) reveals a peculiarity (some change of the slope) near the temperatureT _N=7.5 K, which can be interpreted as an additional magnetic phase transition caused by a change in magnetic ordering of the copper subsystem. Applying a small external magnetic field 50 Oe leads to smearing of the peculiarity inB (T) dependence.     

Ferromagnetic resonance in a gallium substitued garnet film

The ferromagnetic resonance at X, K and Q-band has been studied on LPE₁₁₁ films of composition Y₃Fe_4.2Ga_0.8O₁₂. From the in-plane measurement and measurement in a 11¯2 plane theg-factor,g=2-02 (K, Q),g=2·05 (X band), the total uniaxial anisotropy fieldB _A (80 K)=750 G (75 mT),B _A (300 K)=250 G (25 mT) and the cubic field 2K ₁/M have been dstermined. Besides of the main resonance with the linewidth B =15 G (1·5 mT), B =50 G (5 mT), B _min=10·5 G (1·05 mT) a linear spin-wave spectrum and some high-field modes were observed. A new approximate method of crystal orientation in the plane of the film has been used based on the analysis of the in-plane dependence of the resonance field.The authors wish to express their thanks to Dr. S.Krupika for helpful discussions.     

Electronic excitation spectrum of an antiferromagnetic semiconductor (EuTe)

We study the electronic quasiparticle spectrum of an antiferromagnetic semiconductor, with a special application to EuTe. By use of the commonly accepteds-f model it is shown that the conduction band splits into two quasiparticle subbands, where this splitting persists in the paramagnetic region (T>T _n ), too. Shape, width and degree of overlapping of the two subbands are strongly temperature dependent and quite different for different types off-spin arrangements.—We present furthermore a critical classification of mean field treatments (Zener model), which neglect all spin exchange processes between conduction electrons and localized moments. Within our many body approach the lower conduction band edge of EuTe does not shift significantly with temperature, in agreement with the experiment, while the Zener model predicts a drastic red shift upon cooling belowT _n .     

Antiferromagnetic Ordering of Magnetic Clusters Units in Nb6F15

We have studied the magnetic cluster compound Nb₆F₁₅ which has an odd number of 15 valence electrons per (Nb₆F₁₂)³⁺ cluster core, as a function of temperature using nuclear magnetic resonance, magnetic susceptibility, electron magnetic resonance and neutron powder diffraction. Nuclear magnetic resonance of the ¹⁹F nuclei shows two lines corresponding to the apical F^a?a nucleus, and to the inner Fⁱ nuclei. The temperature dependence of the signal from the Fⁱ nuclei reveals an antiferromagnetic ordering at T < 5 K, with a hyperfine field of ~2 mT. Magnetic susceptibility exhibits a Curie–Weiss behavior with T _N ~5 K, and μ _eff ~1.57 μ_B close to the expected theoretical value for one unpaired electron (1.73 μ_B). Electron magnetic resonance linewidth shows a transition at 5 K. Upon cooling from 10 to 1.4 K, the neutron diffraction shows a decrease in the intensity of the low-angle diffuse scattering below Q ~0.27 Å^?1. This decrease is consistent with emergence of magnetic order of large magnetic objects (clusters). This study shows that Nb₆F₁₅ is paramagnetic at RT and undergoes a transition to antiferromagnetic order at 5 K. This unique antiferromagnetic ordering results from the interaction between magnetic spins delocalized over each entire (Nb₆F ₁₂ ⁱ )³⁺ cluster core, rather than the common magnetic ordering.     

The sub-micrometer thickness n-InSb/i-GaAs epilayers for magnetoresistor applications at room temperatures of operation

Magnetotransport at fields up to 500 mT and LF-noise characteristics are reported for miniature magnetoresistors with ferrite concentrators based on Sn-doped n-InSb/i-GaAs heterostructures grown by MBE. The thickness of the InSb epilayers lie in the range 0.55–1.5 μm giving room temperature mobilities of 2.5–5.5 m² V⁻¹ s⁻¹ with carrier densities of (0.5–1.5)×10¹⁷ cm⁻³. The room temperature magnetoresistance (MR) for our two terminal devices could be as high as 115% at 50 mT which is comparable to the extraordinary MR (ExMR) recently reported in microscopic composite van der Pauw disks four terminal devices [Science 289 (2000) 1530]. In addition, a high signal-to-noise ratio and a good temperature stability of R(B)/R₀=0.5–0.83% K⁻¹ was observed for B<60 mT (below the saturation field B_sat for ferrite). Device resistance stability R₀(T) was equal to 0.27–0.66% K⁻¹ in zero field with a nominal device resistance R₀=197–224 Ω for DC currents in the range I=0.01–1.0 mA. The minimum detectable magnetic field is estimated from the reduced differential MR (∂R/∂B)/R=2000% T⁻¹ at B=31 mT and normalised 1/f current noise power spectral density measured at the same field. The resolution limit B_min=2.6 nT at 10² Hz and B_min=0.82 nT at 10³ Hz. These resolution limits are seven times better than those recently reported for the same material n-InSb/i-GaAs and ferrite fabricated Hall sensors [Magnetotransport and Raman characterization of n-InSb/i-GaAs epilayers, for Hall sensors applications over extremely wide ranges of temperature and magnetic field, Proceedings NGS 10, IPAP Conference Series 2, IPAP, Tokyo, 2001, pp. 151–154].     

Critical current density of a YBa2Cu3O7 film: Comparison between experiment and collective pinning theory

With the vibrating reed technique we have measured the critical current densityJ _c of a Y 123 200 nm thin film as a function of magnetic field perpendicular to the CuO₂ planes (O T<B8 T) and temperature (20KT60 K). At fieldsB<0.1 TJ _c is magnetic field independent and decreases at higher fields. A comparison with theory indicates that a crossover from a single pinning to a small bundle collective pinning regime may explain the observed behaviour. According to our estimate the main pinning centers are weak point pins due to oxygen vacancies. From the temperature dependence ofJ _c atB0 we obtain a temperature dependence of the thermodynamical critical fieldB _c (1–T/T _c )² forT20 K which agrees with the anomalous temperature dependence ofB _c2 observed recently in highly anisotropic high temperature superconductors.     

Two-body correlations and pair formation in the two-dimensional Coulomb gas

We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z₁ e(>0) and Z₂ e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplings=e ²/k _BTc=2/¦Z₁Z₂¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the range _c/2<< _c, due to gradual ion condensation. The usual integral equations for the pair correlation functions admit no solutions in that range. Preliminary Monte Carlo simulations for the symmetric case (Z₁=–Z₂) reveal a striking chemical equilibrium between tightly bound ion pairs and free ions, which is reasonably well described by a simple Bjerrum model.