Free carrier absorption in quantizing magnetic fields: Nonpolar optical phonon scattering

A quantum theory of free carrier absorption in nondegenerate semiconductors and in strong magnetic fields which was previously developed to treat the case when acoustic phonon scattering dominates the free carrier absorption process [1] is extended to treat the case when nonpolar optical scattering is important. When the electromagnetic radiation field is polarized parallel to the direction of the applied magnetic field, results are obtained which are similar to those when acoustic phonon scattering is dominant. The free carrier absorption is an oscillatory function of the magnetic field which on the average increases in magnitude with the magnetic field. However, more structure in the free carrier absorption occurs when nonpolar optical phonon scattering dominates. This is due to the fact that there are two periods in the oscillatory magnetic field dependence associated with the emission or the absorption of optical phonons during the intraband transitions. When the cyclotron frequency exceeds the sum of the photon and optical phonon frequencies, i.e. ω_c > θ + ω_o, the free carrier absorption is predicted to increase linearly with magnetic field when ?ω_c? k_BT. The magnetic field dependence of the free carrier absorption can be explained in terms of phonon-assisted transitions between the various Landau levels in a band involving the emission and absorption of optical phonons.     

CDW instability of electron gas in a strong magnetic field

It is shown that within the Hartree-Fock approximation the electron gas in the quantum limit of a strong magnetic field has an instability as the temperature is lowered toward the charge density wave state with an wave-vector which has finite components in the directions not only parallel but also perpendicular to the field. The critical temperature, T_c, is estimated under the assumption of T_c??_F?ω_c, where ?_F and ω_c are the Fermi energy of the non-interacting system and the cyclotron frequency respectively.     

Cyclotron resonance study of conduction electrons in n-type indium antimonide under a strong magnetic field—I: Thermal equilibrium case

The far IR cyclotron resonance of conduction electrons is investigated in n-type indium antimonide in the quantum regimes, ?ω_ck_BT and ?ω_c?k_BT. The resonance peak position, half width, and the degree asymmetry in the line shape are studied as a function of temperature. In analyzing the experimental data, the three band model has been employed together with modern theoretical results of electron scattering by ionized impurities in the presence of a strong magnetic field. It is found that, for example for an experiment at 84 μm, the Une width depends very little on temperature between 4.2 and 45 K where the ionized impurity scattering is dominant, and increases rapidly with temperature above 45 K where the onset of phonon scattering is expected. Further details of the ionized impurity scattering were investigated by using three different laser wavelengths 84, 119 and 172μm. The line width at the phonon-limited temperature region depends very little on magnetic field and sample. The temperature dependence of the band gap was also determined by analysis of the resonance peak shift.     

Quantum theory of nonresonant electromagnetic and ultrasonic absorption in glasses

We develop quantum theory of nonresonant ultrasonic and electromagnetic absorption in glasses at low temperatures. In the quantum region where ?ω?kT the nonresonant absorption coefficients are proportional to ω³ which seems to be in agreement with the existing experimental data.The existence of characteristic temperature T_c (or characteristic energy E_c = kT_c) of the order of 10 + 20 K is established. At higher interlevel spacing E the concept of two-level systems in their conventional form is not applicable because of their strong coupling to the phonons. Neither the perturbation theory is applicable for calculation of absorption in the frequency interval ?ω?_c or at temperature interval T?T_c = E_c/k.     

The amplification of far-infrared radiation on optically excited p-type germanium

The far-infrared spectrum of cyclotron resonance absorption in the valence band of p-type germanium has been calculated using 6 × 6 k*p Hamiltonian for degenerate valence band for magnetic field 20T and lattice temperature 77K. That has been shown that excitation by pulseCO ₂ laser radiation can lead to the amplification on light hole cyclotron resonance.     

Anticrossing phenomena in a resonator with 2D electrons on liquid helium

We have investigated the details of the eigenmode for a resonator containing a two-dimensional electron system (2DES) formed on the surface of liquid helium. We show that anticrossing phenomena occur near the crossing point ω₀=ω_c, where ω₀ is the eigenmode of the resonator and ω_c is the cyclotron frequency. The structure of the coupling constant is established. It is a flexible parameter, i.e., sensitive especially to magnetic field and electron density. A finite coupling leads to a perturbation, δω, of the eigenmode of the resonator in presence of the 2DES. Corresponding calculations and measurements of δω are presented. The theory fits the experimental data. The influence of anticrossing on the cyclotron resonance absorption line shape is demonstrated.     

Microwave photoresistance of a double quantum well at high filling factors

The effect of millimeter wave radiation on the electronic transport in a GaAs double quantum well at a temperature of 4.2 K in a magnetic field of up to 2 T has been studied. Resistance (conductance) oscillations have been shown to appear in the two-dimensional electronic system under investigation at high filling factors. The magnetic field positions of the oscillation maxima are determined by the condition Δ_SAS/? = lω_c, where Δ_SAS = (E ₂ ? E ₁) is the size quantization sublevel splitting in the quantum well, ω_c is the cyclotron frequency, and l is a positive integer. It has been found that the microwave field substantially modifies the oscillations in the double quantum well, which results in alternating two-frequency oscillations of photoresistance with the inverse magnetic field.     

Formal solutions for response functions of superconductors and 3He(B): II. Applications to acoustic and quasihomogeneous regime

Formal solutions for the autocorrelation functions of density and the transversal current are discussed in the acoustic and quasihomogeneous regime. The poles of these functions are obtained without any restrictions imposed on Landau parameters. The formula for sound dispersion at T = 0 is generalized by the inclusion of terms of the relative order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$, (k is the wave vector, v is the Fermi velocity, Δ is the energy gap, $\text{h}\text{?}\text{≡ 1}$). The dispersion formulae for transversal and longitudinal excitations with a gap for ³He(B) are also given, with an accuracy up to the terms of the order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$, for 0 ? T ? T_c, and without any restrictions imposed on Landau parameters. Under these last assumptions our autocorrelation functions are calculated in the polar as well as non-polar regions. It is shown that if T > 0, the transversal function vanishes at some ω, such that $\text{0 ? ω}{}^2\text{? (}\text{12}\text{5}\text{)Δ}{}^2$. Moreover,the zero of the density autocorrelation function is distanced from its pole by an amount of the order of $\text{(}\text{kv}\text{2Δ}\text{)}{}^2$.     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Equilibrium and stability of the charged particles’ fluxes drifting crosswise to the strong magnetic field at the expense of the Hall charge separation

The current equilibrium is investigated, where the generation of the Hall electric field on the magnetic Debye radius r _B = B ₀/(4πen _e) is considered by the drifting of the relativistic electrons crosswise to the strong magnetic field. In this case, the electron propagation is possible at the distance d that is essentially larger than the electron radius of the backward reflection in the magnetic field r ₀ ? m _e v _z c/(eB ₀). The instability of the joint drift motion of ions and electrons is investigated for the frequency oscillation w much higher than the ion cyclotron frequency w _Bi and by 4π n _i m _i c ² ? B ₀ ² and (k · B ₀) = 0. It is shown that the resonance effects by the ion beam’s plasma frequency w ? kv ₀ = w _pi leads to the generation of the nonpotential perturbations with the characteristic increment Imw ～ 10^?1 ÷ 10^{? 2} w _pi. Estimates show that the instability, associated with the propagation of the high-energy ion beam through the strong magnetic field, can essentially be like the edge-localized mode in tokamaks.     

Spektroskopische Untersuchungen an DyAsO4

DyAsO₄ undergoes a crystallographic phase transition atT _D=11.2K which is induced by a cooperative Jahn-Teller-effect. As deduced from the optical absorption spectra the distance between the two lowest lying Kramers doublets of the Dy³⁺ ion is increased from (6.1±0.5) cm^?1 aboveT _D to (25.0±0.5) cm^?1 at 4.2 K. BelowT _D the splitting factor of the lowest doublet becomes nearly uniaxial with a maximum value ofg _b =17.5±1.0 along the crystallographicb-axis. AtT _N=2.44 K the crystals order antiferromagnetically. The absorption lines of Er³⁺ ions in DyAsO₄ show already a splitting immediately belowT _D which is explained by magnetic short range ordering of the Dy³⁺ ions in the temperature rangeT _{N D} .     

Superconductivity in α- and ω-Zirconium under high pressure

The pressure dependence of the superconducting transition temperatureT _c (p) of α-Zr has been investigated in both solid and liquid pressure transmitting media. Up to about 45 kbardT _c /dp was measured to be + 3.5 × 10^?6 K/bar. Cold working at 4.2 K produced a strong irreversible effect onT _c . The superconductivity of the high pressure phase, ω-Zr, has been studied in its region of stability, i.e. above 60 kbar. For ω-Zr,dT _c /dp=+7.7 × 10^?6K/bar, andT _c (0)=0.72 K (by extrapolation).     

Three-dimensional wake potential in a flowing magnetized plasma

The three-dimensional structure of the wake potential due to ion cyclotron wave in a dusty magnetized plasma with streaming ions is studied. The analysis includes the E×B drift effect in addition to the ions flow with a constant velocity u_io perpendicular to the magnetic field. The result shows that the magnitude of wake potential behind a dust grain is much increased for strongly magnetized plasma.     

Crystalline electric field effects on the resistivity of PrAl2

Calculations in the mean field approximation of the magnetic contribution to the resistivity of a J = 4 ion in a cubic lattice, considering the effects of the crystalline electric field, are presented for both T >T_c and T < T_c (excluding the critical region). The magnetic contribution to the resistivity of ferromagnetic PrAl₂ is discussed in terms of the above calculations and the total crystalline electric field splitting of this system is determined to be 100 K. Results are also presented for the critical behavior of d?/dT.     

Excitation of ion cyclotron waves at the difference frequency of two microwave beams in a semiconductor

This paper presents an investigation of the resonant excitation of the electrostatic ion cyclotron wave at the difference frequency of two microwave beams propagating in a magnetoactive solid state plasma, viz. n InSb. The resonant excitation of the electrostatic ion cyclotron wave occurs when the difference frequency of the two microwave beams and the difference of their propagation vectors satisfy the dispersion relation corresponding to the electrostatic ion cyclotron wave. For typical plasma parameters of n InSb and microwave beams of power densities 1 MW cm^?2, the power density of the excited ion cyclotron wave is 0.40 kW cm^?2 when external magnetic field is $\text{1.46 kG (}\text{Ω}{}_{\mathrm{c}}\text{ω}\text{) = 0.1)}$. The power density of the excited ion cyclotron wave increases with the magnetic field. This study may provide new means for the characterisation and diagnostic of semiconductors.     

The large polaron in a magnetic field: Possible existence of a phase transition

It is shown that the ground state energy of a polaron in a magnetic field (calculated in the Feynman approximation) exhibits a discontinuity in the first derivative with respect to α (the electron-phonon coupling constant) if ω_c/ω_o (cyclotron frequency to LO-phonon frequency) is larger than 2.24. This discontinuity has the characteristics of a first order phase transition if α is interpreted as an inverse temperature. For ω_c/ω_o = 2.24 the transition is second order. We found that below the transition point the phonon cloud cannot follow the electron in its motion in the magnetic field.     

Exciton-magnon interactions in NicMg1−c O single crystals

The effect of chemical composition and temperature on exciton-magnon interactions in Ni_cMg_1?c O single crystals was studied using optical absorption spectra in the region of the magnetic-dipole ³ A _2g (G)→³ T _2g (F) and electric-dipole ³ A _2g (F)→¹ E _g (D) transitions. The two zero-phonon lines at ～7800 and ～7840 cm^?1 on the low-energy side of the magnetic-dipole transition band were assigned to a pure exciton transition and an exciton-one-magnon transition at the center of the Brillouin zone. The intensity of the exciton-one-magnon peak decreases rapidly with increasing magnesium ion concentration and/or temperature, to vanish altogether at T=6 K for c<0.95 and at T=130 K for c≥0.99. Thus, the contribution of long-wavelength magnons in optical absorption spectra of Ni_cMg_1?c O becomes negligible at temperatures substantially lower than the Néel point T _N (the antiferromagnetic ordering temperature). This observation can be explained as being due to a substantial decrease in the characteristic spin-spin interaction length with increasing concentration of the diamagnetic magnesium impurity ions (static disorder) and/or with increasing amplitude of thermal atomic vibrations (dynamic disorder). At the same time, the peak at ～14500 cm^?1, which lies in the electric-dipole transition region and corresponds to excitation of an exciton and two magnons at the Brillouin zone edge, remains visible up to the Néel temperature. This is accounted for by the short-wavelength magnons being sensitive to short-range magnetic order, which persists up to T _N .     

Spectroscopic investigation of rare-earth chromium borates RCr3(BO3)4 (R = Nd, Sm)

The optical absorption spectra of single crystals of neodymium and samarium chromium borates are studied. A magnetic phase transition in NdCr₃(BO₃)₄ (at T _c = 8 ± 1 K) and SmCr₃(BO₃)₄ (at T _c = 5 ± 1 K) is observed. The effective magnetic field acting on the Nd³⁺ ion from the side of the ordered magnetic subsystem of chromium is estimated.     

What can we learn about critical magnetic phenomena from muon spin rotation experiments?

Measurements of the spin precession frequencies ω_μ and transvers relaxation rates Γ₂ of positive muons (μ⁺) magnetic phase of several iron-cobalt alloys and coabalt, and in amorphous Fe_o.91Zr_0.09 alloys are discussed with particular reference to the influence of critical phenomena on ω_μ and Γ₂. Although the temperature dependence ω_μ(T) is well described by scaling law ω_μ ∝ (T_c?T)^β′ where α′ varies strongly with the co concentration in the FeCo alloys, it is shown that the exponent α′ is not identical to the static scalling parameter β describing the critical behaviour of the spontaneous magnetization M. In paramagnetic iron we find Γ₂∝(T-T_c)^0.72, which is attributed to the effect of dynamical spin fluctuations on the μ⁺. Due to the apparent difference between the temperature dependence of ω_μ and that of M below T_c the frequency shifts observed in the paramagnetic regime are probably not directly proportional to the magnetic susceptibility. In amorphous Fe_0.91Zr_0.09 allosy frequency shifts and transverse relaxation rates are found up to nearly 2 T_c. Due to the shape of the Fe_0.91Zr_0.09 sample, demagnetization inhomogeneities certainly play an important rôle.     

Spin relaxation parameters in recombining radical ion pair (diphenylsulfide-d10)+/(p-Terphenyl-d14)− obtained by OD ESR and quantum beats techniques

Parameters of paramagnetic relaxation were determined by OD ESR and quantum beats techniques for a recombining pair of radical ions (DPS-d₁₀)⁺/(PTP-d₁₄)^? inn-hexane, isooctane,cis-decalin, and squalane solutions. TheT ₂ relaxation time determined by quantum beats technique is independent of solvent viscosity and magnetic field strength in the range 170–9600 G. These data are in agreement with the results obtained by OD ESR technique assuming fastT ₁ relaxation for radical cation. Neglecting the contribution of radical anion relaxation, we obtainedT _1c=T _2c?50 ns for (DPS-d₁₀)⁺.