Relaxation Of Conduction Electrons Research Articles

Powder EPR of Gd 3+ in the superconductors SnMo 6S 8 and PbMo 6S 8

EPR spectra at 35 and 60 GHz of Gd 3+ diluted (∼1%) in powdered SnMo 6S 8 and PbMo 6S 8 are presented and interpreted. The crystal field is found to be axial, with D = b 2 0=-760 gauss and -740 Gauss for the tin and lead compounds respectively. Values are obtained for <J(q)> and J(q = 0). Below T c the impurity to conduction electron relaxation rate is no longer proportional to temperature but decreases more rapidly. From this temperature dependence we extract a value for 2Δ kT c of roughly 5 for both compounds.

Ohm's law violation in spin glasses

Electrical resistivity rho s of metal containing ordered (spin glass) magnetic impurities is calculated. Two limiting cases are considered: (i) tau e/ tau i<<1 ( tau e and tau i are the times of collisions of electrons with each other and with nonmagnetic impurities); (ii) square root ( tau i/ tau ph)<<1 ( tau ph is the electron-phonon collision time). In both cases at solution of the kinetic equation it was assumed that at the first stage magnetic impurities do not take part in the conduction electron relaxation. It is shown that dependence of rho s on electric field (or on current density) is strongly nonlinear irrespective of the relaxation regime, and derivatives of rho s with respect to field or current contain a characteristic cusp which can be easily recorded experimentally. The calculated effect can be observed at relatively small current densities j approximately 105-106 A cm-2.

Core Spectra of Metals

By means of model calculations for an independent-electron metal, we calculate the photon absorption and emission spectra of core states, including conduction-electron relaxation. We find an x-ray edge anomaly merging into a spectrum resembling that of screened-exciton theory. Neither of these theoretical limits adequately represents the detailed structure of the exact results.

Optical properties of the sodium-tungsten bronzes and tungsten trioxide

A polarization-modulation ellipsometric technique was used to make direct measurements of the optical dielectric constants of single-crystal specimens of the nonstoichiometric tungsten-bronze compound ${\mathrm{Na}}_{x}\mathrm{W}{\mathrm{O}}_{3}$ ($0.52lxl0.94$) and W${\mathrm{O}}_{3}$, in the energy range from 1.0 to 5.5 eV. A method for determining the optical constants of anisotropic materials from modulation ellipsometry was developed in the study of tungsten trioxide. The behavior of the sodium bronzes as a function of sodium concentration is in agreement with recent calculations of the band structures for these materials. The system exhibits almost rigid-band behavior. The data were fit to the classical Drude free-electron model for the optical properties of metals. The W${\mathrm{O}}_{3}$ dielectric constants were used to directly determine the contribution of higher-energy bound-electron transitions to the optical constants of ${\mathrm{Na}}_{x}\mathrm{W}{\mathrm{O}}_{3}$ in the free-electron region. The results of jointdensity-of-states calculations were used in conjunction with the free-electron model to demonstrate that a relatively large discrepancy between conduction-electron relaxation times derived from the free-electron model alone and those determined from the dc conductivity may result, in part, from underlying interband transitions.

Electron spin resonance ofGdxLa1−xPd3intermetallic compounds

We have extended our ESR study of Gd in the intermetallic compound ${\mathrm{Gd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{3}$ to samples annealed at 940\ifmmode^\circ\else\textdegree\fi{}C and cooled rapidly to room temperature. We have measured the ESR linewidths and $g$ shifts as a function of temperature and concentration of Gd. They were found to exhibit Korringa-like thermal broadening between 6 and 40\ifmmode^\circ\else\textdegree\fi{}K. We have deduced the average value of ${J}_{\mathrm{eff}}$ for the effective-exchange integral to be 0.24 \ifmmode\pm\else\textpm\fi{} 0.03 eV. We have calculated also the magnitudes of the conduction-electron relaxation rates to the lattice, (i) due to the undisturbed host lattice, (ii) by spin-flip scattering due to the magnetic impurity Gd, and (iii) by spin-flip scattering due to the nonmagnetic impurity Th.

Effects of correlation interaction of electrons with deep holes in X‐ray spectra of metals

AbstractAbsorption spectra and spectra of emission excited by the secondary method are calculated. Two modes of emission excitation are considered: (i) the energy of exciting quanta is great with respect to the inner‐level ionization threshold, (ii) the energy of exciting quanta is continuously filling a small interval (about the width of the valence band) near the threshold. The calculations are carried out for a simple metal model by a one‐site approximation using the formalism of an effective non‐hermitian Hamiltonian which enables one to involve in a natural way into the theory the readjustment effects of a valence system in the field of the emerging hole as well as the finite lifetime of that hole. In the whole frequency interval of the observed values of the spectra the calculation results obtained by the non‐hermitian Hamiltonian method are compared with those obtained on the basis of other methods known earlier. The effect of overlap of the absorption and emission spectra for the threshold mode of excitation is made depending on the relation between the hole lifetime and the conduction electron relaxation time.

Observation of intrinsic spin-lattice relaxation of conduction electrons in metallic lithium

Temperature dependent intrinsic spin relaxation of conduction electrons in lithium observed via a spin-echo method is reported. Experimental results obtained are likely to correspond to a spin-current relaxation mechanism predicted earlier by Overhauser.

Electron spin resonance ofGdxLa1−xPd3intermetallic compounds

Electron spin resonance of Gd in ${\mathrm{Gd}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{3}$ intermetallic compounds annealed at 740 and 840\ifmmode^\circ\else\textdegree\fi{}C exhibit a dependence of linewidths and $g$ shifts on the annealing temperature. The linewidths and $g$ shifts were measured as functions of temperature and concentration of Gd. Samples with high Gd concentration (1 at.% or more) were found to have bottleneck effects. All samples annealed at 740\ifmmode^\circ\else\textdegree\fi{}C were found to exhibit Korringa-like thermal broadening between 20 and 40\ifmmode^\circ\else\textdegree\fi{}K and those annealed at 840\ifmmode^\circ\else\textdegree\fi{}C were found to be Korringa-like between 6 and 35\ifmmode^\circ\else\textdegree\fi{}K. Below 20\ifmmode^\circ\else\textdegree\fi{}K, samples annealed at 740\ifmmode^\circ\else\textdegree\fi{}C were found to exhibit ordering effects whereas samples annealed at 840\ifmmode^\circ\else\textdegree\fi{}C did not show such effects even at 6\ifmmode^\circ\else\textdegree\fi{}K. These differences are indicative of the difference in the structural composition of the lattice due to annealing. We have deduced the average values for the exchange integral $J$ to be 0.16 \ifmmode\pm\else\textpm\fi{} 0.03 eV and 0.15 \ifmmode\pm\else\textpm\fi{} 0.03 eV for the samples annealed at 740 and 840\ifmmode^\circ\else\textdegree\fi{}C, respectively. We have obtained also the magnitudes of two contributions to the conduction-electron relaxation rates to the lattice (i) due to undisturbed host lattice and (ii) by spin-flip scattering due to Gd.

Spin relaxation of conduction electrons in GaAs

We have used optical spin orientation techniques to measure T 1 of conduction electrons in GaAs ( NinA ≈ 10 17 cm -3) for 4.7 K ⩽ T ⩽ 200 K. From Hall effect measurements we estimated the electron momentum relaxation time τ p . For 50 K ⩽ T ⩽ 200 K, the product T 1τ p agrees with our earlier order of magnitude estimate of the D'yakonov-Perel' mechanism, in which band structure induced precession is strongly narrowed by momentum relaxation. The Elliott mechanism is one to two orders of magnitude weaker.

Spin relaxation of conduction electrons inAlxGa1−xAs

We report measurements of conduction-electron spin relaxation times ${T}_{1}$ in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ ($0.07\ensuremath{\le}x\ensuremath{\le}0.28$) ($4.7\ensuremath{\le}T\ensuremath{\le}300$ K) using optical spin-orientation techniques. ${T}_{1}$ above about 50 K is strongly temperature dependent, and its order of magnitude and temperature dependence may be accounted for by the D'yakanov-Perel mechanism, in which band-structure-induced spin relaxation is strongly narrowed by momentum relaxation. We estimate that the Elliott mechanism is, however, only one order of magnitude weaker, and it cannot be completely ruled out. At temperatures below about 50 K, ${T}_{1}$ is limited by nuclear hyperfine effects.

Spin relaxation of conduction electrons in highly-doped n-type germanium at low temperature

We present a theory of the spin relaxation time of the conduction electrons in highly-doped n-type germanium at liquid helium temperature. The theory is compared with some of our measurements and the experimental data available in the literature on As-doped germanium. The observed linewidth at T = 10 K is accounted for in the whole metallic concentration range ( N D > 3 × 10 17 cm −3). In the lower concentration range (3 × 10 17 < N D < 10 18 cm −3), the relevant mechanism is the random jumping of the g factor upon intervalley scattering. The agreement with experiment is good without any adjustable parameter. In the higher concentration range ( N D > 10 18 cm −3), the dominant process for the linewidth is the spin-flip scattering by ionized donors (Elliott process); the usual theory is shown to be insufficient and the greater effectiveness of scattering by the localized part of the donor potentials is pointed out. The calculated linewidth is related to the intervalley scattering time T iv. The agreement with experiment is good and predictions are given for the linewidth in the case of other shallow donors in the same concentration range.

Nuclear relaxation ofMn55in Ni-Mn alloys

Nuclear relaxation times of $^{55}\mathrm{Mn}$ have been studied in a series of Ni-Mn alloys containing between 1.0- and 14.4-at.% Mn using spin-echo techniques. ${T}_{1}$ was measured at 77 \ifmmode^\circ\else\textdegree\fi{}K and in some cases at 4.2 \ifmmode^\circ\else\textdegree\fi{}K as a function of external magnetic field. In the 1.0-at.% alloy ${T}_{1}T$ increases from a value of 30 msec \ifmmode^\circ\else\textdegree\fi{}K in zero field to a value of about 90 msec \ifmmode^\circ\else\textdegree\fi{}K at 18 kG. At 18 kG, ${T}_{1}T$ is found to decrease with increasing Mn concentration to a value of about 11 msec \ifmmode^\circ\else\textdegree\fi{}K at 14.4-at.% Mn. Various contributions to the nuclear relaxation are evaluated both in the dilute Mn in Ni alloy and in the more concentrated alloy. In the dilute alloy, spin-wave-enhanced conduction-electron relaxation appears to be the dominant relaxation mechanism, while in the more concentrated alloys the orbital relaxation may be important.

Spin relaxation of conduction electrons in highly-doped n-type germanium at low temperature

Spin relaxation of conduction electrons in highly-doped n-type germanium at low temperature

EPR conduction-electron relaxation by cerium and gadolinium impurities in LaAl 2

The conduction-electron relaxation by cerium impurities is computed by use of the effective exchange Hamiltonian which takes into account both combined spin and orbit exchange scattering and crystalline field effects, which finally can account for recent EPR measurements of Gd in LaAl 2 with cerium impurities.

Spin relaxation of conduction electrons at a surface

Strong surface relaxation effects are found in the transmission conduction electron spin resonance (TESR) at aluminium foils coated by a thin zinc layer. The increase of relaxation rate varies linearly with the inverse of thickness of the aluminium foils and is independent of the direction of the propagation of the radiofrequency field through the sample. Using a phenomenological model due to Dyson (1955), the TESR lineshape is calculated and, in general, good agreement is found between experiment and theory.

Spin diffusion and relaxation in dilute magnetic alloys: Electron-electron interaction

Diffusion and relaxation of conduction electrons is studied without making the usual approximation that the spin-orbit scattering be smaller than the impurity potential scattering. Renormalization of impurity vertices by the electron-electron interaction reduces the potential, enhances the s-d, but does not affect the spin-orbit scattering cross-section.

Optical absorption in virtual bound state alloys

Abstract We present simple models for the absorption of radiation by conduction electron relaxation and by impurity and host electron excitation. The former can be interpreted in terms of a frequency dependent relaxation time.

Spin relaxation of conduction electrons in highly doped semiconductors (InSb, Si, Ge)

AbstractExperimental data of the temperature and concentration dependence of the ESR line‐width in highly doped n‐InSb, Ge: As, and Si: P are compared with theoretical calculations. For the spin–phonon interaction the temperature dependence and the values of the constants obtained agree within one or two orders of magnitude with theoretical results. Only qualitative agreement has been obtained for the contribution of relaxation by ionized impurity scattering. Possible sources of the line‐broadening are discussed in the limit of low temperatures, where the linewidth does not depend on temperature.

Theory of the Spin Relaxation of Conduction Electrons in Solid and Liquid Metals

Theory of the Spin Relaxation of Conduction Electrons in Solid and Liquid Metals

Spin Relaxation of Conduction Electrons in Liquid Metal Alloys. I. Theory

Spin Relaxation of Conduction Electrons in Liquid Metal Alloys. I. Theory