Spin relaxation in metals at very low temperatures

A general theory of spin relaxation in metals is developed from a statistical mechanical point of view. The theory is valid for all temperature domain and the multiple-time characteristics of the relaxation process are completely determined: The relaxation times are strongly dependent on the temperature and magnetic field. At very low temperatures, behaviours of the relaxation times are quite different from the usual ones showing a saturation effect. Temperature varations of the relaxation times for I ? 1 (I the magnitude of spin) are qualitatively different from those for $\text{I =}\text{1}\text{2}$. Namely, in the former case, the largest relaxation time has a maximum as a function of inverse temperature.     

Magnetooptical effects in ferromagnetic metals at low temperatures

Zeroth-order and first-order Boltzmann kinetic equations are found for the frequency-dependent transverse-conductivity tensor for inelastic scattering of electrons, with an account of thermal oscillations of the scattering centers. At low temperatures this tensor, which is linear in the spin-orbit interaction, depends exponentially on the temperature. A relation is found between the magnetooptical effects in ferromagnetic metals and the topology of the Fermi surfaces; from this relation, qualitative conclusions can be drawn regarding the effect of this topology on the magnetooptical effects and regarding the sign of the anomalous magnetooptical parameter (which depends on whether hole or electronic conductivity predominates).Translated from Izvestiya VUZ. Fizika, No. 4, pp. 86–90, April, 1970.     

Electronic properties of metals at low temperatures

A many body theory of an electron gas is developed to find the internal and correlation energies at low but finite temperatures. The contribution from the first order exchange, second order (regular and anomalous) exchange, and ring diagrams are treated. The Fermi momentum and the correlation energy are determined as functions of the density by two different methods, one being based on iteration and the other a direct solution of the number density relation. It was found that the iterative solutions which are correct to ordere ² ore ⁴ become negative forr _s of order 5 while the direct solutions do not, indicating the invalidity of the former. Hence, the correlation energy evaluated to the same orders by iteration will not be satisfactory in the same range. The highest order iterative solution which includes terms of ordere ⁶ does not show such a breakdown. These terms which give the contribution of orderr _s to the correlation energy are therefore important and tend to reduce the magnitude of the correlation energy. The corresponding curve is indeed close to that determined by the direct method for smallr _s but a significant deviation takes place at largerr _s . The Coulomb interaction seems less effective at higher temperatures. The internal energy is also determined as a function of density and temperature.     

Ultrasonic attenuation of metals at low temperatures

At very low temperatures when the mean free path of the electrons in metals becomes large but less than the wavelength of sound wave a relationship between electrical conductivity and attenuation in the normal state has been deduced byMason using the mean free path associated with the electrical conductivity. Similarly, a relationship between thermal conductivity and attenuation can be deduced using the mean free path associated with the thermal conductivity. It has been shown from experimental results that the relationship thus deduced agrees better in the temperature region discussed in the paper. When the mean free path becomes greater than the wavelength, α_s/α_n, the ratio of superconducting attenuation to that in the normal state can be determined in accordance with the theory ofBardeen, Cooper andSchrieffer. It is apparent from experimental results that in the limited region where the scattering of electrons is predominantly by lattice vibrations, K_s/K_n, the ratio of superconducting thermal conductivity to that in the normal state is equal to α_s/α_n.     

Electromagnetically-excited acoustic waves in ferromagnetic metals at low temperatures

Quantitative measurements of the electromagnetic excitation of acoustic waves in a thin nickel single-crystal have been carried out under simple well-defined experimental conditions at liquid-helium temperatures which allow the complementary roles of two different mechanisms of electromagnetic-acoustic coupling to be clearly defined at the surface and in the bulk of the metal. It is pointed out that such measurements can be used as a sensitive a.c. probe of the d.c. magnetic fields at the surface and in the bulk of ferromagnetic metals.     

Electromagnetic generation of ultrasound in metals at low temperatures

Excitation of longitudinal and transverse ultrasound by electromagnetic waves incident on the metal surface is the subject of the present work. This is a simple and convenient experimental technique. The reason for this approach is to overcome the primary difficulty during precise measurements of the frequency or temperature dependences of the velocity and attenuation of ultrasound in pure metals by the conventional methods where it is difficult to achieve reliable acoustic contact between the transducer and the sample. The reasons are (i) the creation of this contact unavoidably results in a deformation of a surface layer of the metal affecting the experimental results, (ii) as the temperature is varied over a broad range, the properties of the acoustic contact itself change resulting in non-reproducible experimental results.     

Phonon-dislocation scattering and phonon equilibration in metals at low temperatures

It is shown that phonon-dislocation scattering does not contribute significantly to equilibrating the phonon system for potassium. The implications of this result are discussed for the phonon-drag contribution to the low-temperature electrical resistivity.     

Transport properties of granular metals at low temperatures

We investigate transport in a granular metallic system at large tunneling conductance between the grains, g(T)>1. We show that at low temperatures, Tg(T)delta) behavior where conductivity is controlled by the scales of the order of the grain size. In three dimensions we predict the metal-insulator transition at the bare tunneling conductance g(C)(T)=(1/6pi)ln((E(C)/delta), where E(C) is the charging energy of a single grain. Corrections to the density of states of granular metals due to the electron-electron interaction are calculated. Our results compare favorably with the logarithmic dependence of resistivity in the high-T(c) cuprate superconductors indicating that these materials may have a granular structure.     

Lattice scattering mobility at low temperatures in quasi one-dimensional metals

We show that for a quasi 1-d metal the resistivity ? varies with temperature T as 1/sinh (? ω /k_BT), ?ω being the energy of the (external) 2k_F phonon involved in the scattering process. The theory fits the observed ? vs. T of (TMTSF)₂PF₆ and other quasi 1-d metals below 60K, where lattice expansion, internal mode scattering and precursor effects of the Peierls transition can be neglected.     

On the conductivity of pure metals at low temperatures

We show that the resistivity of pure metals at low temperatures T due to electron-electron collisions may be proportional to T⁶ in contrast to the T² law valid usually for Fermi systems.     

Lattice vibronics of bcc phase metals (Ti,Zr and Hf) at higher temperatures

Ashcroft’s analytic bare ion pseudopotential form factor with a modified Hartree dielectric function has been employed to represent the temperature dependent interionic potential. This potential includes both direct ion-ion interaction and indirect ion-electron-ion interaction with and without the effects of ‘d’ bands, in some scantily studied complexbcc metals vizbcc Ti, Zr and Hf. The ab initio radial and tangential force constants extending out to 15th nearest neighbours are computed for the metals. The said potential is used for predicting the binding energy, elastic constants and phonon dispersion of the above mentioned metals and the results are satisfactorily compared with the corresponding measured data.     

Cavity formation at indium impurities in bcc metals

The defect formation in the bcc metals W and Mo above annealing stage III and the influence of rare gases on this process were investigated by means of the perturbed angular correlation technique using¹¹¹In as radioactive probe. In both metals a relatively high electric field gradient (EFG) could be observed at the indium site, characterized by the quadrupole interaction frequencies υ_Q=263 MHz, ν=0 and υ_Q=220 MHz, ν≈0.15 for W and Mo, respectively. The observations are assigned to the growth of threedimensional vacancy clusters at the probe atoms with the indium atoms situated in the inner surface of this cavities, thus experiencing the corresponding surface EFG.     

The thermal and electrical conductivities of metals at high temperatures

A method of investigating the electrical and thermal conductivities of metals at high temperatures is described. The theory of the method depends upon the application of ideas which are fundamental in the study of electrical contact phenomena. The ratio of the thermal to the electrical conductivity of platinum has been determined from 1200° C to the melting point (1773° C) and from the melting point to 2300° C by making simultaneous observations of electrical potential and maximum temperature in a short wire through which current is passed. The wire terminates in two blocks of the same metal, and the ends of the wire are not assumed to be plane isothermal (and equipotential) surfaces. The wire remains in place when partly molten so that observations are extended well into the molten range. The method is independent of the exact geometrical configuration of the conducting system. The details of the arrangement of the apparatus and of the method of temperature measurement are given. The results are discussed in relation to the properties of the molten metal bridges formed between the electrodes of electrical contacts and to the value of theLorenz factor in theWiedemann-Franz law.     

Variation of thermopower of alkali metals at high temperatures

We have calculated, in an empirical form, the temperature variation of the thermopower of alkali metals in the 50–300 K region and at their melting points using the finite mean free path correction to the Ziman formulation as suggested by Ferraz and March. The structure factor was evaluated using the phenomenological models of Sharma-Joshi and Krebbs. Three different types of form factors were used in order to give a comparative test of the applied theories. Our results agree to a considerable extent with available experimental results. Finally, we give a brief discussion of some of the factors that could affect the thermopower of the metals investigated.     

Thermodynamics of ice at high pressures and low temperatures

A new equation of state of ice Ih recently proposed by Feistel and Wagner [J. Phys. Chem. Ref. Data 35 (2006) 1021-1047] is used to study the phenomena related to the equilibrium isentropic compression of an ice-water mixture and dynamic loading of solid ice. New results are presented concerning the properties of the new equation of state, equilibrium solid-liquid phase transitions and Hugoniots of low-temperature (100 K) and temperate (263 K) shock-compressed ice.     

The change in the structure of liquid metals at high temperatures

The structures of the models of the Lennard-Jones liquid and mercury, cesium, and rubidium melts have been investigated. According to the local order dominant in a system, three regions have been selected in the phase diagrams of the models. For the Lennard-Jones model, the transition between the selected regions corresponds to a change in the asymptotic behavior of the radial distribution function. For the Hg, Cs, and Rb models, the position of the boundaries between these regions correlates with the specific features of the physical properties of these materials.     

Electron interactions and the electrical resistivity of alkali metals at low temperatures

The contribution of the electron-electron umklapp scattering processes to the electrical resistivity of sodium, potassium, rubidium and cesium at low temperatures has been evaluated using a simplified spherical Fermi-surface model with an isotropic transition probability. Our values of the electrical resistivity so obtained compare fairly well with the recent experimental values for sodium, potassium and rubidium. Our theoretical results have also been compared with the other available data in the literature due to Lawrence and Wilkins and MacDonald and Geldart.