Electron relaxation in metals: Theory and exact analytical solutions

The non-equilibrium dynamics of electrons is of a great experimental and theoretical value providing important microscopic parameters of the Coulomb and electron-phonon interactions in metals and other cold plasmas. Because of the mathematical complexity of collision integrals theories of electron relaxation often rely on the assumption that electrons are in a "quasi-equilibrium" (QE) with a time-dependent temperature, or on the numerical integration of the time-dependent Boltzmann equation. We transform the integral Boltzmann equation to a partial differential Schroedinger-like equation with imaginary time in a one-dimensional "coordinate" space reciprocal to energy which allows for exact analytical solutions in both cases of electron-electron and electron-phonon relaxation. The exact relaxation rates are compared with the QE relaxation rates at high and low temperatures.Comment: Citation list has been extended. The paper is submitted to the Physical Review

Spatial Correlation of Conduction Electrons in Metal with Complicated Geometry Of The Fermi Surface

The "density-density" correlation function of conduction electrons in metal is investigated. It is shown, that the asymptotic behaviour of the CF depends on the shape and the local geometry of the Fermi surface. In particular, the exponent of power law which describes the damping of Friedel oscillations at large r (-4 for an isotropic Fermi gas) is determined by local geometry of the FS. The applications of the obtained results to calculations of the CF in a metal near the electron topological transition and of the RKKY exchange integral are considered as well.Comment: 12 pages, LaTeX, 5 figures upon request (to appear in J.Phys.:CM, 1993

Ultra-fast magnetisation rates within the Landau-Lifshitz-Bloch model

The ultra-fast magnetisation relaxation rates during the laser-induced magnetisation process are analyzed in terms of the Landau-Lifshitz-Bloch (LLB) equation for different values of spin $S$. The LLB equation is equivalent in the limit $S \rightarrow \infty$ to the atomistic Landau-Lifshitz-Gilbert (LLG) Langevin dynamics and for $S=1/2$ to the M3TM model [B. Koopmans, {\em et al.} Nature Mat. \textbf{9} (2010) 259]. Within the LLB model the ultra-fast demagnetisation time ($\tau_{M}$) and the transverse damping ($\alpha_{\perp}$) are parameterized by the intrinsic coupling-to-the-bath parameter $\lambda$, defined by microscopic spin-flip rate. We show that for the phonon-mediated Elliott-Yafet mechanism, $\lambda$ is proportional to the ratio between the non-equilibrium phonon and electron temperatures. We investigate the influence of the finite spin number and the scattering rate parameter $\lambda$ on the magnetisation relaxation rates. The relation between the fs demagnetisation rate and the LLG damping, provided by the LLB theory, is checked basing on the available experimental data. A good agreement is obtained for Ni, Co and Gd favoring the idea that the same intrinsic scattering process is acting on the femtosecond and nanosecond timescale.Comment: 9 pages, 7 figure

Entropy Driven Atomic Motion in Laser-Excited Bismuth

We introduce a thermodynamical model based on the two-temperature approach in order to fully understand the dynamics of the coherent A(1g) phonon in laser-excited bismuth. Using this model, we simulate the time evolution of (111) Bragg peak intensities measured by Fritz et al. [Science 315, 633 (2007)] in femtosecond x-ray diffraction experiments performed on a bismuth film for different laser fluences. The agreement between theoretical and experimental results is striking not only because we use fluences very close to the experimental ones but also because most of the model parameters are obtained from ab initio calculations performed for different electron temperatures

Electron-Phonon Coupling in High-Temperature Cuprate Superconductors Determined from Electron Relaxation Rates

We determined electronic relaxation times via pump-probe optical spectroscopy using sub-15 fs pulses for the normal state of two different cuprate superconductors.We show that the primary relaxation process is the electron-phonon interaction and extract a measure of its strength, the second moment of the Eliashberg function\lambda=800\pm200 meV^{2} for La_{1.85}Sr_{0.15}CuO_{4} and \lambda=400\pm100 meV^{2} for YBa_{2}Cu_{3}O_{6.5}. These values suggest a possible fundamental role of the electron-phonon interaction in the superconducting pairing mechanism.Comment: As published in PR

Quantum Oscillations of Elastic Moduli and Softening of Phonon Modes in Metals

In this paper we present a theoretical analysis of the effect of magnetostriction on quantum oscillations of elastic constants in metals under strong magnetic fields. It is shown that at low temperatures a significant softening of some acoustic modes could occur near peaks of quantum oscillations of the electron density of states (DOS) at the Fermi surface (FS). This effect is caused by a magnetic instability of a special kind, and it can give rise to a lattice instability. We also show that the most favorable conditions for this instability to be revealed occur in metals whose Fermi surfaces include nearly cylindrical segments.Comment: 5 pages, 1 figur

Evolution of the magnetic phase transition in MnO confined to channel type matrices. Neutron diffraction study

Neutron diffraction studies of antiferromagnetic MnO confined to MCM-41 type matrices with channel diameters 24-87 A demonstrate a continuous magnetic phase transition in contrast to a discontinuous first order transition in the bulk. The character of the magnetic transition transforms with decreasing channel diameter, showing the decreasing critical exponent and transition temperature, however the latter turns out to be above the N\'eel temperature for the bulk. This enhancement is explained within the framework of Landau theory taking into consideration the ternary interaction of the magnetic and associated structural order parameters.Comment: 6 pages pdf file, including 4 figures, uses revtex4.cl

The Origin of Anomalous Low-Temperature Downturns in the Thermal Conductivity of Cuprates

We show that the anomalous decrease in the thermal conductivity of cuprates below 300 mK, as has been observed recently in several cuprate materials including Pr$_{2-x}$Ce$_x$CuO$_{7-\delta}$ in the field-induced normal state, is due to the thermal decoupling of phonons and electrons in the sample. Upon lowering the temperature, the phonon-electron heat transfer rate decreases and, as a result, a heat current bottleneck develops between the phonons, which can in some cases be primarily responsible for heating the sample, and the electrons. The contribution that the electrons make to the total low-$T$ heat current is thus limited by the phonon-electron heat transfer rate, and falls rapidly with decreasing temperature, resulting in the apparent low-$T$ downturn of the thermal conductivity. We obtain the temperature and magnetic field dependence of the low-$T$ thermal conductivity in the presence of phonon-electron thermal decoupling and find good agreement with the data in both the normal and superconducting states.Comment: 8 pages, 5 figure

Smearing of phase transition due to a surface effect or a bulk inhomogeneity in ferroelectric nanostructures

The boundary conditions, customarily used in the Landau-type approach to ferroelectric thin films and nanostructures, have to be modified to take into account that a surface of a ferroelectric (FE) is a defect of the ``field'' type. The surface (interface) field is coupled to a normal component of polarization and, as a result, the second order phase transitions are generally suppressed and anomalies in response are washed out. In FE films with a compositional (grading) or some other type of inhomogeneity, the transition into a monodomain state is suppressed, but a transition with formation of a domain structure may occur.Comment: 5 pages, 1 figure; the effective bias field is very large, the estimate is adde