Relaxation Time In Metals Research Articles

Control of hot-carrier relaxation time in Au-Ag thin films through alloying.

The plasmon resonance of a structure is primarily dictated by its optical properties and geometry, which can be modified to enable hot-carrier photodetectors with superior performance. Recently, metal alloys have played a prominent role in tuning the resonance of plasmonic structures through chemical composition engineering. However, it has been unclear how alloying modifies the time dynamics of the generated hot-carriers. In this work, we elucidate the role of chemical composition on the relaxation time of hot-carriers for the archetypal AuxAg1-x thin film system. Through time-resolved optical spectroscopy measurements in the visible wavelength range, we measure composition-dependent relaxation times that vary up to 8× for constant pump fluency. Surprisingly, we find that the addition of 2% of Ag into Au films can increase the hot-carrier lifetime by approximately 35% under fixed fluence, as a result of a decrease in optical loss. Further, the relaxation time is found to be inversely proportional to the imaginary part of the permittivity. Our results indicate that alloying is a promising approach to effectively control hot-carrier relaxation time in metals.

Measurement of hot electron momentum relaxation times in metals by femtosecond ellipsometry

Time-resolved ellipsometric measurements were made upon Au, Cu, Ag, Ni, Pd, Ti, Zr, and Hf thin films. Using an elliptically polarized pump beam, the decay of the optically induced polarization of the sample was observed. Characteristic relaxation times are extracted and interpreted in terms of scattering of linear and angular momentum of hot electrons. A systematic variation is observed between different metals that reflects their underlying band structure.

Magnetic acoustic spectroscopy of electron relaxation times in metals

A procedure has been proposed to recover the temperature dependence of the relaxation frequency for the conduction electrons related to a line in the magnetic spectrum of sound absorption or velocity.

Spin-spin relaxation time in metals at low temperatures

The nuclear spin-spin interaction in several metals (Pt, Pb, Cd) was investigated by spin echo techniques in a magnetic field between 0.05 and 0.30 T. The nuclear spin temperatures T n ranged from 0.4 mK to 30 mK. The T 2 values for Pb and Cd are 330(15) μs and 901(40) μs, respectively. For these metals neither field nor temperature dependence was found. These T 2's are close to those expected from higher temperatures. However, for Pt the spin-spin interaction behaves differently. Not only a field dependence, but also an indication of temperature dependence was found. T 2 was determined for two different samples. At fields above 0.25 T, T 2 was constant and 480(10) μs and 1290(20) μs. At 62 mT, T 2 increased as temperature decreased and reached values of 590(30) μs and 1550(150) μs at T n∼0.6 mK. Conduction electron scattering by impurity moments may be responsible for these observations.

Theory of hydrogen pairing in metals

The nature of hydrogen-hydrogen interaction in simple lithium, aluminum and transition (yttrium, palladium) metals has been studied by calculating, self-consistently, the energetics and electronic structure of hydrogen pairs as a function of their interatomic separation. While the formation of molecular bonds between hydrogen atoms in metals is possible, it is shown that hydrogen prefers to optimize its bonds with metal atoms, and in some cases, such as rare earth metals, hydrogen pairing mediated by the metal atom may be energetically preferable. The metal-hydrogen bond is characterized by charge transfer from metal atoms to hydrogen while the hydrogen atoms involved in the molecular bond in the metal are neutral. The energy barrier between the two kinds of bonding minima is found to be dependent on the number of metal atoms in the embedding medium. The consequences of this observation in explaining the temperature dependence of proton spin-lattice relaxation time in metals vs. organometallic complexes are discussed.

Theory of hydrogen pairing in metals

The nature of hydrogen-hydrogen interaction in simple lithium, aluminum and transition (yttrium, palladium) metals has been studied by calculating, self-consistently, the energetics and electronic structure of hydrogen pairs as a function of their interatomic separation. While the formation of molecular bonds between hydrogen atoms in metals is possible, it is shown that hydrogen prefers to optimize its bonds with metal atoms, and in some cases, such as rare earth metals, hydrogen pairing mediated by the metal atom may be energetically preferable. The metal-hydrogen bond is characterized by charge transfer from metal atoms to hydrogen while the hydrogen atoms involved in the molecular bond in the metal are neutral. The energy barrier between the two kinds of bonding minima is found to be dependent on the number of metal atoms in the embedding medium. The consequences of this observation in explaining the temperature dependence of proton spin-lattice relaxation time in metals vs . organometallic complexes are discussed.

Green's function calculation of effective nuclear relaxation times in metals

Abstract Abstract A two-times Green's function formalism is used together with linear response theory to derive general equations, valid at any temperature, for the effective nuclear relaxation times in metals. The results obtained by selecting the smallest-order pole in the Green's function as the first approximation are in complete correspondence to experimental evidence at high temperatures and exhibit a maximum when the temperature is lowered below the nuclear spin temperature. The results are also compared with those given by Shibata et al. and good agreement is obtained in the supposition of a single-exponential spin-lattice relaxation process.

Plasmon loss function related to relaxation time in metals and alloys

The loss function ε 2/ ε 2 1 + ε 2 2 for plasmons in terms of the real (ε 1) and imaginary (ε 2) parts of the dielectric function ε( q, ω) is first analyzed phenomenologically. The total width at half maximum is thereby related to electron relaxation time and plasma frequency. Some contact is made with experiments on metallic alloys.

Generation of ultrasonic replica wave packets.

Conduction electrons on closed orbits in pure copper single crystals at low temperatures can interact with an ultrasonic wave packet to produce replicas of the wave packet nearby. Measurements of the ratio of replica amplitude to primary amplitude for magnetic fields between 50 and 260 G are reported. The measurements are compared with the predictions of existing theoretical models. A semiquantitative model for the generation of replica wave packets is presented which explains many of the features of the magnetic field dependence of the replica amplitude and suggests new ways to calculate the electron relaxation time in metals. The use of replica wave generation in a device to produce a continuously variable signal delay is proposed, and an application of the measurements of replica-wave-packet amplitude to the theory of electromagnetic generation of ultrasound is discussed.

Frequency dependence of the optical relaxation time in metals

The optical relaxation times for electron-phonon and for impurity scattering are shown to have the form ${\ensuremath{\tau}}^{\ensuremath{-}1}(\ensuremath{\omega})={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}+b{\ensuremath{\omega}}^{2}$, and values of $b$ for impurity and electron-phonon effects (including umklapp processes) are calculated. The values of $b$ for electron-phonon scattering are compared with estimates for electron-electron scattering and with experiment for the alkali and noble metals. It appears that the observed frequency dependence in these materials at room temperature derives from correction terms of higher order in $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{{E}_{F}}$ to the electron-phonon interaction. For impurity scattering $b$ is predicted to be negative.

The Peierls condition and phonon-phonon scattering in metals

A derivation is presented of the phonon-phonon scattering relaxation time for metals that takes explicit account of the Peierls condition, which states that normal phonon-phonon scattering cannot by itself equilibrate the phonon system. The expression for the phonon-phonon scattering relaxation time depends, in a complicated way, on the phonon-electron scattering relaxation time because of the coupling between phonon-electron scattering and phonon-phonon scattering that results from the Peierls condition. Analysis of the resulting expression shows that at low temperatures, the effect of the Peierls condition is to decrease phonon-phonon scattering very dramatically. The expression for the phonon-phonon scattering relaxation time is evaluated numerically for potassium as a function of temperature at a characteristic point in the Brillouin zone. It is found that at 1 K, the Peierls condition reduces phonon-phonon scattering for potassium by nearly an order of magnitude. A discussion is presented of the implication of these results for the phonon-drag contribution to the low-temperature electrical resistivity of the alkali metals. Comparison is made with other recent work.

Direct optical determination of carrier relaxation times

We propose a new method for the optical determination of carrier relaxation times in metals. It is based on a recently observed effect involving the excitation of surface electromagnetic waves (surface plasmons) in a prism (substrate)-thin film (metal) configuration. In this geometry the dispersion curve ω( q) bends back at a maximum wavevector q m. The value of q m, which may be determined experimentally, is a sensitive measure of the relaxation time τ. Although the calculations are based on the Drude model of conductivity, the method presented may be extended to other models and also to semiconducting and dielectric materials.

Diffusion model and the anisotropic relaxation time in metals: Application to potassium

The Boltzmann equation for the anisotropic relaxation time leads to a generalization of the diffusion model in which umklapp electron-phonon scattering is treated explicitly, and does not require Fermi-surface distortion or intersection with zone boundaries. The diffusion equation contains an anisotropic function which may be interpreted as the zeroth-order relaxation time in the iteration sequence of the Boltzmann equation, and which has been used commonly as an approximation to the true relaxation time. The solution of the diffusion equation tends toward this zeroth-order relaxation time at higher temperatures, where the latter is known to become a good approximation. The importance of treating umklapp explicitly is illustrated by calculating deviations from Matthiessen's rule in the electrical resistivity of potassium, for which previous diffusion models were of course not intended. Comparison with data and with previous numerical calculations by others lends credence to the model.

Effect of Paramagnetic Impurities on Nuclear Spin-Lattice Relaxation: A Numerical Study

The effect of paramagnetic impurities on the nuclear spin-lattice relaxation time in metals is investigated by applying the theory of Blume and Hubbard in an appropriately generalized form. The calculations are carried out at finite temperature and magnetic field strength assuming that the Ruderman-Kittel-Kasuya-Yosida interaction couples the impurity spins. The effect of approximating this interaction by $\frac{1}{{r}^{3}}$ is examined as is the temperature, magnetic field, and impurity-concentration dependence of the relaxation time. Quantitative results are obtained using parameters appropriate to the rare-earth alloy ${\mathrm{La}}_{1\ensuremath{-}c}{\mathrm{Gd}}_{c}{\mathrm{Al}}_{2}$ and a comparison is made with experiment; agreement is generally good.

Many-electron enhancement effects on the nuclear spin-lattice relaxation times in metals

The nuclear spin-lattice relaxation times T 1 z and T 1 dd have been measured in Na, Li and Rb at 4.2 K and 77 K. The martensitic phase transformation is thought to affect the measurements in Li, whilst in Rb extensive faulting precludes measurement of T 1 dd . The values of ϵ = ( T 1 z − 2 T 1 dd ) T 1 dd −1 and of ( K 2 T 1 z T) for Na and Li are compared with current theories of the effects of electron-electron enhancements.

Determination of Anisotropic Relaxation Times in Copper by Cyclotron Resonance

A theoretical and experimental technique has been developed for the study of conduction-electron relaxation times in metals through the use of cyclotron resonance spectra in single crystals. The relaxation times of electrons in two orbits in a magnetic field in copper have been compared in two specimens of differing purity. One orbit is the [111] belly ($B$); the other orbit is one which was first seen in this study and is attributed to the six-cornered rosette ($R$). Computer programs have been written to curve-fit data to the nonlinear functions describing the experimental spectra which contain effective masses in the ratio $\frac{{{m}_{R}}^{*}}{{{m}_{B}}^{*}}=1.12$. The experimental results give $\frac{{\ensuremath{\tau}}_{B}}{{\ensuremath{\tau}}_{R}}=1.6\ifmmode\pm\else\textpm\fi{}0.5$ for the ratio of the impurity relaxation times when each sample has the same scattering anisotropy.

Can electron relaxation times be measured by helicon waves?

We criticize a recent suggestion by Kao that, utilizing helicon waves, it is possible to determine experimentally the anisotropy of relaxation times in metals, without any information on the Fermi surface.

Determination of electron relaxation-time in metals by weakly-damped helicon waves

A method for making direct determinations of ω cτ of electrons in metals is proposed. In conjunction with the cyclotron resonance results, accurate measurements of the anisotropy of electron relaxation-time in metals are feasible.

Quadrupole Interaction of Nuclei with Conduction Electrons

The nuclear spin-lattice relaxation time in metals is calculated taking into account the following three interactions between the nuclei and the conductions electrons: (1) the usual contact part of the hyperfine interaction, which is the dominant mechanism; (2) the noncontact part of the hyperfine interaction; (3) the quadrupole interaction for nuclei of spin I≥1. It is found that the latter two interactions are of the same order of magnitude. If the electronic wave function at the Fermi surface has a p-wave component comparable with its s-wave component, these two mechanisms may appreciably shorten the relaxation time as calculated using only the contact part of the hyperfine interaction.

Nuclear magnetic relaxation and resonnance line shift in metals

A detailed theory is given of the nuclear relaxation time in metals. The 1/ T law of H e i t l e r and T e l l e r, which is imposed by the statistics of the electrons, is obtained by using the Bloch approximation of metals. An approximate relation is derived between the relaxation time τ and the relative line shift ΔH/H, viz. τ( ΔH H ) 2 = ℏ π kTg 2 where g is the nuclear g-factor in Bohr-units. The experimental results on 7Li, 27Al and 63Cu are discussed with special reference to the influence of the correlation between the electrons. The deviations from the 1/ T law for Li are all or nearly all attributed to the influence of paramagnetic impurities.