Gerd Bergmann

Weak localization in thin films: a time-of-flight experiment with conduction electrons

Abstract The resistance of two-dimensional electron systems such as thin disordered films shows deviations from Boltzmann theory, which are caused by quantum corrections and are called “weak localization”. Theoretically weak localization is originated by the Langer-Neal graph in the Kubo formalism. In this review article the physics of weak localization is discussed. It represents an interference experiment with conduction electrons spl into pairs of waves interfering in the back-scattering direction. The intensity of the interference (integrated over the time) can be easily measured b the resistance of the film. A magnetic field introduces a magnetic phase shift in the electronic wave functionand suppresses the interference after a “flight” time proportional to 1/ H . Therefore the application of a magnetic field allows a time-of-flight experiment with conduction electrons. Spin-orbit scattering rotates the spin of the electrons and yields an observable destructive interference. Magnetic impurities destroy the coherence of the phase. The experimental results as well as the theory is reviewed. The role of the spin-orbit scattering and the magnetic scattering are discussed. The measurements give selected information about the inelastic lifetime of the conduction electrons in disordered metals and raise new questions in solid state physics. Future applications of the method of weak localization are considered and expected.

Amorphous metals and their superconductivity

Abstract Quite a number of metals and alloys can be forced into the amorphous state by quenching. In particular, condensation onto a substrate cooled to He-temperature is very effective. The superconductivity and related properties of these metals are considered in this article. The influence of the amorphous structure on the electron and the phonon system is discussed. In simple metals the electrons show a free electron behaviour. The transverse phonons are softened but maintainn the ω3-density of states at low frequencies. The electron-phonon interaction does not conserve momentum due to the loss of translational invariance in the amorphous metal and yields a large contribution to α2F(ω) at low frequencies. Therefore the amorphous superconductors are strong coupling. The strong coupling character alters the temperature dependence of several superconducting parameters such as critical fields etc. The characteristic superconducting properties and superconducting fluctuations are discussed.

Inelastic life-time of the conduction electrons in some noble metal films

Magneto-conductance measurements of thin films of Cu, Ag and Au are reported. The measurements are evaluated with the theory of weak localization and yield for the noble metals a very good agreement with the theory in the whole field range up to 5T. No adjustment of the theoretical prefactor is necessary. The magneto-conductance curves show a pronounced structure caused by spin-orbit coupling. The measurements yield the inelastic life-time and the spin-orbit coupling of the conduction electrons for Cu, Ag and Au. τi obeys a 1/Tp law withp=1.65.

Superconducting fluctuations in a magnetic field

The rounding of the transition curve is measured for superconducting bismuth films in a perpendicular magnetic field. The contribution of the fluctuating superconducting wave function to the conductivity aboveTc in an applied magnetic field is calculated with a simple model. The allowed states of the fluctuations are cylinders in momentum space. During their life time the fluctuating superconducting electrons can be accelerated by an electrical field and contribute to the conductivity. Experiment and theory are in fair agreement. We obtain some information about the Pauli spin paramagnetism of the electrons.

The hall effect of amorphous-non transition metals

The amorphous metals Bi, Ga, Sn and Pb are obtained by quenched condensation. Their Hall effect is measured and compared with the model of free electrons. For Ga and Sn we find a good agreement with the free electron model. However, the Hall coefficient of Bi and Pb is only half as large as the theoretical value. This is particularly surprising because the corresponding liquids agree well with the free electron model and the amorphous state closely resembles the liquid. A trace effect of band structure may be responsible for the deviation.

Energy gap, transition temperature and electron-electron interaction of the weak coupling superconductors tin and indium as a function of the mean free path of the electrons

The energy gap and the transition temperature of the weak coupling superconductors tin and indium are measured as a function of the mean free path of the electrons. Both of them increase with decreasing mean free path. The ratioα=2Δ0/kTc increases proportionally to the reciprocal mean free path from 3.6 to 4.0 for tin and from 3.6 to 3.95 for indium. A theoretical consideration is presented showing that the electron-electron interaction is increased in dirty superconductors. Without any fit we find from the theoretical calculation an increase inNV for indium ofδNV=5 · 10−10 m/ltr and for tinδNV=2 · 10−10 m/ltr (ltr is the transport mean free path of the electrons). The experiments give an increase inNV for indium ofδNV=4.2 · 10−10 m/ltr and for tinδNV=1.7 · 10−10 m/ltr. The agreement is surprisingly good.

Investigation of magnetic films by the anomalous Hall-effect

Abstract Magnetic moments scatter conduction electrons asymmetrically and yield the anomalous Hall-effect (AHE). This method has been applied to measure the suppression of the magnetism of Ni on top of different non-magnetic metals. Ni looses its magnetic moments on polyvalent metals such as Mg, In and Sn up to thicknesses ranging between 2 and about 3 atomic layers whereas on top of the noble metals it already shows magnetic moments for thicknesses of 1 atomic layer of Ni. Fe on top of the polyvalent metals Sn, In and Pb show with increasing coverage between 2% of a monolayer and 1.6 monolayer a transition from magnetically free moments via a two-dimensional spin glass to a ferromagnetic state. The magnetic behavior of Fe on top of a Pd surface suggests a reduced Stoner enhancement of the Pd surface, compared with the bulk Pd.

The anomalous Hall effect

The Hall effect is observed when a magnetic field is applied to a metal through which a current flows: The current carriers are deflected in the field, giving rise to a transverse electric field. In a ferromagnetic metal the embedded magnetic moments produce an anomalous Hall effect. Because it depends on both electronic and magnetic properties of the metal, the anomalous Hall effect has become a useful experimental tool for solid‐state physicists. In our laboratory in Julich, for example, we have used the effect to study extremely thin magnetic layers and to observe the propagation of conduction electrons in a metal.

WEAK LOCALIZATION AND ITS APPLICATIONS AS AN EXPERIMENTAL TOOL

The resistance of two-dimensional electron systems such as thin disordered films shows deviations from Boltzmann theory, which are caused by quantum corrections and are called weak localization. The theoretical origin of weak localization is the Langer–Neal graph in Kubo formalism. It represents an interference experiment with conduction electrons split into pairs of waves interfering in the back-scattering direction. The intensity of the interference (integrated over the time) can easily be measured by the resistance of the film. The application of a magnetic field B destroys the phase coherence after a time which is proportional to 1/B. For a field of 1 T this time is of the order of 1 ps. Therefore with a dc experiment, one can measure characteristic times of the electron system in the range of picoseconds. Weak localization has been applied to measure dephasing, spin-orbit scattering, tunneling times, etc. One important field of application is the investigation of magnetic systems and magnetic impurities by measuring the magnetic dephasing time and its temperature dependence. Here the Kondo maximum of spin-flip scattering, spin-fluctuations, Fermi liquid behavior and magnetic d-resonances have been investigated. Another field is the detection of magnetic moments for very dilute alloys and surface impurities. This article given a brief survey of different applications of weak localization with a focus on magnetic impurities.

Dependence of the Phase-Coherence Time in Weak Localization on Electronic Mean Free Path and Film Thickness

Magneto-resistance measurements on thin disordered films yield the phase-coherence time τ i of the conduction electrons (weak localization). The dependence of τ i on film thickness and residual resistivity are reported for disordered Au, Ag and Mg films in the temperature range between 4.5 and 20 K. The resistivity of the films was varied between .13 and 1.1×10 -6 Ωm. The temperature dependence of 1/τ i follows a T p -law. The exponent is essentially two, but varies slightly with the resistivity. 1/τ j depends much less on the resistivity than the linear prediction of the theory. No direct influence of the film thickness on τ i was observed. This excludes the impurity induced Coulomb interaction as the relevant mechanism and suggests that τ i is essentially determined by electron-phonon interaction. However, at the present time there is no theory available that reproduces the experimental results. Measurements of the (temperature independent) Hall-constant suggest that the thin films are rather homogeneou...