Pierre-Alain Probst

Multiple‐channel digital lock‐in amplifier with PPM resolution

A digital lock‐in amplifier built with a couple of input/output boards in a personal computer is described. The use of direct memory access allows the generation of a reference sinewave and the sampling of up to eight channels synchronously with it, leaving enough time for the processor to calculate the in phase and in quadrature responses at and only at selected harmonics (h1,h2,...) of the reference frequency. This digital lock‐in is drift free and has the gain stability of the analog‐to‐digital converter, that is within ±1 ppm for a few minutes, increasing to ±20 ppm for 24 h. Even a simple Mac IIci can monitor in real time h1 at 24 ksamples/s for two channels, corresponding to an upper frequency of 3 kHz, with no limitations on the low‐frequency side. Higher sampling rates and processing power are available with more recent hardware.

Low‐frequency digital lock‐in amplifier

A digital lock‐in amplifier which simultaneously measures in phase and in quadrature components at a reference frequency and at twice this frequency is described. It is drift free, insensitive to harmonics, has a very high gain stability (25 ppm/K), and operates up to 1250 Hz with no limitations on the low‐frequency side.

Marginal oscillator optimized for radiofrequency size effect measurements

A marginal oscillator (1–50 MHz) operating at relatively high, stable oscillation levels, with very low noise, is described. Phase‐sensitive detection of the real and imaginary parts of the surface impedance of metals or the nuclear susceptibility can be carried out from 0.5 Hz as a result of the low 1/f noise. The noise is dominated by this 1/f noise below 200 Hz, while at higher frequencies it is white and the oscillator has a noise factor of 1.15 or 0.6 dB.

Electron-electron scattering in copper and silver from radio-frequency size effect measurements

High-precision measurements of the scattering rates nu (T) in Cu and Ag have been performed between 0.5 and 8 K for electrons on extremal belly orbits perpendicular to the (111) and (110) directions. The behaviour of he electron-phonon contribution nu ep(T) can be accounted for with simple models which include a change in scattering effectiveness with temperature and energy averaging of the scattering rate. A term nu ee= alpha T2 from electron-electron scattering is observed and can even be dominating in Cu below 1.5 K when the electron-phonon collisions are made ineffective by decreasing the radio-frequency to 10 kHz. The value of alpha is nearly independent of the radio-frequency used. It amounts to 2.4*106 s-1 K-2 for the (111) orbit and 2.0*106 for the (100) orbit in Cu and 1.7*106 and 1.0*106 s-1 K-2 for the same orbits in Ag. These results are compared with data from transport measurements and with theoretical calculations.

Radiofrequency size-effect measurements of the electron scattering frequency in cadmium

Precise parallel- and tilted-field radiofrequency size-effect measurements of the temperature dependence of the electron scattering frequency v(T) have been made on symmetric orbits on the first-, second-, and third-band Fermi surface sheets in samples with normals 〈11\-20〉 and 〈10\-10〉. The limiting point measurements on the third-band lens near 〈0001〉 provide the clearest evidence for a T2 contribution to v(T) that is the right order of magnitude for electron-electron scattering in cadmium. In parallel field measurements on orbits on the first and second bands (including a “broken” orbit) we find v(T) ≃ αT2 + βT3. On these orbits the values for α are 5–20 times larger than for the limiting point and other orbits on the third band. The temperature dependence of v(T\> 2 K) on extremal, limiting point, and open orbits on the second- and third-band Fermi surface sheets can be well accounted for by a simple plane wave model for electron-phonon intersheet scattering. This contribution to v(T) “turns on” approximately as exp (−Tt/T) above Tt/10, where Tt is the minimum “gap” temperature on the orbit for intersheet scattering by quasi-transversely polarized phonons. The fitted gap temperatures as well as the other parameters of the plane wave model agree well with the known dimensions of the Fermi surface of cadmium. While clear evidence is lacking, we note that this intersheet scattering model can also be used to explain the large T2coefficients obtained for the first- and second-band orbits, where, in fact, one has gap temperatures Tt smaller than 1 K.

Study of the audio-frequency magnetic field penetration in cadmium using the radio-frequency size effect

In radio-frequency size effect (RFSE) measurements the Gantmakher resonance signals are not in phase with the modulation magnetic field when the latter is screened by the induced audio-frequency currents. The dependence of this phase lag on modulation frequency (1-1000 Hz) has been studied as a function of temperature (1.4 to 4.2K) and orientation in cadmium. This gives relaxation times associated with the first two modes of the induced electric field which exhibit similar anisotropy as found in bulk resistivity and RFSE measurements at low temperatures. The mode-mode, off-diagonal relaxation times are found experimentally to be non-negligible, contrary to previous numerical calculations of Brandli and Cotti (1965, 1969).

New evidence for electron-electron scattering in noble metals from radio-frequency-size-effect measurements

High precision radio-frequency-size-effect measurements of the temperature dependent scattering rate have been performed in Cu and Ag down to 0.5K. The data can only be described by introducing a term αT2 from electron-electron scattering with α\cong2106 [s-1 K-2] in fair agreement with resistivity data and theoretical calculations.

Anistropic electron-electron and electron-phonon scattering rates in aluminium from high-precision RFSE measurements between 0.2 and 10 K

High-precision low-temperature radio frequency size effect (RFSE) experiments have been carried out to extract local values of the electron-phonon (e-p) and electron-electron (e-e) scattering rates (SRs) in aluminium. The RF was varied to help separate these two contributions. For the first time an unexpected large anisotropy of the e-e SR has been observed, suggesting that the phonon mediated e-e SR dominates the Coulomb contribution. Comparison of the experimental data with recent calculated values of the e-e SR confirm the importance of this mechanism.

Low-temperature features of electron scattering in cadmium

The scattering rates nu (T) of various groups of electrons in cadmium have been measured down to 0.25 K using the radio-frequency size effect. For electrons on the third band lens of the fermi Surface nu (T) can be analyzed below about 2.5 K as the superposition of two terms, alpha T2 and beta T3. While the latter is associated with electron-phonon scattering the former component can be attributed to electron-electron scattering. On two triangular orbits in the first and second bands an apparently large T2 term is observed between 5 and 1.5 K. At lower temperatures nu (T) drops rapidly suggesting that this behaviour is due to electron-phonon scattering. An explanation for large T2 terms has been proposed by Lawrence et al. (1986) on the basis of Umklapp electron-phonon scattering together with the particular shape of the Fermi surface of cadmium. Simple calculations on these lines are shown to reproduce semi-quantitatively the observed variation of nu (T) and to aid in the interpretation of another second band orbit.

Temperature dependent electron scattering rates in aluminium from high precision RFSE measurements between 0.2 and 10K.

Abstract High precision low temperature Radio Frequency Size Effect (RFSE) experiments have been made to extract local values of the electron-phonon and electron-electron scattering rates (SR) in Aluminium. The RF was varied to help separate these contributions. Comparison with calculated values reported in another contribution 1 suggests that the phonon mediated e-e SR dominates the Coulomb interaction. A very sensitive detection system including a digital lock-in amplifier is described.