Ultrasound Pulse-Echo Measurements with the GHFLI Lock-in Amplifier for the Investigation of Superconductors

Until recently, ultrasound measurement setups were developed in-house and required a high level of electrical engineering. This is particularly true for the pulse-echo ultrasound technique, which can selectively probe acoustic modes of different symmetries. The principle is the following. Initially, a radio-frequency (RF) electrical pulse is sent to a transducer glued to the crystal under study (see Fig. 1a). The resulting acoustic wave travels back and forth inside the sample while being progressively attenuated (Fig. 1b). The different acoustic echoes of the acoustic wave are converted back into electrical signals through the same or a second transducer.

For a successful measurement, one needs to measure:

1. The amplitude of the different echoes whose decay is directly related to sound attenuation, and
2. The phase of (at least) one echo, which allows one to extract the relative variation of the sound velocity.

Indeed, for a fixed-frequency RF signal and to a very good approximation, the relative variation of acoustic phase \(\Delta\)\(\phi_i\)/\(\phi_i\) is directly \(-\Delta v/v\), where \(v\) is the sound velocity of the symmetry-specific acoustic mode.

All the above requirements are met by the single Zurich Instrument GHFLI 1.8 GHz Lock-in  Amplifier. This capability was already demonstrated by the UHFLI 600 MHz Lock-in Amplifier (see [1]) and is now extended to higher frequencies. With feedback from Romain Stomp, Heidi Potts, and Kivanç Esat from Zurich Instruments, Quentin Barthelemy and Mehdi Frachet at Institut Néel (Grenoble, France) developed an ultrasound measurement setup based on a single instrument for pulse detection and measurement. A picture of the setup is shown in Figure 2.

The GHFLI generates the RF electrical pulse that is converted into a sound wave with a transducer. The different echoes from the sample are transmitted to the GHFLI input and demodulated at the same frequency. From the evolution of the demodulated signal amplitude, one extracts the sound attenuation variations, while the signal phase is directly related to the sound velocity variations. The high sensitivity, fast demodulation bandwidth and high data transfer rate of the GHFLI are crucial for this experiment, as it requires the measurement of short pulses since the time between the generated pulse and the echoes is very short. In this specific case, ultrasound pulses with a length of 200 ns and a modulation frequency of a few hundred MHz were generated using the GHFLI, and the phase and amplitude of the transmitted signal were measured as a function of temperature and magnetic field.

To facilitate streamlined experiments, Quentin wrote a Python-based GUI that allows us to control the modulation frequency, the pulse’s repetition rate, the output amplitude, the echoes’ trace duration, etc. Additionally, the current implementation allows for working retrospectively on any echo of the initial pulse and checking for reproducibility, and it enables saving all echoes' patterns, which is crucial for in-depth data analysis.

The first measurements on a Niobium test sample demonstrated the reliability and effectiveness of the setup, together with the convenience of the Python-based user interface (see Fig. 3a). Figure 3b shows the amplitude of the echo as a function of temperature around the critical temperature of Tc = 9.2 K. A clear exponential increase in the echo’s amplitude (or downturn in the attenuation) is observed as expected [2]. The coincident anomaly in the sound velocity (not shown) gives information on the symmetry-specific coupling between the crystal lattice and the superconducting order parameter with a state-of-the-art ppm resolution. These promising results demonstrate the ability to perform high-resolution ultrasound measurements in superconductors using the GHFLI.