Ultrasound

Left: Experimental setup, with a small sample of Nd₃BWO₉ attached to two gold-plated LiNbO₃ transducers. Right: Raw ultrasound amplitude measured in a block of aluminum, showing the arrival of several "echoes" of the originally excited sound wave.

In real materials, magnetic degrees of freedom always display some coupling to the lattice, which may lead to a variety of interesting effects, such as magneto-structural distortions or magnon-phonon hybridization. This makes ultrasound measurements an extremely useful tool in our arsenal. The elastic tensor is sensitive to all phase transitions (even multipolar order), usually leading to abrupt changes in sound velocity across T_c for some of its components. As a "bonus", the same experiment also reveals dynamical information through the acoustic attenuation, i.e., the damping of sound waves.

In practice, samples are polished and bonded to two piezoelectric transducers. One of them excites a sound wave, traveling back and forth inside the sample, while the other acts as our detector, capturing the phase and amplitude of each consecutive "echo" using lock-in techniques.

Here is an example of magnetoelastic effects in the frustrated quantum magnet Cs₂CoBr₄. We observe clear anomalies in the sound velocity (top) and attenuation (bottom) at all five field-induced phase transitions.