De Haas–van Alphen effect

The de Haas–van Alphen effect, often abbreviated to dHvA, is a quantum mechanical effect in which the magnetic moment of a pure metal crystal oscillates as the intensity of an applied magnetic field B is increased. Other quantities also oscillate, such as the resistivity (Shubnikov–de Haas effect), specific heat, and sound attenuation and speed. It was discovered in 1930 by Wander Johannes de Haas and his student Pieter M. van Alphen.

The period, when plotted against $1/B$, is inversely proportional to the area $S$ of the extremal orbit of the Fermi surface, in the direction of the applied field.

$\Delta \left( \frac{1}{B} \right) = \frac{2 \pi e}{\hbar S}$

where S is the area of the Fermi surface normal to the direction of B.

This effect is due to Landau quantization of electron energy in an applied magnetic field. A strong magnetic field — typically several teslas — and a low temperature are required to cause a material to exhibit the dHvA effect.

In 1952, Lars Onsager explained the physics behind the effect, and, due to his interpretation, this effect can be used to image the Fermi surface of a metal, to measure the carrier density and more, which makes this a very powerful probing technique in condensed-matter physics.