# 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.[1][2][3] It was discovered in 1930 by Wander Johannes de Haas and his student P. 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.[4]

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

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.[5]

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.

## References

1. ^ Zhang Mingzhe. "Measuring FS using the de Haas-van Alphen effect". Introduction to Solid State Physics. National Taiwan Normal University. Retrieved 2010-02-11.
2. ^ T. Holstein (1973). "de Haas-van Alphen Effect and the Specific Heat of an Electron Gas". Physical Review B 8: 2649. Bibcode:1973PhRvB...8.2649H. doi:10.1103/PhysRevB.8.2649.
3. ^ A.Suslov, O.Svitelskiy, E.Palm, T.Murphy, D.Shulyatev (2006). "Pulse-echo technique for angular dependent magnetoacoustic studies". AIP Conference Proceedings 850: 1661.
4. ^ C. Kittel (2005). Introduction to Solid-State Physics (8th ed.). Wiley.
5. ^ N. Harrison. "de Haas-van Alphen Effect". National High Magnetic Field Laboratory at the Los Alamos National Laboratory. Retrieved 2010-02-11.