# 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 Pieter M. van Alphen.[4]

The oscillation period, when plotted against ${\displaystyle 1/B}$, is inversely proportional to the area ${\displaystyle S}$ of the extremal orbit of the Fermi surface, in the direction of the applied field.[5]

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

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

Even though the de Haas–van Alphen effect was predicted theoretically by Lev Landau in 1930,[6] he discarded it as he thought that the magnetic fields necessary for its demonstration could not yet be created in a laboratory.[7] The effect is described mathematically using 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.[8]

After 1952, the dHvA effect gained wider relevance after Lars Onsager pointed out that the phenomenon could be used to image the Fermi surface of a metal.[9] The modern formulation allows one to measure several properties of the charge carriers, which makes it a very powerful probing technique in solid state physics.

## References

1. ^ Zhang Mingzhe. "Measuring FS using the de Haas-van Alphen effect" (PDF). Introduction to Solid State Physics. National Taiwan Normal University. Retrieved 2010-02-11.
2. ^ Holstein, Theodore D.; Norton, Richard E.; Pincus, Philip (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. ^ Suslov, Alexey; Svitelskiy, Oleksiy; Palm, Eric C.; Murphy, Timothy P.; Shulyatev, Dmitry A. (2006). "Pulse-echo technique for angular dependent magnetoacoustic studies". AIP Conference Proceedings. 850: 1661.
4. ^ de Haas, W.J.; van Alphen, P.M. (1930). "The dependence of the susceptibility of diamagnetic metals upon the field" (PDF). Proc.Acad.Sci.Amst. 33: 1106–1118.
5. ^ Kittel, Charles (2005). Introduction to Solid-State Physics (8th ed.). Wiley. ISBN 978-0-471-41526-8.
6. ^ Landau, L. D. "Diamagnetismus der Metalle." Zeitschrift für Physik 64.9 (1930): 629-637.
7. ^ Marder, Michael P. (2000). Condensed Matter Physics. Wiley.
8. ^ Harrison, Neil. "de Haas-van Alphen Effect". National High Magnetic Field Laboratory at the Los Alamos National Laboratory. Retrieved 2010-02-11.
9. ^ Onsager, Lars (1952). "Interpretation of the de Haas-van Alphen effect". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 43: 1006–1008 – via Taylor & Francis.