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 oscillation period, when plotted against , is inversely proportional to the area of the extremal orbit of the Fermi surface, in the direction of the applied field.
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, he discarded it as he thought that the magnetic fields necessary for its demonstration could not yet be created in a laboratory. 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.
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. 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.
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- 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.
- 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.
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- Marder, Michael P. (2000). Condensed Matter Physics. Wiley.
- Harrison, Neil. "de Haas-van Alphen Effect". National High Magnetic Field Laboratory at the Los Alamos National Laboratory. Retrieved 2010-02-11.
- 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.
- Suzuki, Masatsugu; Suzuki, Itsuko S. (26 April 2006). "Lecture note on Solid State Physics: de Haas-van Alphen effect" (PDF). State University of New York at Binghamton. Retrieved 2010-02-11.
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