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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 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.[5]

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

Even when the de Haas-van Alphen effect was predicted theoretically by Lev Landau in 1930[6], he discarded it as it thought that the magnetic fields necessary for its demonstration could not be created in a laboratory yet[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]

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.


  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 A Hadrons and Nuclei 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. 

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