De Haas–van Alphen effect
The de Haas–van Alphen effect, often abbreviated to dHvA, is a quantum mechanical effect in which the magnetic susceptibility of a pure metal crystal oscillates as the intensity of an applied magnetic field H is increased. Other quantities also oscillate, such as the electrical resistivity (Shubnikov–de Haas effect), specific heat, and sound attenuation and speed. It is named after 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, that is
The modern formulation allows the experimental determination of the Fermi surface of a metal from measurements performed with different orientations of the magnetic field around the sample.
Experimentally it was discovered in 1930 by W.J. de Haas and P.M. van Alphen under careful study of the magnetization of a single crystal of bismuth. The magnetization oscillated as function of the field. The inspiration for the experiment was the recently discovered Shubnikov–de Haas effect by Lev Shubnikov and de Haas, which showed oscillations of the electrical resistivity as function of a strong magnetic field. De Haas thought that the magnetoresistance should behave in an analogous way. 
The theoretical prediction of the phenomenon was formulated before the experiment, in the same year, by Lev Landau, but he discarded it as he thought that the magnetic fields necessary for its demonstration could not yet be created in a laboratory. The effect was described mathematically using Landau quantization of the electron energies in an applied magnetic field. A strong homogeneous magnetic field — typically several teslas — and a low temperature are required to cause a material to exhibit the dHvA effect. Later in life, in private discussion, David Shoenberg asked Landau why he thought that an experimental demonstration was not possible. He answered by saying that Pyotr Kapitsa had convinced him that such homogeneity in the field was impractical.
After 1956, the dHvA effect gained wider relevance after Lars Onsager, and independently, Ilya Lifshitz and Arnold Kosevich, pointed out that the phenomenon could be used to image the Fermi surface of a metal.
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