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{{Short description|Quantum mechanical magnetic effect}}
The '''De Haas–Van Alphen effect''', often abbreviated to '''DHVA''', is a [[Quantum mechanics|quantum mechanical]] effect in which the [[magnetic susceptibility]] of a pure metal [[crystal]] oscillates as the intensity of the [[magnetic field]] ''B'' is increased. It can be used to determine the [[Fermi surface]] of a material. Other quantities also oscillate, such as the [[resistivity|electrical resistivity]] ([[Shubnikov–de Haas effect]]), [[Specific heat capacity|specific heat]], and sound [[attenuation]] and speed.<ref>
{{cite web
 |author=Zhang Mingzhe
 |title=Measuring FS using the De Haas–Van Alphen effect
 |url=http://phy.ntnu.edu.tw/~changmc/Teach/SS/SSG_note/grad_chap14.pdf
 |work=Introduction to Solid State Physics
 |publisher=[[National Taiwan Normal University]]
 |access-date=2010-02-11
}}</ref><ref>
{{cite journal
 |first1=Theodore D. |last1=Holstein |first2=Richard E. |last2=Norton |first3=Philip |last3=Pincus
 |year=1973
 |title=De Haas–Van Alphen Effect and the Specific Heat of an Electron Gas
 |journal=[[Physical Review B]]
 |volume=8 |issue=6 |pages=2649
 |doi=10.1103/PhysRevB.8.2649
|bibcode = 1973PhRvB...8.2649H }}</ref><ref>
{{cite journal
 |first1=Alexey |last1=Suslov |first2=Oleksiy |last2=Svitelskiy |first3=Eric C. |last3=Palm |first4=Timothy P. |last4=Murphy |first5=Dmitry A. |last5=Shulyatev
 |year=2006
 |title=Pulse-echo technique for angular dependent magnetoacoustic studies
 |journal=[[AIP Conference Proceedings]]
 |volume=850 |pages=1661–1662
  |doi=10.1063/1.2355346 |bibcode=2006AIPC..850.1661S }}</ref>  It is named after [[Wander Johannes de Haas]] and his student Pieter M. van Alphen.<ref name=":1">{{cite journal|last1=De Haas|first1=W.J.|last2=Van Alphen|first2=P.M.|date=1930|title=The dependence of the susceptibility of diamagnetic metals upon the field|url=http://www.dwc.knaw.nl/DL/publications/PU00015989.pdf|journal=Proc.Acad.Sci.Amst.|volume=33|pages=1106–1118}}</ref> The DHVA effect comes from the orbital motion of itinerant electrons in the material. An equivalent phenomenon at low magnetic fields is known as [[Landau diamagnetism]].

== Description ==
The differential magnetic susceptibility of a material is defined as
:<math>\chi=\frac{\partial M}{\partial H}</math>
where <math>H</math> is the applied external magnetic field and <math>M</math> the [[magnetization]] of the material. Such that <math>\mathbf{B}=\mu_0 (\mathbf{H}+\mathbf{M})</math>, where <math>\mu_0</math> is the [[vacuum permeability]]. For practical purposes, the applied and the measured field are approximately the same <math>\mathbf{B}\approx\mu_0 \mathbf{H}</math> (if the material is not [[ferromagnetic]]).

The oscillations of the differential susceptibility when plotted against <math>1/B</math>, have a period <math>P</math> (in [[Tesla (unit)|tesla]]s<sup>−1</sup>) that is inversely proportional to the area <math>S</math> of the extremal orbit of the [[Fermi surface]] (m<sup>−2</sup>), in the direction of the applied field, that is

:<math>P\left( B^{-1} \right) = \frac{2 \pi e}{\hbar S}</math>,

where <math>\hbar</math> is [[Planck constant]] and <math>e</math> is the [[elementary charge]].<ref>{{cite book|title=Introduction to Solid-State Physics|last=Kittel|first=Charles|publisher=[[John Wiley & Sons|Wiley]]|year=2005|isbn=978-0-471-41526-8|edition=8th|url-access=registration|url=https://archive.org/details/isbn_9780471415268}}</ref> The existence of more than one extremal orbit leads to multiple periods becoming superimposed.<ref>{{Cite book|last=Neil Ashcroft|first=N. David Mermin|title=Solid State Physics|publisher=Holt, Rinehart and Winston|year=1976|isbn=0-03-049346-3|location=London|pages=264–275|language=English}}</ref> A more precise formula, known as [[Lifshitz–Kosevich formula]], can be obtained using [[Semiclassical physics|semiclassical approximations]].<ref name=":2">{{Cite journal|last1=Peschanskii|first1=V. G.|last2=Kolesnichenko|first2=Yu. A.|date=2014|title=On the 60th anniversary of the Lifshitz-Kosevich theory|url=http://aip.scitation.org/doi/10.1063/1.4871744|journal=Low Temperature Physics|language=en|volume=40|issue=4|pages=267–269|doi=10.1063/1.4871744|bibcode=2014LTP....40..267P|issn=1063-777X}}</ref><ref>{{Cite book|last=Kübler|first=Jürgen|url=https://books.google.com/books?id=M70tL9xaOxoC&q=lifshitz+kosevich+equation|title=Theory of Itinerant Electron Magnetism|date=2000-08-17|publisher=OUP Oxford|isbn=978-0-19-850028-5|language=en}}</ref><ref name=":3">{{Cite journal|last1=Peschanskii|first1=V. G.|last2=Kolesnichenko|first2=Yu A.|date=2014-05-02|title=On the 60th anniversary of the Lifshitz-Kosevich theory|url=https://aip.scitation.org/doi/abs/10.1063/1.4871744|journal=Low Temperature Physics|language=en|volume=40|issue=4|pages=267|doi=10.1063/1.4871744|bibcode=2014LTP....40..267P|issn=1063-777X}}</ref>

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.

== History ==
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 a function of the field.<ref name=":1" /> 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.<ref name=":0" />

The theoretical prediction of the phenomenon was formulated before the experiment, in the same year, by [[Lev Landau]],<ref>Landau, L. D. "Diamagnetismus der Metalle." Zeitschrift für Physik 64.9 (1930): 629-637.</ref> but he discarded it as he thought that the magnetic fields necessary for its demonstration could not yet be created in a laboratory.<ref>{{Cite book|title=Low Temperature Physics LT9|last=Shoenberg|first=David|publisher=Springer|year=1965|isbn=978-1-4899-6217-1|editor-last=Daunt|editor-first=J.G.|location=Boston|pages=665–676|chapter=The De Haas–Van Alphen Effect|doi=10.1007/978-1-4899-6443-4_6|author-link=David Shoenberg|editor-last2=Edwards|editor-first2=D.O.|editor-last3=Milford|editor-first3=F.J.|editor-last4=Yaqub|editor-first4=M.}}</ref><ref>{{cite book|title=Condensed Matter Physics|last=Marder|first=Michael P.|publisher=[[John Wiley & Sons|Wiley]]|year=2000}}</ref><ref name=":0">{{Cite book|title=Solid state science : past, present, and predicted|last=Shoenberg|first=David|date=1987|publisher=A. Hilger|isbn=978-0852745847|editor-last=Weaire|editor-first=D.L.|location=Bristol, England|pages=115|chapter=Electrons at the Fermi Surface|oclc=17620910|author-link=David Shoenberg|editor-last2=Windsor|editor-first2=C.G.}}</ref> The effect was described mathematically using [[Landau quantization]] of the [[electron]] energies in an applied magnetic field.  A strong homogeneous magnetic field &mdash; typically several [[Tesla (unit)|teslas]] &mdash; and a low temperature are required to cause a material to exhibit the DHVA effect.<ref>{{cite web|url=http://www.lanl.gov/orgs/mpa/nhmfl/users/pages/deHaas.htm|title=De Haas–Van Alphen Effect|last=Harrison|first=Neil|publisher=[[National High Magnetic Field Laboratory]] at the [[Los Alamos National Laboratory]]|access-date=2010-02-11}}</ref> 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]], Shoenberg's advisor, had convinced him that such homogeneity in the field was impractical.<ref name=":0" />

After the 1950s, the DHVA effect gained wider relevance after [[Lars Onsager]] (1952),<ref>{{Cite journal|last=Onsager|first=Lars|author-link=Lars Onsager|date=1952|title=Interpretation of the De Haas–Van Alphen effect|journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|volume=43|issue=344|pages=1006–1008|doi=10.1080/14786440908521019|via=Taylor & Francis}}</ref> and independently, [[Ilya Lifshitz]] and [[Arnold Kosevich]] (1954),<ref>Lifschitz, I. M., and A. M. Kosevich. "On the theory of the De Haas–Van Alphen effect for particles with an arbitrary dispersion law." ''Dokl. Akad. Nauk SSSR''. Vol. 96. 1954.</ref><ref>{{Cite journal|last1=Lifshitz|first1=Ilya Mikhailovich|author-link=Ilya Lifshitz|last2=Kosevich|first2=Arnold M.|author-link2=Arnold Kosevich|date=1956|title=Theory of magnetic susceptibility in metals at low temperatures|url=http://www.jetp.ac.ru/cgi-bin/dn/e_002_04_0636.pdf|journal=Soviet Physics JETP|volume=2|pages=636–645|via=Journal of Experimental and Theoretical Physics|access-date=2018-05-03|archive-date=2018-05-03|archive-url=https://web.archive.org/web/20180503180730/http://www.jetp.ac.ru/cgi-bin/dn/e_002_04_0636.pdf|url-status=dead}}</ref> pointed out that the phenomenon could be used to image the Fermi surface of a metal.<ref name=":0" /> In 1954, Lifshitz and [[Aleksei Pogorelov]] determined the range of applicability of the theory and described how to determine the shape of any arbitrary convex Fermi surface by measuring the extremal sections. Lifshitz and Pogorelov also found a relation between the temperature dependence of the oscillations and the cyclotron mass of an electron.<ref name=":2" />

By the 1970s the Fermi surface of most metallic elements had been reconstructed using De Haas–Van Alphen and Shubnikov–de Haas effects.<ref name=":2" /> Other techniques to study the Fermi surface have appeared since like the [[angle-resolved photoemission spectroscopy]] (ARPES).<ref name=":3" />

==References==
{{reflist}}

==External links==
*{{cite web
 |first1=Masatsugu
 |last1=Suzuki
 |first2=Itsuko S.
 |last2=Suzuki
 |date=26 April 2006
 |url=http://www2.binghamton.edu/physics/docs/note-dhva.pdf
 |title=Lecture note on Solid State Physics: De Haas–Van Alphen effect
 |publisher=[[Binghamton University|State University of New York at Binghamton]]
 |access-date=2010-02-11
 |archive-url=https://web.archive.org/web/20110718064004/http://www2.binghamton.edu/physics/docs/note-dhva.pdf
 |archive-date=18 July 2011
 |url-status=dead
 }}

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{{DEFAULTSORT:De Haas-Van Alphen effect}}
[[Category:Magnetism]]