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{{Short description|Electromagnetic effect in physics}} | {{Short description|Electromagnetic effect in physics}} | ||
{{About||the | {{About||the music band|The Hall Effect (band)|}} | ||
[[File:Hall effect. | [[File:Hall effect 1.gif|thumb|upright=1.4|In diagram '''A''', the flat conductor possesses a negative charge on the top (symbolized by the blue color) and a positive charge on the bottom (red color). In '''B''' and '''C''', the direction of the electrical and the magnetic fields are changed respectively which switches the polarity of the charges around. In '''D''', both fields change direction simultaneously which results in the same polarity as in diagram '''A'''. | ||
{{ordered list|electrons|flat conductor, which serves as a Hall element ''([[Hall effect sensor]])''|magnet|magnetic field|power source | {{ordered list|electrons|flat conductor, which serves as a Hall element ''([[Hall effect sensor]])''|magnet|magnetic field|power source | ||
}}]] | }}]] | ||
{{Electromagnetism|Topic=Hall effect}} | {{Electromagnetism|Topic=Hall effect}} | ||
The '''Hall effect''' is the production of a [[voltage|potential difference]], across an [[electrical conductor]], that is [[wikt:transverse|transverse]] to an [[electric current]] in the conductor and to an applied [[magnetic field]] [[wikt:perpendicular|perpendicular]] to the current. Such potential difference is known as the '''Hall voltage'''. It was discovered by [[Edwin Hall]] in 1879 | The '''Hall effect''' is the production of a [[voltage|potential difference]], across an [[electrical conductor]], that is [[wikt:transverse|transverse]] to an [[electric current]] in the conductor and to an applied [[magnetic field]] [[wikt:perpendicular|perpendicular]] to the current. Such potential difference is known as the '''Hall voltage'''. It was discovered by [[Edwin Hall]] in 1879<ref>{{cite journal|title = On a New Action of the Magnet on Electric Currents|author = Edwin Hall|author-link = Edwin Hall|journal = American Journal of Mathematics|volume = 2|year = 1879|pages = 287–92|url = http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|access-date = 2008-02-28|doi = 10.2307/2369245|issue = 3|jstor = 2369245 | s2cid=107500183 |archive-url = https://web.archive.org/web/20110727010116/http://www.stenomuseet.dk/skoletj/elmag/kilde9.html|archive-date=2011-07-27 |ref = hallpdf|url-access = subscription}}</ref><ref>{{Cite web|url=https://www.britannica.com/science/Hall-effect|title=Hall effect {{!}} Definition & Facts|website=Encyclopedia Britannica|language=en|access-date=2020-02-13}}</ref> through a study of the [[electromagnetic theory]] of [[James Clerk Maxwell]], becoming a critical confirmation of that theory.<ref>{{Cite journal |last=Buchwald* |first=J. Z. |date=1979 |title=The Hall Effect and Maxwellian Electrodynamics in the 1880's. Part I: The Discovery of a New Electric Field |url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0498.1979.tb00360.x |journal=Centaurus |language=en |volume=23 |issue=1 |pages=51–99 |doi=10.1111/j.1600-0498.1979.tb00360.x |issn=1600-0498|url-access=subscription }}</ref> | ||
The '''Hall coefficient''' is defined as the ratio of the induced [[electric field]] to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the [[charge carriers]] that constitute the current. | The '''Hall coefficient''' is defined as the ratio of the induced [[electric field]] to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the [[charge carriers]] that constitute the current. | ||
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In the 1820s, [[André-Marie Ampère]] observed this underlying mechanism that led to the discovery of the Hall effect.<ref name=":1">{{Cite book |last=Ramsden |first=Edward |url=https://books.google.com/books?id=R8VAjMitH1QC |title=Hall-Effect Sensors: Theory and Application |date=2011-04-01 |publisher=Elsevier |isbn=978-0-08-052374-3 |page=2 |language=en}}</ref> However it was not until a solid mathematical basis for [[electromagnetism]] was systematized by [[James Clerk Maxwell]]'s "[[On Physical Lines of Force]]" (published in 1861–1862) that details of the interaction between magnets and electric current could be understood. | In the 1820s, [[André-Marie Ampère]] observed this underlying mechanism that led to the discovery of the Hall effect.<ref name=":1">{{Cite book |last=Ramsden |first=Edward |url=https://books.google.com/books?id=R8VAjMitH1QC |title=Hall-Effect Sensors: Theory and Application |date=2011-04-01 |publisher=Elsevier |isbn=978-0-08-052374-3 |page=2 |language=en}}</ref> However it was not until a solid mathematical basis for [[electromagnetism]] was systematized by [[James Clerk Maxwell]]'s "[[On Physical Lines of Force]]" (published in 1861–1862) that details of the interaction between magnets and electric current could be understood. | ||
[[Edwin Hall]] then explored the question of whether magnetic fields interacted with the conductors ''or'' the electric current, and reasoned that if the force was specifically acting on the current, it should crowd current to one side of the wire, producing a small measurable voltage.<ref name=":1" /> In 1879, he discovered this ''Hall effect'' while he was working on his doctoral degree at [[Johns Hopkins University]] in [[Baltimore]], [[Maryland]].<ref name="bridgeman-momoir">{{cite book|last=Bridgeman|first=P. W.|title=Biographical Memoir of Edwin Herbert Hall|year=1939|publisher=National Academy of Sciences|url=https://docs.google.com/viewer?a=v&q=cache:qWPFjF1DGJcJ:books.nap.edu/html/biomems/ehall.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESiwi2QsmBBlJQ-CGCqOI-5jo7JVHR8KlVBUlYQg7o3jZTM3Hf2pSa3VeYGFgqCsepNg2dtCFeumBvFAX35h7vFrDq29vFqmPQsXXinsEp4aY1iC4-Tyws_IxDAUX0Gacg8xWCGQ&sig=AHIEtbSYLSS-LvLf1yfIKBflgxKm-7Qwdw}}</ref> Eighteen years before the [[electron]] was discovered, his measurements of the tiny effect produced in the apparatus he used were an experimental [[wikt:tour de force|tour de force]], published under the name "On a New Action of the Magnet on Electric Currents".<ref>{{cite journal | last=Hall | first=E. H. | title=On a New Action of the Magnet on Electric Currents | journal=American Journal of Mathematics | publisher=JSTOR | volume=2 | issue=3 | year=1879 | pages=287–292 | issn=0002-9327 | doi=10.2307/2369245 | jstor=2369245 |doi-access=free}}</ref><ref>{{Cite web|title = Hall Effect History|url = http://phareselectronics.com/products/hall-effect-sensors/hall-effect-history/|access-date = 2015-07-26|archive-url=https://web.archive.org/web/20150529002229/http://phareselectronics.com/products/hall-effect-sensors/hall-effect-history|archive-date=29 May 2015 | [[Edwin Hall]] then explored the question of whether magnetic fields interacted with the conductors ''or'' the electric current, and reasoned that if the force was specifically acting on the current, it should crowd current to one side of the wire, producing a small measurable voltage.<ref name=":1" /> In 1879, he discovered this ''Hall effect'' while he was working on his doctoral degree at [[Johns Hopkins University]] in [[Baltimore]], [[Maryland]].<ref name="bridgeman-momoir">{{cite book|last=Bridgeman|first=P. W.|title=Biographical Memoir of Edwin Herbert Hall|year=1939|publisher=National Academy of Sciences|url=https://docs.google.com/viewer?a=v&q=cache:qWPFjF1DGJcJ:books.nap.edu/html/biomems/ehall.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESiwi2QsmBBlJQ-CGCqOI-5jo7JVHR8KlVBUlYQg7o3jZTM3Hf2pSa3VeYGFgqCsepNg2dtCFeumBvFAX35h7vFrDq29vFqmPQsXXinsEp4aY1iC4-Tyws_IxDAUX0Gacg8xWCGQ&sig=AHIEtbSYLSS-LvLf1yfIKBflgxKm-7Qwdw}}</ref> Eighteen years before the [[electron]] was discovered, his measurements of the tiny effect produced in the apparatus he used were an experimental [[wikt:tour de force|tour de force]], published under the name "On a New Action of the Magnet on Electric Currents".<ref>{{cite journal | last=Hall | first=E. H. | title=On a New Action of the Magnet on Electric Currents | journal=American Journal of Mathematics | publisher=JSTOR | volume=2 | issue=3 | year=1879 | pages=287–292 | issn=0002-9327 | doi=10.2307/2369245 | jstor=2369245 |doi-access=free}}</ref><ref>{{Cite web|title = Hall Effect History|url = http://phareselectronics.com/products/hall-effect-sensors/hall-effect-history/|access-date = 2015-07-26|archive-url=https://web.archive.org/web/20150529002229/http://phareselectronics.com/products/hall-effect-sensors/hall-effect-history|archive-date=29 May 2015 }}</ref><ref>{{Cite book|title = Hall-Effect Sensors|last = Ramsden|first = Edward|publisher = Elsevier Inc.|year = 2006|isbn = 978-0-7506-7934-3|page = xi}}</ref> | ||
==Theory== | ==Theory== | ||
The Hall effect is due to the nature of the current in a conductor. Current consists of the movement of many small [[charge carrier]]s, typically [[electron]]s, [[Electron hole|holes]], [[ion]]s (see [[Electromigration]]) or all three. When a magnetic field is present, these charges experience a force, called the [[Lorentz force]].<ref>{{cite web|url=http://www.eeel.nist.gov/812/effe.htm|access-date=2008-02-28|title=The Hall Effect|publisher=[[NIST]]|archive-url=https://web.archive.org/web/20080307092429/http://www.eeel.nist.gov/812/effe.htm|archive-date=2008-03-07 | The Hall effect is due to the nature of the current in a conductor. Current consists of the movement of many small [[charge carrier]]s, typically [[electron]]s, [[Electron hole|holes]], [[ion]]s (see [[Electromigration]]) or all three. When a magnetic field is present, these charges experience a force, called the [[Lorentz force]].<ref>{{cite web|url=http://www.eeel.nist.gov/812/effe.htm|access-date=2008-02-28|title=The Hall Effect|publisher=[[NIST]]|archive-url=https://web.archive.org/web/20080307092429/http://www.eeel.nist.gov/812/effe.htm|archive-date=2008-03-07}}</ref> When such a magnetic field is absent, the charges follow approximately straight paths between collisions with impurities, [[phonons]], etc. However, when a magnetic field with a perpendicular component is applied, their paths between collisions are curved; thus, moving charges accumulate on one face of the material. This leaves equal and opposite charges exposed on the other face, where there is a scarcity of mobile charges. The result is an asymmetric distribution of charge density across the Hall element, arising from a force that is perpendicular to both the straight path and the applied magnetic field. The separation of charge establishes an [[electric field]] that opposes the migration of further charge, so a steady [[electric potential]] is established for as long as the charge is flowing.<ref>{{Cite web|url=https://www.electronics-tutorials.ws/electromagnetism/hall-effect.html|title=Hall Effect Sensor|website=Electronic Tutorials|date=13 August 2013 }}</ref> | ||
In [[classical electromagnetism]], electrons move in the opposite direction of the current {{math|''I''}} (by [[Electric current#Conventions|convention]] "current" describes a theoretical "hole flow"). In some metals and semiconductors it ''appears'' "holes" are actually flowing because the direction of the voltage is opposite to the derivation below. | In [[classical electromagnetism]], electrons move in the opposite direction of the current {{math|''I''}} (by [[Electric current#Conventions|convention]] "current" describes a theoretical "hole flow"). In some metals and semiconductors it ''appears'' "holes" are actually flowing because the direction of the voltage is opposite to the derivation below. | ||
[[File:Hall effect Setup Electrons Holes.svg|frame|Hall effect measurement setup for electrons. Initially, the electrons follow the curved arrow, due to the magnetic force. At some distance from the current-introducing contacts, electrons pile up on the left side and deplete from the right side, which creates an electric field in the direction of the assigned {{math|''V''<sub>H</sub>}}. If holes are dominant, {{math|''V''<sub>H</sub>}} is positive and if electrons are dominant it is negative. In steady-state, the electric field will be strong enough to exactly cancel out the magnetic force, thus the electrons follow the straight arrow (dashed).]] | |||
[[File:Hall | [[File:Hall Sensor.webm|thumb|The animation shows the action of a magnetic field on a beam of electric charges in vacuum, or in other terms, exclusively the action of the [[Lorentz force]]. This animation is an illustration of a typical error performed in the framework of the interpretation of the Hall effect. Indeed, at stationary regime and inside a Hall-bar, the electric current is longitudinal whatever the magnetic field and there is no transverse current <math>{j_y = 0}</math> (in contrast to the case of the corbino disc). Only the electric field is modified by a transverse component <math>{E_y}</math>.<ref>{{Cite journal|last1=Creff|first1=M.|last2=Faisant|first2=F.|last3=Rubì|first3=J. M.|last4=Wegrowe|first4=J.-E.|date=2020-08-07|title=Surface currents in Hall devices|url=https://aip.scitation.org/doi/10.1063/5.0013182|journal=Journal of Applied Physics|volume=128|issue=5|page=054501|doi=10.1063/5.0013182|arxiv=1908.06282 |bibcode=2020JAP...128e4501C |hdl=2445/176859 |s2cid=201070551 |issn=0021-8979}}</ref>]] | ||
[[File:Hall Sensor.webm|thumb|The animation shows the action of a magnetic field on a beam of electric charges in vacuum, or in other terms, exclusively the action of the [[Lorentz force]]. This animation is an illustration of a typical error performed in the framework of the interpretation of the Hall effect. Indeed, at stationary regime and inside a Hall-bar, the electric current is longitudinal whatever the magnetic field and there is no transverse current <math>{j_y = 0}</math> (in contrast to the case of the corbino disc). Only the electric field is modified by a transverse component <math>{E_y}</math>.<ref>{{Cite journal|last1=Creff|first1=M.|last2=Faisant|first2=F.|last3=Rubì|first3=J. M.|last4=Wegrowe|first4=J.-E.|date=2020-08-07|title=Surface currents in Hall devices|url=https://aip.scitation.org/doi/10.1063/5.0013182|journal=Journal of Applied Physics|volume=128|issue=5| | |||
For a simple metal where there is only one type of [[charge carrier]] (electrons), the Hall voltage {{math|''V''<sub>H</sub>}} can be derived by using the [[Lorentz force]] and seeing that, in the steady-state condition, charges are not moving in the {{math|''y''}}-axis direction. Thus, the magnetic force on each electron in the {{math|''y''}}-axis direction is cancelled by a {{math|''y''}}-axis electrical force due to the buildup of charges. The {{math|''v<sub>x</sub>''}} term is the [[drift velocity]] of the current which is assumed at this point to be holes by convention. The {{math|''v<sub>x</sub>B<sub>z</sub>''}} term is negative in the {{math|''y''}}-axis direction by the right hand rule. | For a simple metal where there is only one type of [[charge carrier]] (electrons), the Hall voltage {{math|''V''<sub>H</sub>}} can be derived by using the [[Lorentz force]] and seeing that, in the steady-state condition, charges are not moving in the {{math|''y''}}-axis direction. Thus, the magnetic force on each electron in the {{math|''y''}}-axis direction is cancelled by a {{math|''y''}}-axis electrical force due to the buildup of charges. The {{math|''v<sub>x</sub>''}} term is the [[drift velocity]] of the current which is assumed at this point to be holes by convention. The {{math|''v<sub>x</sub>B<sub>z</sub>''}} term is negative in the {{math|''y''}}-axis direction by the right hand rule. | ||
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This property of the Hall effect offered the first real proof that electric currents in most metals are carried by moving electrons, not by protons. It also showed that in some substances (especially [[p-type semiconductor]]s), it is contrarily more appropriate to think of the current as positive "[[Electron hole|holes]]" moving rather than negative electrons. A common source of confusion with the Hall effect in such materials is that holes moving one way are really electrons moving the opposite way, so one expects the Hall voltage polarity to be the same as if electrons were the [[charge carriers]] as in most metals and [[n-type semiconductor]]s. Yet we observe the opposite polarity of Hall voltage, indicating positive charge carriers. However, of course there are no actual [[positrons]] or other positive [[elementary particle]]s carrying the charge in [[p-type semiconductor]]s, hence the name "holes". In the same way as the oversimplistic picture of light in glass as photons being absorbed and re-emitted to explain [[refraction]] breaks down upon closer scrutiny, this apparent contradiction too can only be resolved by the modern quantum mechanical theory of [[quasiparticles]] wherein the collective quantized motion of multiple particles can, in a real physical sense, be considered to be a particle in its own right (albeit not an elementary one).<ref>N.W. Ashcroft and N.D. Mermin "Solid State Physics" {{ISBN|978-0-03-083993-1}}</ref> | This property of the Hall effect offered the first real proof that electric currents in most metals are carried by moving electrons, not by protons. It also showed that in some substances (especially [[p-type semiconductor]]s), it is contrarily more appropriate to think of the current as positive "[[Electron hole|holes]]" moving rather than negative electrons. A common source of confusion with the Hall effect in such materials is that holes moving one way are really electrons moving the opposite way, so one expects the Hall voltage polarity to be the same as if electrons were the [[charge carriers]] as in most metals and [[n-type semiconductor]]s. Yet we observe the opposite polarity of Hall voltage, indicating positive charge carriers. However, of course there are no actual [[positrons]] or other positive [[elementary particle]]s carrying the charge in [[p-type semiconductor]]s, hence the name "holes". In the same way as the oversimplistic picture of light in glass as photons being absorbed and re-emitted to explain [[refraction]] breaks down upon closer scrutiny, this apparent contradiction too can only be resolved by the modern quantum mechanical theory of [[quasiparticles]] wherein the collective quantized motion of multiple particles can, in a real physical sense, be considered to be a particle in its own right (albeit not an elementary one).<ref>N.W. Ashcroft and N.D. Mermin "Solid State Physics" {{ISBN|978-0-03-083993-1}}</ref> | ||
Unrelatedly, inhomogeneity in the conductive sample can result in a spurious sign of the Hall effect, even in ideal [[Van der Pauw method|van der Pauw]] configuration of electrodes. For example, a Hall effect consistent with positive carriers was observed in evidently n-type semiconductors.<ref>{{Cite journal | doi=10.1557/JMR.2008.0300|bibcode = 2008JMatR..23.2293O|title = Positive Hall coefficients obtained from contact misplacement on evident ''n''-type ZnO films and crystals| journal=Journal of Materials Research| volume=23| issue=9| | Unrelatedly, inhomogeneity in the conductive sample can result in a spurious sign of the Hall effect, even in ideal [[Van der Pauw method|van der Pauw]] configuration of electrodes. For example, a Hall effect consistent with positive carriers was observed in evidently n-type semiconductors.<ref>{{Cite journal | doi=10.1557/JMR.2008.0300|bibcode = 2008JMatR..23.2293O|title = Positive Hall coefficients obtained from contact misplacement on evident ''n''-type ZnO films and crystals| journal=Journal of Materials Research| volume=23| issue=9| page=2293|last1 = Ohgaki|first1 = Takeshi| last2=Ohashi| first2=Naoki| last3=Sugimura| first3=Shigeaki| last4=Ryoken| first4=Haruki| last5=Sakaguchi| first5=Isao| last6=Adachi| first6=Yutaka| last7=Haneda| first7=Hajime| year=2008| s2cid=137944281 }}</ref> Another source of artefact, in uniform materials, occurs when the sample's aspect ratio is not long enough: the full Hall voltage only develops far away from the current-introducing contacts, since at the contacts the transverse voltage is shorted out to zero. | ||
===Hall effect in semiconductors=== | ===Hall effect in semiconductors=== | ||
When a current-carrying [[semiconductor]] is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges. | When a current-carrying [[semiconductor]] is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges. | ||
The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single [[charge carrier]]. However, in semiconductors and many metals the theory is more complex, because in these materials conduction can involve significant, simultaneous contributions from both [[electrons]] and [[Electron hole|holes]], which may be present in different concentrations and have different [[Electron mobility|mobilities]]. For moderate magnetic fields the Hall coefficient is<ref name='Kasap2001'>{{cite web|url=http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf |title=Hall Effect in Semiconductors |last=Kasap |first=Safa |archive-url=https://web.archive.org/web/20080821202757/http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf | The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single [[charge carrier]]. However, in semiconductors and many metals the theory is more complex, because in these materials conduction can involve significant, simultaneous contributions from both [[electrons]] and [[Electron hole|holes]], which may be present in different concentrations and have different [[Electron mobility|mobilities]]. For moderate magnetic fields the Hall coefficient is<ref name='Kasap2001'>{{cite web|url=http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf |title=Hall Effect in Semiconductors |last=Kasap |first=Safa |archive-url=https://web.archive.org/web/20080821202757/http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf |archive-date=2008-08-21 }}</ref><ref>{{Cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Hall.html|title=Hall Effect|website=hyperphysics.phy-astr.gsu.edu|access-date=2020-02-13}}</ref><!-- O.V. Emelyanenko, T.S. Lagunova, D.N. Nasledov and G.N. Talakin, Sov. Phys. Sol. Stat. '''7''' 1063 (1965).--> | ||
<math display="block">R_\mathrm{H}=\frac{p\mu_\mathrm{h}^2 - n\mu_\mathrm{e}^2}{e(p\mu_\mathrm{h} + n\mu_\mathrm{e})^2}</math> | <math display="block">R_\mathrm{H}=\frac{p\mu_\mathrm{h}^2 - n\mu_\mathrm{e}^2}{e(p\mu_\mathrm{h} + n\mu_\mathrm{e})^2}</math> | ||
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===Relationship with star formation=== | ===Relationship with star formation=== | ||
Although it is well known that magnetic fields play an important role in star formation, research models<ref>{{cite journal|title = Star Formation and the Hall Effect|author = Mark Wardle|journal = Astrophysics and Space Science|volume = 292|year = 2004|pages = 317–323|doi = 10.1023/B:ASTR.0000045033.80068.1f|issue = 1|arxiv = astro-ph/0307086 |bibcode = 2004Ap&SS.292..317W |citeseerx = 10.1.1.746.8082|s2cid = 119027877}}</ref><ref>{{Cite journal |arxiv = 1109.1370|bibcode = 2012MNRAS.422..261B|title = The Hall effect in star formation|journal = Monthly Notices of the Royal Astronomical Society|volume = 422|issue = 1| | Although it is well known that magnetic fields play an important role in star formation, research models<ref>{{cite journal|title = Star Formation and the Hall Effect|author = Mark Wardle|journal = Astrophysics and Space Science|volume = 292|year = 2004|pages = 317–323|doi = 10.1023/B:ASTR.0000045033.80068.1f|issue = 1|arxiv = astro-ph/0307086 |bibcode = 2004Ap&SS.292..317W |citeseerx = 10.1.1.746.8082|s2cid = 119027877}}</ref><ref>{{Cite journal |arxiv = 1109.1370|bibcode = 2012MNRAS.422..261B|title = The Hall effect in star formation|journal = Monthly Notices of the Royal Astronomical Society|volume = 422|issue = 1|page = 261|last1 = Braiding|first1 = C. R.|last2 = Wardle|first2 = M.|year = 2012|doi = 10.1111/j.1365-2966.2012.20601.x| doi-access=free |s2cid = 119280669}}</ref><ref>{{Cite journal |arxiv = 1208.5887|bibcode = 2012MNRAS.427.3188B|title = The Hall effect in accretion flows|journal = Monthly Notices of the Royal Astronomical Society|volume = 427|issue = 4|page = 3188|last1 = Braiding|first1 = C. R.|last2 = Wardle |first2 = M.|year = 2012|doi = 10.1111/j.1365-2966.2012.22001.x| doi-access=free |s2cid = 118410321}}</ref> indicate that Hall diffusion critically influences the dynamics of gravitational collapse that forms protostars. | ||
===Quantum Hall effect=== | ===Quantum Hall effect=== | ||
{{Main|Quantum Hall effect}} | {{Main|Quantum Hall effect}} | ||
For a two-dimensional electron system which can be produced in a [[MOSFET]], in the presence of large [[magnetic field]] strength and low [[temperature]], one can observe the quantum Hall effect, in which the Hall [[Electrical conductance|conductance]] {{mvar|σ}} undergoes [[quantum Hall transitions]] to take on quantized values. | For a two-dimensional electron system which can be produced in a [[MOSFET]], in the presence of large [[magnetic field]] strength and low [[temperature]], one can observe the quantum Hall effect, in which the Hall [[Electrical conductance|conductance]] {{mvar|σ}} undergoes [[quantum Hall transitions]] to take on quantized values. | ||
===Spin Hall effect=== | ===Spin Hall effect=== | ||
{{Main|Spin Hall effect}} | {{Main|Spin Hall effect}} | ||
The spin Hall effect consists in the spin accumulation on the lateral boundaries of a current-carrying sample. No magnetic field is needed. It was predicted by [[Mikhail Dyakonov]] and [[V. I. Perel]] in 1971 and observed experimentally more than 30 years later, both in semiconductors and in metals, at cryogenic as well as at room temperatures. | The spin Hall effect consists in the spin accumulation on the lateral boundaries of a current-carrying sample. No magnetic field is needed. It was predicted by [[Mikhail Dyakonov]] and [[V. I. Perel]] in 1971 and observed experimentally more than 30 years later, both in semiconductors and in metals, at cryogenic as well as at room temperatures. | ||
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<math>\theta_{SH}=\frac{2e}{\hbar}\frac{|j_s|}{|j_e|}</math> | <math>\theta_{SH}=\frac{2e}{\hbar}\frac{|j_s|}{|j_e|}</math> | ||
Where <math>j_s</math> is the spin current generated by the applied current density <math>j_e</math>.<ref>{{Cite journal |last1=Deng |first1=Yongcheng |last2=Yang |first2=Meiyin |last3=Ji |first3=Yang |last4=Wang |first4=Kaiyou |date=2020-02-15 |title=Estimating spin Hall angle in heavy metal/ferromagnet heterostructures |url=https://www.sciencedirect.com/science/article/pii/S0304885318337077 |journal=Journal of Magnetism and Magnetic Materials |language=en |volume=496 | | Where <math>j_s</math> is the spin current generated by the applied current density <math>j_e</math>.<ref>{{Cite journal |last1=Deng |first1=Yongcheng |last2=Yang |first2=Meiyin |last3=Ji |first3=Yang |last4=Wang |first4=Kaiyou |date=2020-02-15 |title=Estimating spin Hall angle in heavy metal/ferromagnet heterostructures |url=https://www.sciencedirect.com/science/article/pii/S0304885318337077 |journal=Journal of Magnetism and Magnetic Materials |language=en |volume=496 |article-number=165920 |doi=10.1016/j.jmmm.2019.165920 |bibcode=2020JMMM..49665920D |s2cid=209989182 |issn=0304-8853|url-access=subscription }}</ref> | ||
===Quantum spin Hall effect=== | ===Quantum spin Hall effect=== | ||
{{Main|Quantum spin Hall effect}} | {{Main|Quantum spin Hall effect}} | ||
For [[mercury telluride]] two dimensional quantum wells with strong spin-orbit coupling, in zero magnetic field, at low temperature, the quantum spin Hall effect has been observed in 2007.<ref>{{Cite journal|last1=König|first1=Markus| last2=Wiedmann | first2=Steffen|last3=Brüne|first3=Christoph| last4=Roth|first4=Andreas|last5=Buhmann|first5=Hartmut| last6=Molenkamp | first6=Laurens W.|last7=Qi|first7=Xiao-Liang| last8=Zhang|first8=Shou-Cheng| date=2007-11-02| title=Quantum Spin Hall Insulator State in HgTe Quantum Wells|url=https://www.science.org/doi/10.1126/science.1148047|journal=Science|language=en | volume=318 | issue=5851|pages=766–770|doi=10.1126/science.1148047|issn=0036-8075|pmid=17885096|arxiv=0710.0582|bibcode=2007Sci...318..766K |s2cid=8836690}}</ref> | For [[mercury telluride]] two dimensional quantum wells with strong spin-orbit coupling, in zero magnetic field, at low temperature, the quantum spin Hall effect has been observed in 2007.<ref>{{Cite journal|last1=König|first1=Markus| last2=Wiedmann | first2=Steffen|last3=Brüne|first3=Christoph| last4=Roth|first4=Andreas|last5=Buhmann|first5=Hartmut| last6=Molenkamp | first6=Laurens W.|last7=Qi|first7=Xiao-Liang| last8=Zhang|first8=Shou-Cheng| date=2007-11-02| title=Quantum Spin Hall Insulator State in HgTe Quantum Wells|url=https://www.science.org/doi/10.1126/science.1148047|journal=Science|language=en | volume=318 | issue=5851|pages=766–770|doi=10.1126/science.1148047|issn=0036-8075|pmid=17885096|arxiv=0710.0582|bibcode=2007Sci...318..766K |s2cid=8836690}}</ref> | ||
===Anomalous Hall effect=== | ===Anomalous Hall effect=== | ||
In [[ferromagnetism|ferromagnetic]] materials (and [[paramagnetism|paramagnetic]] materials in a [[magnetic field]]), the Hall resistivity includes an additional contribution, known as the '''anomalous Hall effect''' (or the '''extraordinary Hall effect'''), which depends directly on the [[magnetization]] of the material, and is often much larger than the ordinary Hall effect. (Note that this effect is ''not'' due to the contribution of the [[magnetization]] to the total [[magnetic field]].) For example, in nickel, the anomalous Hall coefficient is about 100 times larger than the ordinary Hall coefficient near the Curie temperature, but the two are similar at very low temperatures.<ref>{{cite journal| journal=Phys. Rev. |volume=95 |pages=1154–1160 |year=1954 |author=Robert Karplus and J. M. Luttinger |title=Hall Effect in Ferromagnetics |doi=10.1103/PhysRev.95.1154| issue=5|bibcode = 1954PhRv...95.1154K }}</ref> Although a well-recognized phenomenon, there is still debate about its origins in the various materials. The anomalous Hall effect can be either an ''extrinsic'' (disorder-related) effect due to [[Spin (physics)|spin]]-dependent [[scattering]] of the [[charge carrier]]s, or an ''intrinsic'' effect which can be described in terms of the [[geometric phase|Berry phase]] effect in the crystal momentum space ({{math|''k''}}-space).<ref name="sinitsyn-08jpa">{{cite journal|title=Semiclassical Theories of the Anomalous Hall Effect|author=N. A. Sinitsyn|journal=Journal of Physics: Condensed Matter|volume=20|year=2008| | In [[ferromagnetism|ferromagnetic]] materials (and [[paramagnetism|paramagnetic]] materials in a [[magnetic field]]), the Hall resistivity includes an additional contribution, known as the '''anomalous Hall effect''' (or the '''extraordinary Hall effect'''), which depends directly on the [[magnetization]] of the material, and is often much larger than the ordinary Hall effect. (Note that this effect is ''not'' due to the contribution of the [[magnetization]] to the total [[magnetic field]].) For example, in nickel, the anomalous Hall coefficient is about 100 times larger than the ordinary Hall coefficient near the [[Curie temperature]], but the two are similar at very low temperatures.<ref>{{cite journal| journal=Phys. Rev. |volume=95 |pages=1154–1160 |year=1954 |author=Robert Karplus and J. M. Luttinger |title=Hall Effect in Ferromagnetics |doi=10.1103/PhysRev.95.1154| issue=5|bibcode = 1954PhRv...95.1154K }}</ref> Although a well-recognized phenomenon, there is still debate about its origins in the various materials. The anomalous Hall effect can be either an ''extrinsic'' (disorder-related) effect due to [[Spin (physics)|spin]]-dependent [[scattering]] of the [[charge carrier]]s, or an ''intrinsic'' effect which can be described in terms of the [[geometric phase|Berry phase]] effect in the crystal momentum space ({{math|''k''}}-space).<ref name="sinitsyn-08jpa">{{cite journal|title=Semiclassical Theories of the Anomalous Hall Effect|author=N. A. Sinitsyn|journal=Journal of Physics: Condensed Matter|volume=20|year=2008|article-number=023201|arxiv=0712.0183|doi=10.1088/0953-8984/20/02/023201|bibcode = 2008JPCM...20b3201S | issue=2 |s2cid=1257769}}</ref><!-- N.A. Sinitsyn 2008 J. Phys.: Condens. Mater. '''20''' 023201 --> | ||
=== Hall effect in ionized gases === | === Hall effect in ionized gases === | ||
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=== Other Hall effects === | === Other Hall effects === | ||
The Hall Effects family has expanded to encompass other quasi-particles in semiconductor nanostructures. Specifically, a set of Hall Effects has emerged based on excitons<ref>{{cite journal |last1=Onga |first1=Masaru |last2=Zhang |first2=Yijin |last3=Ideue |first3=Toshiya |last4=Iwasa |first4=Yoshihiro |title=Exciton Hall effect in monolayer MoS2 |journal=Nature Materials |date=December 2017 |volume=16 |issue=12 |pages=1193–1197 |doi=10.1038/nmat4996 |pmid=28967914 |url=https://www.nature.com/articles/nmat4996 |language=en |issn=1476-4660|url-access=subscription }}</ref><ref>{{cite journal |last1=Kozin |first1=V. K. |last2=Shabashov |first2=V. A. |last3=Kavokin |first3=A. V. |last4=Shelykh |first4=I. A. |title=Anomalous Exciton Hall Effect |journal=Physical Review Letters |date=21 January 2021 |volume=126 |issue=3 | | The Hall Effects family has expanded to encompass other quasi-particles in semiconductor nanostructures. Specifically, a set of Hall Effects has emerged based on excitons<ref>{{cite journal |last1=Onga |first1=Masaru |last2=Zhang |first2=Yijin |last3=Ideue |first3=Toshiya |last4=Iwasa |first4=Yoshihiro |title=Exciton Hall effect in monolayer MoS2 |journal=Nature Materials |date=December 2017 |volume=16 |issue=12 |pages=1193–1197 |doi=10.1038/nmat4996 |pmid=28967914 |url=https://www.nature.com/articles/nmat4996 |language=en |issn=1476-4660|url-access=subscription }}</ref><ref>{{cite journal |last1=Kozin |first1=V. K. |last2=Shabashov |first2=V. A. |last3=Kavokin |first3=A. V. |last4=Shelykh |first4=I. A. |title=Anomalous Exciton Hall Effect |journal=Physical Review Letters |date=21 January 2021 |volume=126 |issue=3 |article-number=036801 |doi=10.1103/PhysRevLett.126.036801 |pmid=33543953 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.036801|arxiv=2006.08717 |bibcode=2021PhRvL.126c6801K }}</ref> and exciton-polaritons<ref>{{cite journal |last1=Kavokin |first1=Alexey |last2=Malpuech |first2=Guillaume |last3=Glazov |first3=Mikhail |title=Optical Spin Hall Effect |journal=Physical Review Letters |date=19 September 2005 |volume=95 |issue=13 |article-number=136601 |doi=10.1103/PhysRevLett.95.136601 |pmid=16197159 |bibcode=2005PhRvL..95m6601K |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.95.136601|url-access=subscription }}</ref> in 2D materials and quantum wells. | ||
== Applications == | == Applications == | ||
{{Main article|Hall effect sensor}} | {{Main article|Hall effect sensor}} | ||
[[Hall sensors]] amplify and use the Hall effect for a variety of sensing applications. | [[Hall sensors]] amplify and use the Hall effect for a variety of sensing applications. | ||
[[Hall-effect thruster]]s use the Hall effect to limit electrons' axial motion and use them to accelerate a propellant. | |||
==Corbino effect== | ==Corbino effect== | ||
[[File:Corbino disc by Zureks.svg|class=skin-invert-image|thumb|Corbino disc – dashed curves represent [[logarithmic spiral]] paths of deflected electrons|225x225px]] | [[File:Corbino disc by Zureks.svg|class=skin-invert-image|thumb|Corbino disc – dashed curves represent [[logarithmic spiral]] paths of deflected electrons.|225x225px]] | ||
The Corbino effect, named after its discoverer [[Orso Mario Corbino]], is a phenomenon involving the Hall effect, but a disc-shaped metal sample is used in place of a rectangular one. Because of its shape the Corbino disc allows the observation of Hall effect–based [[magnetoresistance]] without the associated Hall voltage. | The Corbino effect, named after its discoverer [[Orso Mario Corbino]], is a phenomenon involving the Hall effect, but a disc-shaped metal sample is used in place of a rectangular one. Because of its shape the Corbino disc allows the observation of Hall effect–based [[magnetoresistance]] without the associated Hall voltage. | ||
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== See also == | == See also == | ||
{{Portal|Electronics}} | {{Portal|Electronics}} | ||
* [[Hall effect sensor]] | |||
* [[Electromagnetic induction]] | * [[Electromagnetic induction]] | ||
* [[Nernst effect]] | * [[Nernst effect]] | ||
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==Further reading== | ==Further reading== | ||
{{Refbegin}} | {{Refbegin}} | ||
* {{cite journal|doi=10.1103/PhysRevB.74.165426|title=Classical Hall effect in scanning gate experiments|journal=Physical Review B |volume=74|issue=16|year=2006|last1=Baumgartner|first1=A.|last2=Ihn|first2=T.|last3=Ensslin|first3=K.|last4=Papp|first4=G.| last5=Peeters|first5=F.| last6=Maranowski|first6=K.|last7=Gossard|first7=A. C.| | * {{cite journal|doi=10.1103/PhysRevB.74.165426|title=Classical Hall effect in scanning gate experiments|journal=Physical Review B |volume=74|issue=16|year=2006|last1=Baumgartner|first1=A.|last2=Ihn|first2=T.|last3=Ensslin|first3=K.|last4=Papp|first4=G.| last5=Peeters|first5=F.| last6=Maranowski|first6=K.|last7=Gossard|first7=A. C.|article-number=165426 |bibcode=2006PhRvB..74p5426B| hdl=10067/613600151162165141 | url=https://repository.uantwerpen.be/docman/irua/df27b2/61360.pdf|hdl-access=free}} | ||
* Annraoi M. de Paor. [https://web.archive.org/web/20160304065302/http://gcdcc.hebut.edu.cn/ydzl/19-Correction%20to%20the%20classical%20two-species%20Hall%20Coefficient%20using%20twoport%20network%20theory.pdf ''Correction to the classical two-species Hall Coefficient using twoport network theory'']. International Journal of Electrical Engineering Education 43/4. | * Annraoi M. de Paor. [https://web.archive.org/web/20160304065302/http://gcdcc.hebut.edu.cn/ydzl/19-Correction%20to%20the%20classical%20two-species%20Hall%20Coefficient%20using%20twoport%20network%20theory.pdf ''Correction to the classical two-species Hall Coefficient using twoport network theory'']. International Journal of Electrical Engineering Education 43/4. | ||
* [https://www.feynmanlectures.caltech.edu/III_14.html#Ch14-S3 The Hall effect - The Feynman Lectures on Physics] | * [https://www.feynmanlectures.caltech.edu/III_14.html#Ch14-S3 The Hall effect - The Feynman Lectures on Physics] | ||
* University of Washington [ | * University of Washington [https://courses.washington.edu/phys431/hall_effect/hall_effect.pdf The Hall Effect] | ||
{{Refend}} | {{Refend}} | ||
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* [http://www.fxsolver.com/solve/share/xZGOEQABCTLZvFU08CT9Pg==/ Hall effect calculators] | * [http://www.fxsolver.com/solve/share/xZGOEQABCTLZvFU08CT9Pg==/ Hall effect calculators] | ||
* [https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/hall-effect Interactive Java tutorial on the Hall effect] {{Webarchive|url=https://web.archive.org/web/20200709054706/https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/hall-effect |date=2020-07-09 }} National High Magnetic Field Laboratory | * [https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/hall-effect Interactive Java tutorial on the Hall effect] {{Webarchive|url=https://web.archive.org/web/20200709054706/https://nationalmaglab.org/education/magnet-academy/watch-play/interactive/hall-effect |date=2020-07-09 }} National High Magnetic Field Laboratory | ||
* [ | * [https://scienceworld.wolfram.com/physics/HallEffect.html Science World (wolfram.com)] article. | ||
* "[https://web.archive.org/web/20080307092429/http://www.eeel.nist.gov/812/effe.htm The Hall Effect]". nist.gov. | * "[https://web.archive.org/web/20080307092429/http://www.eeel.nist.gov/812/effe.htm The Hall Effect]". nist.gov. | ||
* [http://it.stlawu.edu/~koon/HallTable.html Table with Hall coefficients of different elements at room temperature] {{Webarchive|url=https://web.archive.org/web/20141221212222/http://it.stlawu.edu/~koon/HallTable.html |date=2014-12-21 }}. | * [http://it.stlawu.edu/~koon/HallTable.html Table with Hall coefficients of different elements at room temperature] {{Webarchive|url=https://web.archive.org/web/20141221212222/http://it.stlawu.edu/~koon/HallTable.html |date=2014-12-21 }}. | ||