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| [[Image:Arrott plot mean field.png|230px|thumb|right|Arrott plot for a simple mean field ferromagnetic phase transition.]]
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| In [[condensed matter physics]], an '''Arrott plot''' is a plot of the square of the [[magnetization]] <math>M^2</math> of a substance, against the ratio of the applied magnetic field to magnetization <math>H/M</math> at one (or several) fixed temperature(s). Arrott plots are an easy way of determining the presence of [[ferromagnetism|ferromagnetic order]] in a material.<ref name=yeung86>
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| {{cite journal
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| |last1=Yeung |first1=I.
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| |last2=Roshko |first2=R.
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| |last3=Williams |first3=G.
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| |year=1986
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| |title=Arrott-plot criterion for ferromagnetism in disordered systems
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| |journal=[[Physical Review B]]
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| |volume=34 |issue=5 |pages=3456–3457
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| |bibcode=1986PhRvB..34.3456Y
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| |doi=10.1103/PhysRevB.34.3456
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| }}</ref><ref name=magnetism-book>
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| {{cite book
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| |editor-last1=du Trémolet de Lacheisserie |editor-first1=E.
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| |title=Magnetism
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| |year=2005
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| |publisher=[[Springer (publisher)|Springer]]
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| |isbn=978-0-387-22967-6
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| }}</ref> They are named after American physicist Anthony Arrott who introduced them as a technique for studying magnetism in 1957.<ref name=arrott>
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| {{cite journal
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| |last1=Arrott |first1=A.
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| |year=1957
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| |title=Criterion for Ferromagnetism from Observations of Magnetic Isotherms
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| |journal=[[Physical Review]]
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| |volume=108 |issue=6 |pages=1394–1396
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| |bibcode = 1957PhRv..108.1394A
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| |doi=10.1103/PhysRev.108.1394
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| }}</ref>
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| ==Details==
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| According to the [[Ginzburg-Landau theory|Ginzburg-Landau]] mean field picture for magnetism, the [[Thermodynamic free energy|free energy]] of a ferromagnetic material close to a phase transition can be written as:
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| <math>
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| F(M)=-H M+a (T-T_c) M^2+BM^4+\ldots
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| </math>
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| where <math>M</math>, the magnetization, is the order parameter, <math>H</math> is the applied magnetic field, <math>T_c</math> is the critical temperature, and <math>a,b</math> are arbitrary constants.
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| Close to the phase transition, this gives a relation for the magnetization order parameter:
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| <math>
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| M^2=\frac{1}{b}\frac{H}{M}-\frac{a}{b}\epsilon
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| </math>
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| where <math>\epsilon=\frac{T-T_c}{T_c}</math> is a dimensionless measure of the temperature.
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| Thus in a graph plotting <math>M^2</math> vs. <math>H/M</math> for various temperatures, the line without an intercept corresponds to the dependence at the critical temperature. Thus along with providing evidence for the existence of a ferromagnetic phase, the Arrott plot can also be used to determine the critical temperature for the phase transition.<ref name=Hadimani2008>
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| {{cite journal
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| |last1=Hadimani |first1=R. L.
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| |last2=Melikhov |first2=Y.
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| |last3=Snyder |first3=J. E.
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| |last4=Jiles |first4=D. C.
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| |year=2008
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| |title=Determination of Curie temperature by Arrott plot technique in Gd<sub>5</sub>(Si<sub>''x''</sub>Ge<sub>1−''x''</sub>)<sub>4</sub> for ''x''>0.575
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| |journal=[[Journal of Magnetism and Magnetic Materials]]
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| |volume=320 |issue=20 |pages=e696–e698
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| |doi=10.1016/j.jmmm.2008.04.035
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| }}</ref>
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| ==See also==
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| *[[Curie–Weiss law]]
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| ==References==
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| {{reflist}}
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| [[Category:Condensed matter physics]]
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| [[Category:Magnetic ordering]]
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