Arrott plot

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Arrott plot for a simple mean field ferromagnetic phase transition.

In condensed matter physics, an Arrott plot is a plot of the square of the magnetization M^2 of a substance, against the ratio of the applied magnetic field to magnetization H/M at one (or several) fixed temperature(s). Arrott plots are an easy way of determining the presence of ferromagnetic order in a material.[1][2] They are named after American physicist Anthony Arrott who introduced them as a technique for studying magnetism in 1957.[3]

Details[edit]

According to the Ginzburg-Landau mean field picture for magnetism, the free energy of a ferromagnetic material close to a phase transition can be written as:


F(M)=-H M+a (T-T_c) M^2+bM^4+\ldots

where M, the magnetization, is the order parameter, H is the applied magnetic field, T_c is the critical temperature, and a,b are arbitrary constants.

Close to the phase transition, this gives a relation for the magnetization order parameter:


M^2=\frac{1}{b}\frac{H}{M}-\frac{a}{b}\epsilon

where \epsilon=\frac{T-T_c}{T_c} is a dimensionless measure of the temperature.

Thus in a graph plotting M^2 vs. H/M 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.[4]

See also[edit]

References[edit]

  1. ^ Yeung, I.; Roshko, R.; Williams, G. (1986). "Arrott-plot criterion for ferromagnetism in disordered systems". Physical Review B 34 (5): 3456–3457. Bibcode:1986PhRvB..34.3456Y. doi:10.1103/PhysRevB.34.3456. 
  2. ^ du Trémolet de Lacheisserie, E., ed. (2005). Magnetism. Springer. ISBN 978-0-387-22967-6. 
  3. ^ Arrott, A. (1957). "Criterion for Ferromagnetism from Observations of Magnetic Isotherms". Physical Review 108 (6): 1394–1396. Bibcode:1957PhRv..108.1394A. doi:10.1103/PhysRev.108.1394. 
  4. ^ Hadimani, R. L.; Melikhov, Y.; Snyder, J. E.; Jiles, D. C. (2008). "Determination of Curie temperature by Arrott plot technique in Gd5(SixGe1−x)4 for x>0.575". Journal of Magnetism and Magnetic Materials 320 (20): e696–e698. Bibcode:2008JMMM..320E.696H. doi:10.1016/j.jmmm.2008.04.035.