TY - JOUR

T1 - Mean-field cluster model for the critical behaviour of ferromagnets

AU - Chamberlin, Ralph

PY - 2000/11/16

Y1 - 2000/11/16

N2 - Two separate theories are often used to characterize the paramagnetic properties of ferromagnetic materials. At temperatures T well above the Curie temperature, T(C) (where the transition from paramagnetic to ferromagnetic behaviour occurs), classical mean-field theory yields the Curie-Weiss law for the magnetic susceptibility: χ(T) proportional to 1/(T - Θ), where Θ is the Weiss constant. Close to T(C), however, the standard mean-field approach breaks down so that better agreement with experimental data is provided by critical scaling theory: χ(T) proportional to 1/(T - T(C))(γ) where γ is a scaling exponent. But there is no known model capable of predicting the measured values of γ nor its variation among different substances. Here I use a mean-field cluster model based on finite-size thermostatistics to extend the range of mean-field theory, thereby eliminating the need for a separate scaling regime. The mean-field approximation is justified by using a kinetic-energy term to maintain the microcanonical ensemble. The model reproduces the Curie-Weiss law at high temperatures, but the classical Weiss transition at T(C) = Θ is suppressed by finite-size effects. Instead, the fraction of clusters with a specific amount of order diverges at T(C), yielding a transition that is mathematically similar to Bose-Einstein condensation. At all temperatures above T(C) the model matches the measured magnetic susceptibilities of crystalline EuO, Gd, Co and Ni, thus providing a unified picture for both the critical-scaling and Curie-Weiss regimes.

AB - Two separate theories are often used to characterize the paramagnetic properties of ferromagnetic materials. At temperatures T well above the Curie temperature, T(C) (where the transition from paramagnetic to ferromagnetic behaviour occurs), classical mean-field theory yields the Curie-Weiss law for the magnetic susceptibility: χ(T) proportional to 1/(T - Θ), where Θ is the Weiss constant. Close to T(C), however, the standard mean-field approach breaks down so that better agreement with experimental data is provided by critical scaling theory: χ(T) proportional to 1/(T - T(C))(γ) where γ is a scaling exponent. But there is no known model capable of predicting the measured values of γ nor its variation among different substances. Here I use a mean-field cluster model based on finite-size thermostatistics to extend the range of mean-field theory, thereby eliminating the need for a separate scaling regime. The mean-field approximation is justified by using a kinetic-energy term to maintain the microcanonical ensemble. The model reproduces the Curie-Weiss law at high temperatures, but the classical Weiss transition at T(C) = Θ is suppressed by finite-size effects. Instead, the fraction of clusters with a specific amount of order diverges at T(C), yielding a transition that is mathematically similar to Bose-Einstein condensation. At all temperatures above T(C) the model matches the measured magnetic susceptibilities of crystalline EuO, Gd, Co and Ni, thus providing a unified picture for both the critical-scaling and Curie-Weiss regimes.

UR - http://www.scopus.com/inward/record.url?scp=0034676459&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034676459&partnerID=8YFLogxK

U2 - 10.1038/35042534

DO - 10.1038/35042534

M3 - Article

C2 - 11099035

AN - SCOPUS:0034676459

SN - 0028-0836

VL - 408

SP - 337

EP - 339

JO - Nature

JF - Nature

IS - 6810

ER -