Static universality class for gadolinium

Abstract

High-precision magnetization, (Formula presented) data have been taken along the c axis (easy direction of magnetization) of a high-purity Gd single crystal in the critical region near the ferromagnetic-paramagnetic phase transition. Elaborate data analyses demonstrate that the single power laws, by themselves, do not adequately describe the observed field dependence of M at the Curie point (Formula presented) (Formula presented) and the temperature variations of spontaneous magnetization, (Formula presented) and initial susceptibility, (Formula presented) in the asymptotic critical region (Formula presented) but do so only when the multiplicative logarithmic corrections (LC), predicted by the renormalization group (RG) calculations for dipolar Ising (spin dimensionality (Formula presented) spin systems at the upper marginal space dimension (Formula presented) are taken into account. Such data analyses also permit the first accurate determination of LC exponents (Formula presented) the asymptotic critical exponents (Formula presented) (Formula presented) and (Formula presented) and critical amplitudes (Formula presented) (Formula presented) and (Formula presented) for (Formula presented) (Formula presented) and (Formula presented) The exponents (Formula presented) x, (Formula presented) (Formula presented) and (Formula presented) as well as the universal amplitude ratio (Formula presented) possess the same (within the uncertainty limits) values as those yielded by the RG calculations for a (Formula presented) uniaxial dipolar ferromagnet. Moreover, the presently determined values of (Formula presented) (Formula presented) and (Formula presented) together with the reported value of the specific heat critical exponent (Formula presented) obey the scaling relations (Formula presented) and (Formula presented) accurately. By establishing that gadolinium belongs to the (Formula presented) (Formula presented) dipolar static universality class, the present results resolve the long-standing controversy surrounding the nature of the asymptotic critical behavior of Gd. © 1999 The American Physical Society.