Static universality class for gadolinium

Abstract

High-precision magnetization, M(T,H), 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 T_C, M(T_C,H), and the temperature variations of spontaneous magnetization, M(T,0), and initial susceptibility, χ (T), in the asymptotic critical region |ε |=|(T-T_C)/T_C|<~2×10^-3, but do so only when the multiplicative logarithmic corrections (LC), predicted by the renormalization group (RG) calculations for dipolar Ising (spin dimensionality n=1) spin systems at the upper marginal space dimension d^∗ =3, are taken into account. Such data analyses also permit the first accurate determination of LC exponents (x',x), the asymptotic critical exponents β , γ , and δ , and critical amplitudes B, Γ and D for M(T,0), χ (T), and M(TC,H). The exponents x', x, β , γ , and δ , as well as the universal amplitude ratio R_χ=D^-B^{δ -1}Γ possess the same (within the uncertainty limits) values as those yielded by the RG calculations for a d=3 uniaxial dipolar ferromagnet. Moreover, the presently determined values of β , γ , and δ , together with the reported value of the specific heat critical exponent α , obey the scaling relations β+γ =βδ and α +2β+γ =2 accurately. By establishing that gadolinium belongs to the d=3, n=1 dipolar static universality class, the present results resolve the long-standing controversy surrounding the nature of the asymptotic critical behavior of Gd.