Nonlinear scaling and its application to ferromagnetic systems

Abstract

Making use of renormalization-group ideas, a scaling equation of state applicable to ferromagnetic systems and involving the nonlinear scaling variables ε =ε/t and h^- =h/t, instead of the usual linear scaling variables ε =(T-T_c)/Tc = t-1 and h=H (ordering field), has been derived. The magnetic equation of state so obtained is then generalized to take into account the effect of nonlinear relevant and irrelevant scaling fields. To facilitate a comparison with experiments, the analytic (non-analytic) corrections to the dominant singular behaviour of spontaneous magnetization (order parameter) M(T, 0), 'zero-field' susceptibility χ (T, 0), and specific heat in zero field that the nonlinear relevant (irrelevant) scaling fields give rise to are explicitly calculated up to third order in ε Due consideration is also given to the modifications in the Arrott-Noakes form of the scaling equation of state and the Kouvel-Fisher definition of the effective susceptibility exponent brought about by these scaling fields. A detailed analysis of the M(T, 0) and χ (T, 0) data for crystalline and amorphous ferromagnets in terms of the theoretical expressions derived in this work reveals that i) in conformity with the theoretical predictions, the ";non-analytic"; corrections to the singular behaviour dominate over the ";analytic"; ones for temperatures in the immediate vicinity of the critical point Tc, whereas reverse is the case for temperatures far away from Tc and (ii) the expression for χ(T, 0), based on the nonlinear scaling arguments, which includes the leading ";analytic"; correction, reproduces closely the observed variation of χ with T over a wide range of temperatures T_c ≤ T ≤ 1.5T_c (in some cases, up to 3T_c) for both ordered as well as quench-disordered ferromagnets.