Criteria for the occurence of ferromagnetism and weak magnetic order in narrow-band metals

Phenomenological correlations between the occurence of different types of magnetic order, the value of the electronic specific heat divided by temperature γ^*, and the shortest distance d between Ce and U atoms in a number of metallic compounds are presented. Ferromagnetism is found to occur over restricted ranges of d and γ^*, and the magnetic ordering temperature T_m and the ordered moment μ_or are maximized for d≈4.0-4.2 Å. "Weak magnetic order", for which μ_or≪0.5μ_B, is found to occur in two distinct regimes: Large values of T_m occur for d less than the "Hill limits" d _H≈3.4 Å (Ce) and 3.5 Å (U), with γ^*≈3.5×10⁴erg cm^-3K^-2, while very low T_m are found in several heavy fermion compounds near d≈4.15 Å and γ^*≈1×10⁵erg cm^-3K^-2. A plot of T_m vs. volume-scaled μ_or implies that metallic 4f, 5f and 3d transition metal materials can be systematically described within a unified picture. The small exchange enhancement of the magnetic susceptibility of heavy fermion compounds and the surprising trend that ferromagnetism occurs in relatively strongly hybridized systems may be explained by the wavevector dependence of the electronic self-energy that is responsible for large effective mass.