Resistive Anomalies at Magnetic Critical Points

The electrical resistivity associated with spin scattering near magnetic critical points is calculated in the model where conduction electrons interact with another electron system such as d electrons through the spin exchange interaction using the temperature Green's functions and diagram technique. It is shown that the origin of the resistive anomaly near the ferromagnetic critical point is different from that near other critical points such as the antiferromagnetic transition point. In the ferromagnetic case the resistive anomaly arises from scattering associated with the short-range spin fluctuations and consequently the temperature derivative of the resistivity dρ/dT should vary like the magnetic specific heat, as was suggested by Fisher and Langer. On the other hand, in other magnetic cases with periodic magnetic structures such as rare earth metals, resistive anomalies originate from critical scattering due to long-range spin fluctuations around the magnetic lattice vector. In such cases dρ/dT shows that anomaly proportional to -sign(t)|t|-(α+γ-1), as was shown by Suezaki and Mori, where t=(T-Tc)/Tc and α and γ are the critical indices of the specific heat and the magnetic susceptibility respectively. Higher order effects of spin fluctuations are examined and shown to be negligible as far as singularities in ρ are concerned.