Spin-wave and spin-fluctuation contributions to the magnetoresistance of weak itinerant-electron ferromagnets

The spin-wave and exchange-enhanced spin-density fluctuation contributions to the electrical resistivity, ρ(T), of weak itinerant-electron ferromagnets are calculated in the absence and presence of the magnetic field, H, employing the two-band (s-and d-band) model and the version of spin-fluctuation theory for d-band that makes use of the Ginzburg-Landau formalism. These self-consistent calculations (i) mark a substantial improvement over the previous theoretical treatments in that they completely dispense with the unrealistic electron-gas approximation, (ii) account for the effect of H on the contributions to ρ(T) arising from spin waves (spin-density fluctuations) at low temperatures (at intermediate temperatures and for temperatures close to the Curie point, TC), and (iii) regardless of the nature of the low-lying magnetic excitations that dominantly contribute to the negative magnetoresistance, Δρ/ρ, in different temperature ranges, yield analytical expressions that basically have a simple general form Δρ/ρ=1-[ρ(T,H) /ρ(T,H=0)]∼ aH-bH2. The expressions, so obtained, not only permit a quantitative determination of the suppression of spin waves and spin fluctuations by the magnetic field, H, in weakly ferromagnetic metals from the magnetoresistance data but are also capable of yielding useful information about the band structure