Magnon-induced interband spin-flip scattering contribution to resistivity and magnetoresistance in a nanocrystalline itinerant-electron ferromagnet: Effect of crystallite size

We report the results of an exhaustive study of `zero-field' electrical resistivity ρ(T) and magnetoresistance (MR) (in magnetic fields up to 90 kOe) over the temperature range 1.8--300 K in nanocrystalline (nc-) Ni with average crystallite size d ranging from 10 nm to 40 nm. A quantitative comparison of our results with the predictions of the recent self-consistent calculations permits us to unambiguously identify the scattering mechanisms responsible for ρ(T) and MR in different temperature ranges and accurately determine their relative magnitudes in nc-Ni samples of different d. Like in bulk $3d$ transition metal ferromagnets, ρ varies with temperature as T² at T15 K. Contrary to the widely-held view that the T² variation of ρ at low temperatures arises from the electron-magnon (e-m) scattering, this contribution to ρ(T) is shown to originate from the electron-electron (Baber) scattering. In the temperature range 154.pt0exK≤T≤300 K, the phonon-induced non-spin-flip (NSF) intraband [i.e., s^↑↓-0.16em0exs^↑↓, d^↑↓-0.16em0exd^↑↓ electron-phonon (e-p)] scattering and magnon-induced spin-flip (SF) interband (i.e., s^↑↓-0.16em0exd^↓↑4pt0exe-m) scattering contributions completely account for the intrinsic resistivity. The former contribution dominates over the latter at T>T^ whereas the reverse is true at temperatures 15 K ≤0.16em0exT<T^. T^, the temperature at which the SF interband e-m and NSF intraband e-p scattering contributions become equal, increases from ~30 K for d=100.28em0exnm to ~650.28em0exK for bulk Ni. At T>T^, ρ_e-m(T,H=0) becomes comparable in magnitude to ρ_e-p(T,H=0) for d≥25 nm. By contrast, the MR in nc-Ni is entirely due to the s^↑↓-0.16em0exd^↓↑4pt0exe-m scattering. The present work clearly brings out the importance of the thermal renormalization of magnon mass (caused mainly by the magnon-magnon interactions) over the temperature range 154.pt0exK≤T≤300 K. Irrespective of the value of d (including the bulk, d=∞), phonon-induced s^↑↓-0.16em0exs^↑↓, d^↑↓-0.16em0exd^↑↓ transitions are more frequent than the e-p4pt0exs^↑↓-0.16em0exd^↑↓ transitions over the entire temperature range 1.84.pt0exK≤T≤300 K. The saturation magnetization at 0 K, spin wave stiffness at 0 K, Debye temperature as well as the parameters that are a direct measure of the strength of e-p coupling, e-m coupling, and level of suppression of e-m scattering by external magnetic field, all exhibit power law variations with d. The power law behavior asserts that the average crystallite size is the dominant length scale so far as the magnetism, electrical transport, and magnetotransport in nc-Ni are concerned.