Theory of the spin depolarisation rate of μ+ SR in pure Fe

The diffusion constant (D) and the spin depolarisation rate (λ_S) of the positive muon in the ferromagnetic b.c.c. lattices such as Fe have been calculated on the basis of the small polaron (SP) model with particular attention to the hopping and the coherent motions. They have been obtained in the forms: $\text{D=}\text{d}{}^2\text{w}{}_{\mathrm{D}}\text{6}$ and $\text{λ}{}_{\mathrm{S}}\text{=}\text{4γ}{}^2{}_{\mathrm{\mu }}\text{H}{}^2{}_{\mathrm{d}}\text{3w}{}_{\mathrm{S}}$, where d is a jump length, and H_d is a magnitude of internal dipolar field. At high temperatures, the activated-type hopping motion gives a dominant contribution to w_D, and w_S coincides with w_D. With decreasing temperature, w_D turns to be increasing owing to the coherent motion. Whereas w_S deviates from w_D, after passing the minimum, to have a maximum, and then decreases in inverse proportion to a lifetime (_B) of the SP band states. Because of the cell periodicity of the internal fields, the spin in an SP band state feels a definite magnetic field corresponding to the state, and sees various fields if scattered to other states. These scattering processes succeeding in a time shorter than (γ_μH_d)^-1 result in the motional narrowing of the spectra, with λ_{S ?} γ²_μH_d_B.