Berry phase and adiabaticity of a spin diffusing in a nonuniform magnetic field

An electron spin moving adiabatically in a strong, spatially nonuniform mag netic field accumulates a geometric phase or Berry phase, which might be ob servable as a conductance oscillation in a mesoscopic ring. Two contradicti ng theories exist for how strong the magnetic field should be to ensure adi abaticity if the motion is diffusive. To resolve this controversy, we study the effect of a nonuniform magnetic field on the spin polarization and on the weak-localization effect. The diffusion equation for the Cooperon is so lved exactly. Adiabaticity requires that the spin-precession time is short compared to the elastic scattering time-it is not sufficient that it is sho rt compared to the diffusion time around the ring. This strong condition se verely complicates the experimental observation. [S0163-1829(99) 10103-6].