On Aharonov-Bohm oscillation in a ferromagnetic ring
Aharonov-Bohm effect in a ferromagnetic thin ring in diffusive regime is theoretically studied by calculating the Cooperon and Diffuson. In addition to the spin-orbit interaction, we include the spin-wave excitation and the spin splitting, which are expected to be dominant sources of dephasing in ferromagnets at low temperatures. The spin splitting turns out to kill the spin-flip channel of Cooperon but leaves the spin-conserving channel untouched. For the experimental confirmation of interference effect (described by Cooperons) such as weak localization and Aharonov-Bohm oscillation with period $h/2e$, we need to suppress the dominant dephasing by orbital motion. To do this we propose experiments on a thin film or thin ring with magnetization and external field perpendicular to the film, in which case the effective field inside the sample is equal to the external field (magnetization does not add up). The field is first applied strong enough to saturate the magnetization and then carrying out the measurement down to zero field keeping the magnetization nearly saturated, in order to avoid domain formations (negative fields may also be investigated if the coercive field is large enough).