  The role of electron-phonon scattering in finite-temperature anomalous Hall
effect is still poorly understood. In this work, we present a Boltzmann theory
for the side-jump contribution from electron-phonon scattering, which is
derived from the microscopic quantum mechanical theory. We show that the
resulting phonon side-jump conductivity generally approaches different limiting
values in the high and low temperature limits, and hence can exhibit strong
temperature dependence in the intermediate temperature regime. Our theory is
amenable to ab initio treatment, which makes quantitative comparison between
theoretical and experimental results possible.
