Adiabatically induced orbital magnetization

A semiclassical theory for the orbital magnetization due to adiabatic evolutions of Bloch electronic states is proposed. It renders a unified periodic-evolution pumped and magnetoelectric response in insulators by revealing that these two phenomena are only instances where induced gauge invariant. This also accounts electric-field-induced intrinsic two-dimensional metals Chern insulators. We illustrate microscopic local rotations atoms, which correspond phonon modes with angular momentum, toy models based on honeycomb lattice, results comparable spin via strong Rashba spin-orbit coupling. show vital role magnetoelectricity validating Mott relation between nonlinear anomalous Hall Ettingshausen effects.