Spin evolution of two valence electrons in two separated ions

Synopsis The spin evolution of two spin-1/2 valence electrons, located at two separated ions, is investigated with the help of Breit equation. This evolution that arise solely depends on their dipole-dipole magnetic interaction. Special attention is paid to the effects beyond the leading order of the dipole-dipole magnetic interaction. In contrast to just including the leading order, it is found that the spin-spin interactions flips the spin of both electrons together, while the spin-orbit interactions typically changes the spin of just single electron. As a consequence, different behaviour is observed in the time evolution of two different entangled Bell states.