(color online) (a) Schematic diagram of the superexchange and inter-orbital spin-exchange interactions at unit-filling of the e atoms. (b) Time evolution of spin imbalance N_gz (black solid). The envelopes of at unit-filling (red solid) and half-filling (blue dashed) have been shown. and are the collapse and revival periods, respectively. The parameters are , , . The envelope (red solid) is . The collapse and revival happen at and , respectively. (c) Energy levels in the low-energy effective Hamiltonian (left) and the eigenstates (right). . and are the coupling matrix elements. is the energy shift. The red solid and blue dashed arrows indicate the near-resonant and far-off-resonant couplings, respectively.