New superexchange paths due to breathing-enhanced hopping in corner-sharing cuprates

We present ab initio calculations of the superexchange antiferromagnetic spin coupling $J$ for two cuprates, Sr$_2$CuO$_3$ and La$_2$CuO$_4$. Good agreement with experimental estimates is obtained. We find that $J$ increases substantially as the distance between Cu and apical O is increased. There is an important synergetic effect of the Coulomb interaction, expanding the Cu $3d$ orbital when an electron hops into this orbital, and the O-Cu hopping, being increased by this orbital expansion (breathing). This is a new ingredient in superexchange models. In a model with a fixed basis, breathing effects can be described as a mixing of $3d$ and $4d$ orbitals or as a single $3d \to 4d$ excitation.