Real-space fluctuations of effective exchange integrals in high-Tc cuprates

We present ab-initio calculations of effective magnetic exchange, $J$, as well as Hubbard parameters ($t$, $U$ and $\delta \varepsilon$) as a function of the local distribution of doping atoms for the high-$T_c$ superconducting $\rm (Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_3O_y$ family. We found that both the exchange and the energies of the magnetic orbitals are strongly dependant on the local dopant distribution, both through the induced modification of the apical oxygen location and of the induced local electrostatic potential. The $J$ real-space map, for a random distribution of dopants, positively compares with observed STS gap inhomogeneity maps. Similarly, the orbital energy fluctuations induce weak charge inhomogeneities on copper sites, that can be positively compared with the observed LDOS inhomogeneities. These results clearly support an extrinsic origin of both the gap inhomogeneities and LDOS.