Invalidity Of A Localized Spin Mechanism For $SrRuO3$ and $CaRuO3$

We have calculated the electronic structure for $CaRuO3$ and $SrRuO3$ within first principles electronic structure calculations. We find that the experimentally observed ferromagnetic state is favoured in the case of $SrRuO3,$ while our calculations also suggest that no state with long range magnetic order will be stabilised for $CaRuO3.$ Mapping the total energies for different magnetic configurations to an extended Heisenberg model, we find that a localized spin model is found to be invalid to describe the magnetic state of these systems.