The bilayer ruthenate Sr$_{3}$Ru$_{2}$O$_{6}$ an hypothetical electrically anisotropic compound*

The bilayer ruthenate Sr$_{3}$Ru$_{2}$O$_{7}$ depending on its preparation it can be ferromagnetic or paramagnetic. In this study the hypothetical compound; Sr$_{3}$Ru$_{2}$O$_{6}$ is studied with quantum-mechanical calculations using the WIEN2k package. This compound is obtained from Sr$_{3}$Ru$_{2}$O$_{7}$ by removing an oxygen atom, then the unit cell is relaxed both in its internal atom positions and the cell dimensions. Before relaxation Sr$_{3}$Ru$_{2}$O$_{6}$ is weakly ferromagnetic, while after relaxation it becomes strongly antiferromagnetic. The parent compound, Sr$_{3}$Ru$_{2}$O$_{7}$, is electrically anisotropic, conducting mainly in the ab plane and Sr$_{3}$Ru$_{2}$O$_{6}$ is much more anisotropic. The electronic structure and magnetic calculations will be presented