A process for chemical mechanical polishing a substrate containing cobalt, zirconium oxide, poly-silicon and silicon dioxide, wherein the cobalt, zirconium, and poly-silicon removal rates are selective over silicon dioxide. The chemical mechanical polishing composition includes water, a benzyltrialkyl quaternary ammonium compound, cobalt chelating agent, corrosion inhibitor, colloidal silica abrasive, optionally a biocide and optionally a pH adjusting agent, and a pH greater than 7, and the chemical mechanical polishing compositions are free of oxidizing agents.