The invention provides a chemical-mechanical polishing composition comprising (a) an abrasive selected from the group consisting of alumina, ceria, titania, zirconia, and combinations thereof, wherein the abrasive is surface-coated with a copolymer comprising a combination of sulfonic acid monomeric units and carboxylic acid monomeric units a combination of sulfonic acid monomeric units and phosphonic acid monomeric units, (b) an oxidizing agent, and (c) water, wherein the polishing composition has a pH of about 2 to about 5. The invention further provides a method of chemically-mechanically polishing a substrate with the inventive chemical-mechanical polishing composition. Typically, the substrate comprises tungsten or cobalt and silicon oxide.