The patterning of multilayer thin-film stacks to create spin valves, with dimensions similar to 100 nm, for magnetic-random-access memories presents novel fabrication challenges since the materials commonly used (e.g., Co, Cu, and Ni) do not form volatile compounds, and hence cannot be reactive-ion etched. The consequent necessity of using ion-beam etching (''ion milling'') demands a solution to the twin problems of faceting and redepostion of sputtered material. In addition, antireflection layers are not used during lithography because of the necessity of avoiding high-temperature curing, which would harm the spin valve characteristics. By using a thin SiOx phase-shifting layer under the resist, we obtained adequate resist profiles; and by using a 15-nm-thick W hard mask, no measurable redeposition was observed after ion milling of cobalt. Improved etch selectivity of W relative to Co is achieved by using neon as the ion-milling gas rather than argon. A simple model for the enhanced ion-milling selectivity is presented.