In one embodiment, a method for etching a workpiece including a lower electrode and a multi-layer film disposed on the lower electrode, the multi-layer film including a first magnetic layer, a second magnetic layer, and an insulating layer interposed between the first magnetic layer and the second magnetic layer, through a mask, is provided. The method includes exposing the workpiece to plasma of first processing gas which contains first rare gas and second rare gas having an atomic number larger than that of the first rare gas, and does not contain hydrogen gas.