Stacks of high temperature superconducting tape, magnetized using pulsed fields, provide a new type of permanent magnet using superconductors. To optimise the trapped field in such stacks, the role of stabilization layers was investigated by pulse magnetizing a 12 mm square stack of 15 tape layers over a temperature range of 15 – 77 K. The stacks consisted of commercial tape with a silver stabilizer of 1 – 3 µm or tape with an additional 20 µm layer of copper on top of 1 µm of silver. It was found that the trapped field and flux are relatively insensitive to the stabilizer thickness, and 1 µm of silver only, led to the highest trapped field. An FEM model was also developed for a stack that considered for the first time both the actual thickness of metallic and superconducting layers, to investigate the effect of heating and heat transfer when a stack of tapes is magnetized.