The invention comprises a novel composite multi-stack seed layer (CMSL) having lattice constant matched crystalline structure with the Co layer in above perpendicular magnetic pinning layer (pMPL) so that an excellent epitaxial growth of magnetic super lattice pinning layer [Co/(Pt, Pd or Ni)]n along its FCC (111) orientation can be achieved, resulting in a significant enhancement of perpendicular magnetic anisotropy (PMA) for perpendicular spin-transfer-torque magnetic-random-access memory (pSTT-MRAM) using perpendicular magnetoresistive elements as basic memory cells which potentially replace the conventional semiconductor memory used in electronic chips, especially mobile chips for power saving and non-volatility.