A perpendicular magnetoresistive element includes a novel recording layer being a multi-layer comprising a first Co-alloy layer including at least one of CoFeB, CoFeB/CoFe and CoFe/CoFeB, a second Co-alloy layer including at least one of CoFeB and CoB, an insertion layer provided between the first Co-alloy layer and the second Co-alloy layer and containing at least one element selected from Zr, Nb, W, Mo, Ru and having a thickness less than 0.5 nm, and a novel buffer layer having rocksalt crystal structure(s) interfacing to the recording layer with lattice parameter mismatch between 3% and 18%. The magnetoresistive element is annealed at an elevated temperature and both the first Co-alloy layer and the second Co-alloy layer are crystallized to form body-center cubic (bcc) CoFe or bcc Co grain having epitaxial growth with (100) plane parallel to substrate and with in-plane expansion and out-of-plane contraction.