A composite free layer having a FL1/insertion/FL2 configuration is disclosed for achieving high dR/R, low RA, and low λ in TMR or GMR sensors. Ferromagnetic FL1 and FL2 layers have (+) λ and (−) λ values, respectively. FL1 may be CoFe, CoFeB, or alloys thereof with Ni, Ta, Mn, Ti, W, Zr, Hf, Tb, or Nb. FL2 may be CoFe, NiFe, or alloys thereof with Ni, Ta, Mn, Ti, W, Zr, Hf, Tb, Nb, or B. The thin insertion layer includes at least one magnetic element such as Co, Fe, and Ni, and at least one non-magnetic element selected from Ta, Ti, W, Zr, Hf, Nb, Mo, V, Cr, or B. In a TMR stack with a MgO tunnel barrier, dR/R>60%, λ˜1×10−6, and RA=1.2 ohm-um2 when FL1 is CoFe/CoFeB/CoFe, FL2 is CoFe/NiFe/CoFe, and the insertion layer is CoTa or CoFeBTa.