A magnetic detection element capable of maintaining the .DELTA.RA at a
high level and reducing the magnetostriction by improving a material for
a free magnetic layer, as well as a method for manufacturing the same, is
provided. The free magnetic layer includes a laminate composed of a CoMnX
alloy layer formed from a metal compound represented by a compositional
formula Co.sub.aMn.sub.bX.sub.c (where X represents at least one of Ge,
Ga, In, Si, Pb, Zn, and Sb and a+b+c=100 atomic percent) and a CoMnZ
alloy layer formed from a metal compound represented by a compositional
formula Co.sub.dMn.sub.eZ.sub.f (where Z represents at least one of Sn
and Al and d+e+f=100 atomic percent). In this manner, the
magnetostriction of the free magnetic layer can be reduced.