A method of making a magnetic alloy material includes the steps of: preparing a melt of an alloy material having a predetermined composition; rapidly cooling and solidifying the melt to obtain a rapidly solidified alloy represented by: Fe100-a-b-cREaAbTMc where RE is at least one rare-earth element selected from La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er and Tm and including at least about 90 at % of La; A is at least one element selected from Al, Si, Ga, Ge and Sn; TM is at least one transition metal element selected from Sc, Ti, V, Cr, Mn, Co, Ni, Cu and Zn; and 5 at %≦a≦10 at %, 4.7 at %≦b≦18 at % and 0 at %≦c≦9 at %; and producing a compound phase having an NaZn13-type crystal structure in at least about 70 vol % of the rapidly solidified alloy.