Embodiments of the present disclosure are directed to an Fe-based amorphous magnetic alloy and method that includes 4 at. % or less of a low temperature annealing-enabling element M and 10 at. % or less of nickel (Ni). The total amount of the low temperature annealing-enabling element M and nickel (Ni) may be 2 at. % or more and 10 at. % or less.