A magnetic fiber comprises a core comprising a spinel ferrite of formula Me1-xMxFeyO4, wherein Me is Mg, Mn, Fe, Co, Ni, Cu, Zn, or a combination thereof, x=0 to 0.25, and y=1.5 to 2.5, wherein the core is solid or at least partially hollow; and a shell at least partially surrounding the core, and comprising a Me1-xMxFey alloy, wherein when the core is solid with Me=Ni and x=0 the magnetic fiber has a diameter of greater than 0.3 micrometer. A magneto-dielectric material having a magnetic loss tangent of less than or equal to 0.03 at 1 GHz comprises a polymer matrix; and a plurality of the magnetic fibers.