Ferromagnetic resonance study of magnetic order-disorder phase transition in amorphous Fe_90-xCo_xZr₁₀ alloys

The utility of the ferromagnetic-resonance (FMR) technique to determine accurately the spontaneous magnetization and initial susceptibility critical exponents β and γ, which characterize the ferromagnetic (FM) -paramagnetic (PM) phase transition at the Curie temperature T_C for ferromagnetic materials is demonstrated through a detailed comparative study on amorphous Fe₉₀Zr₁₀ alloy, which involves bulk magnetization and FMR measurements performed on the same sample in the critical region. Magnetization data deduced from the FMR measurements taken on amorphous Fe_90-xCo_xZr₁₀ alloys with x=0, 1, 2, 4, 6, and 8 in the critical region satisfy the magnetic equation of state characteristic of a second-order phase transition. Contrary to the anomalously large values of the exponents β and γ reported earlier, the present values, β=0.38±0.03 and γ=1.38±0.06, are composition-independent and match very well the three-dimensional Heisenberg values. The fraction of spins that actually participates in the FM-PM phase transition, c, is found to increase with the Co concentration as c(x)-c(0)≃ax² and possess a small value of 11% for the alloy with x=0. The ‘‘peak-to-peak’’ FMR linewidth (ΔH_pp) varies with temperature in accordance with the empirical relation ΔH_pp(T)=ΔH(0)+[A/M_s(T)], where M_s is the saturation magnetization. Both the Landé splitting factor g as well as the Gilbert damping parameter λ are independent of temperature, but, with increasing Co concentration (x), λ decreases slowly while g stays constant at a value 2.07±0.02.