Dynamics of spin clusters in amorphous Fe₂O₃

Abstract

The dynamic magnetic properties of powdered "x-ray amorphous" Fe₂O₃ sample with mean particle size ~12.0 nm (σ=± 0.36) have been investigated using frequency dependent real part of ac susceptibility Xac' and time dependent dc magnetization studies. A frequency-dependent peak was observed in Xac' vs T measurements. The frequency dependence of the T_p, the temperature at which the maximum in the ac susceptibility curve is observed, is described well by the Vogel-Fulcher law as well as the power law. The fitting with the Vogel-Fulcher law yields the relaxation time constant T₀=5× 10^-8 s and the interaction parameter T₀=34.0± 0.2 K. Whereas, the fitting with the conventional critical slowing-down law, the power law, yields T₀=3.5× 10^-11 s, the freezing temperature τ_g=35.1± 0.1 K and critical exponent zv=5.3± 0.4. The value of τ₀=5× 10^-8 s obtained from the Vogel-Fulcher law fit gives an evidence of the presence of interacting spin clusters in our system and that obtained from the power law fit suggests the freezing of these spin clusters at ~35.1 K. Time dependence of the thermoremanent magnetization (TRM), represented well by the stretched exponential function, supports the presence of relaxing spin clusters with no unique relaxation time. The TRM is found to scale according to T log₁₀(t/τ₀), with T₀=3.5× 10^-11 s.