Impedance spectroscopy and scaling behaviors of Sr₃Co₂Fe₂₄O₄₁ hexaferrite

The impedance spectroscopy of Z-type hexaferrite Sr₃Co₂Fe₂₄O₄₁ (SCFO) has been investigated as a function of temperature from 303 to 503 K. The frequency dependent impedance (Z ″) and modulus (M ″) spectra show that for the air annealed SCFO, the electrical responses of SCFO are thermal activated and there is a distribution of relaxation times. The scaling behaviors of Z ″ and M ″ spectra further suggest that the distribution of relaxation times is temperature independent. The Cole-Cole plots in impedance formalism show that the electrical response of SCFO originates from both the grain and the grain-boundaries. The activation energies for grain and grain boundary are 0.66 eV and 0.67 eV, respectively. The frequency dependent conductivity (σ ′) spectra follow the universal power law. The fitting results of σ ′ spectra show that the small polaron hopping is the most probable conduction mechanism for SCFO. Moreover, the scaling behavior of σ ′ spectra further confirms that the distribution of local electrical response times is temperature independent. The air plus O₂ annealed SCFO shows thermally activated electrical responses and scaling behaviors as well. The above results show that although the electrical responses of SCFO are temperature dependent, the relaxation mechanism in SCFO is temperature independent.