Negative capacitance switching in size-modulated Fe₃O₄ nanoparticles with spontaneous non-stoichiometry: confronting...

Persistent low-frequency negative capacitance (NC) dispersion has been detected in half-metallic polycrystalline magnetite (Fe3O4) nanoparticles with varying sizes from 13 to 236 nm under the application of moderate dc bias. Using the Havriliak-Negami model, 3D Cole-Cole plots were employed to recapitulate the relaxation times (τ) of the associated oscillating dipoles, related shape parameters (α, β) and resistivity for the nanoparticles with different sizes. The universal Debye relaxation (UDR) theory requires a modification to address the shifted quasi-static NC-dispersion plane in materials showing both +ve and -ve capacitances about a transition/switching frequency (f0). A consistent blue-shift in 'f0' is observed with increasing external dc field and decreasing particle size. Based on this experimental data, a generalized dispersion scheme is proposed to fit the entire positive and negative capacitance regime, including the diverging transition point. In addition, a comprehensive model is discussed using phasor diagrams to differentiate the underlying mechanisms of the continuous transition from -ve to +ve capacitance involving localized charge recombination or time-dependent injection/displacement currents, which has been adequately explored in the scientific literature, and the newly proposed 'capacitive switching' phenomenon. An inherent non-stoichiometry due to iron vacancies [Fe3(1-δ)O4], duly validated from first principles calculations, builds up p-type nature, which consequently promotes more covalent and heavier dipoles and slows the dipolar relaxations; this is incommensurate with Maxwell-Wagner interfacial polarization (MWIP) dynamics. This combinatorial effect is likely responsible for the sluggish response of the associated dipoles and the stabilization of NC.