Change of orbital ordering in Fe3O4 probed through low frequency-low magnetic field magnetoimpedance effect mediated by magnetic inhomogeneity

Fe ₃O ₄ is a fascinating material due to its charge localization physics, variable range hopping (VRH) and its potential implications in the field of spintronics. In this investigation, we explore the formation and interaction of charge-ordered clusters and change of orbital order in cold-pressed Fe ₃O ₄ , employing a comprehensive magnetoimpedance analysis in the low-frequency, low magnetic field domain spanning the Verwey transition. The physical and magnetic inhomogeneities due to particle size distribution and capacitive interparticle contact, are found to induce a substantial dispersion in the impedance response. Exploiting the variation in relaxation time as a function of temperature and magnetic field, we meticulously monitor the reorientation of orbitals and the consolidation of charge-ordered clusters, a consequence of localization phenomena. The shielding and deshielding of charge-ordered clusters are interpreted through AC magnetoresistance, which exhibits a sign inversion from negative to positive, synchronous with the dissolution of the charge order. The AC magnetoresistance showed the interaction of clusters of ‘charge -ion order’ in the higher and lower frequency regimes. This study reveals the chage of orbital order at around 39 K and 150 K along with the one at 120 K due to change in relaxation time associated with the impedance responce mediated by magbetic inhomogenity. Notably, across the studied frequency range, the charge conduction mechanism remains consistent, as elucidated by a variable range hopping model. Our study demonstrates that Fe ₃O ₄ nanoparticles exhibit a complex interplay of charge ordering and magnetic ordering, with implications for understanding the electrical properties of such materials. This research provides insight into the charge conduction processes and its coupling to change of orbital ordering in Fe ₃O ₄, a material of considerable interest for its promising electronic applications.