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In this study, we investigated hierarchical microarchitecture formation of magnetic barium hexaferrite (BF) platelets inside the polydimethylsiloxane (PDMS) matrix using electric and magnetic field colloidal assembly technique. First, external fields were applied to the colloidal solution to form the microstructure before curing the composites. After microstructure formation the composites were cured to freeze the microstructure by the application of heat. We investigated two different cases in this study-(1) magnetic field processed composites and (2) multi-field processed composites which were processed under both magnetic and electric field. We observed that macro-chains formed due to the electric and magnetic field had much higher length compared to the macro-chains formed due to the just magnetic field. For both cases individuals BHF are found to be oriented in the direction of external field. The analysis of SEM microstructures using ImageJ and MATLAB showed that at least two different level of hierarchies are present in the microstructure for both cases which can be named as BHF stacks and micro-chains. From the microstructure analysis, we found that compared to just magnetic field processed composites, the orientation of individual particles, BHF stacks and micro-chains in relation to the external field were found to be higher for the multi-field processed composites. Magneto-electro-hydrodynamics modeling of the polymer-particulate mixture predicted similar behavior. Computational simulations were performed wherein particulates, subjected to both DEP forces and additional magnetic dipole interactions, were allowed to form quasi-equilibrium structures before locking in a final structure to represent curing. Results show that dielectrophoretic (DEP) force produced from the local non-uniform electric field facilitates the translation of the platelets towards formation of chain-like structure, while external magnetic field augmented the rotation of particles inside the chain-like structure. Analysis of the simulation of microstructures confirms that multiple level of hierarchies are present in the composites microstructure for both cases, while the case with both electric and magnetic fields produced longer chains. The understanding of the hierarchical microstructure formation using the multi-field processing technique will help in the future to fabricate more complex microarchitectures with resulting multi-material properties.