Fundamental and harmonic magneto-dielectricity studied for varied perovskite systems-- Pb0.98Gd0.02(Mg1/3Nb2/3)0.995O3 (A-site co-doped PGMN magneto-relaxor), La0.95Ca0.05CoO3 (A-site doped spin-state LCCO), and La2NiMnO6 (double-perovskite LNMO multiglass) characterize intricately polarized phases. First-harmonic signal ({epsilon}2) of magnetically co-doped PGMN manifests finite polarization P(H) below 270K, corroborated by the measured remnant P-E traces. Second-harmonic ({epsilon}3) reveals the effect of random E-fields causing electrical vitreousity, latter indicated by the divergent timescale of the fundamental response. LCCO features mixed-dipoles phase over appreciable temperature window, affiliated to the coexistent low-spins (LS) and intermediate-spins (IS). Across the 65K-start of IS-to-LS state transition (SST), dc- and ac-conductivities of LCCO exhibit mechanism-changeovers whereas the harmonic susceptibilities evidence IS/LS-interfacial hyper-polarizations. Below the 30K-end of SST, harmonics corroborate the vitreous phase of dipoles in the LS-matrix state. In the LNMO, positive and negative (dual) magneto-dielectricity observed is respectively attributed to the charge-hopping between Ni2+ and Mn4+ ions and the interfacial polarization. Second-harmonic signal here also features dispersion corresponding to the activation energy required for the electron transfer between Ni- and Mn-cations. Results from three different perovskite systems signify the combined importance of first- and second-harmonics, for a detailed understanding of electrical configurations.
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