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Magnetization of antiferromagnetic nanoparticles is known to generally scaleup inversely to their diameter (d) according to N\'eel's model. Here we reporta deviation from this conventional linear 1/d dependence, altered significantlyby the microstrain, in Ca and Ti substituted BiFeO3 nanoparticles. Magneticproperties of microstrain-controlled Bi1-xCaxFe1-yTiyO3-delta (y = 0 and x = y)nanoparticles are analyzed as a function of their size ranging from 18 nm to200 nm. A complex interdependence of doping concentration (x or y), annealingtemperature (T), microstrain (epsilon) and particle size (d) is established.X-ray diffraction studies reveal a linear variation of microstrain with inverseparticle size, 1/d nm-1 (i.e. epsilon.d = 16.5 nm.%). A rapid increase in thesaturation magnetization below a critical size dc ~ 35 nm, exhibiting a(1/d)^alpha (alpha ~ 2.6) dependence, is attributed to the influence ofmicrostrain. We propose an empirical formula M is proportional to(1/d)epsilon^beta (beta ~ 1.6) to highlight the contributions from both thesize and microstrain towards the total magnetization in the doped systems. Themagnetization observed in nanoparticles is thus, a result of competing magneticcontribution from the terminated spin cycloid on the surface and counteractingmicrostrain present at a given size. Large magnetodielectric response of ~ 9.5% is observed in spark plasma sintered pellets with optimal size and dopingconcentration, revealing a strong correlation between magnetic andferroelectric order parameters.

Microstrain induced deviation from N\'eel's 1/d behaviour: Size-dependent magnetization in Bi1-xCaxFe1-yTiyO3-delta nanoparticles