  Magnetization of antiferromagnetic nanoparticles is known to generally scale
up inversely to their diameter (d) according to N\'eel's model. Here we report
a deviation from this conventional linear 1/d dependence, altered significantly
by the microstrain, in Ca and Ti substituted BiFeO3 nanoparticles. Magnetic
properties 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 to
200 nm. A complex interdependence of doping concentration (x or y), annealing
temperature (T), microstrain (epsilon) and particle size (d) is established.
X-ray diffraction studies reveal a linear variation of microstrain with inverse
particle size, 1/d nm-1 (i.e. epsilon.d = 16.5 nm.%). A rapid increase in the
saturation magnetization below a critical size dc ~ 35 nm, exhibiting a
(1/d)^alpha (alpha ~ 2.6) dependence, is attributed to the influence of
microstrain. We propose an empirical formula M is proportional to
(1/d)epsilon^beta (beta ~ 1.6) to highlight the contributions from both the
size and microstrain towards the total magnetization in the doped systems. The
magnetization observed in nanoparticles is thus, a result of competing magnetic
contribution from the terminated spin cycloid on the surface and counteracting
microstrain present at a given size. Large magnetodielectric response of ~ 9.5
% is observed in spark plasma sintered pellets with optimal size and doping
concentration, revealing a strong correlation between magnetic and
ferroelectric order parameters.
