  We report results of a comprehensive study of the phase transition at T_N
(~643 K) as a function of particle size in multiferroic BiFeO3 system. We
employed electrical, thermal, and temperature dependent X-ray diffraction (XRD)
studies in order to characterize the transition in a host of samples. We also
carried out detailed magnetic measurements over a temperature regime 2-300 K
under a magnetic field 100-10000 Oe both on bulk and nano-crystalline systems.
While in the bulk system a sharp endothermic peak at T_N together with a broad
feature, ranging over nearly ~150 K (Delta_T), could be observed in
calorimetry, the nanoscale systems exhibit only the broad feature. The
characteristic dielectric anomaly, expected at T_N, is found to occur both at
T_O and T_N across Delta_T in the bulk sample. The Maxwell-Wagner component due
to interfaces between heterogenous regions with different conductivities is
also present. The magnetic properties, measured at lower temperature,
corroborate our observations in calorimetry. The metastability increases in the
nanoscale BiFeO3 with divergence between zero-field cooled (ZFC) and field
cooled (FC) magnetization below ~100 K and faster magnetic relaxation.
Interestingly, in nanoscale BiFeO3, one also observes finite coercivity at
lower temperature which points out that suitable design of particle size and
shape may induce ferromagnetism. The inhomogeneous distribution of Bi/Fe-ions
and/or oxygen non-stoichiometry seems to be giving rise to broad features in
thermal, magnetic as well as in electrical responses.
