  Bismuth ferrite (BiFeO3) is one of the most promising multiferroics with a
sufficiently high ferroelectric (FE) and antiferromagnetic transition
temperatures, and magnetoelectric (ME) coupling coefficient at room
temperature, and thus it is highly sensitive to the impact of cross-influence
of applied electric and magnetic fields. According to the urgent demands of
nanotechnology miniaturization for ultra-high density data storage in advanced
nonvolatile memory cells, it is very important to reduce the sizes of
multiferroic nanoparticles in the self-assembled arrays without serious
deterioration of their properties. We study size effects of the phase diagrams,
FE and ME properties of semi-ellipsoidal BiFeO3 nanoparticles clamped to a
rigid conductive substrate. The spatial distribution of the spontaneous
polarization vector inside the nanoparticles, phase diagrams and
paramagnetoelectric (PME) coefficient were calculated in the framework of
modified Landau-Ginzburg-Devonshire (LGD) approach. Analytical expressions were
derived for the dependences of the FE transition temperature, average
polarization, linear dielectric susceptibility and PME coefficient on the
particle sizes for a general case of a semi-ellipsoidal nanoparticles with
three different semi-axes a, b and height c. The analyses of the obtained
results leads to the conclusion that the size effect of the phase diagrams,
spontaneous polarization and PME coefficient is rather sensitive to the
particle sizes aspect ratio in the polarization direction, and less sensitive
to the absolute values of the sizes per se.
