  Magnetism of oxide antiferromagnets (AFMs) has been studied in single
crystals and extended thin films. The properties of AFM nanostructures still
remain underexplored. Here, we report on the fabrication and magnetic imaging
of granular 100-nm-thick magnetoelectric Cr$_2$O$_3$ films patterned in
circular bits with diameters ranging from 500 down to 100 nm. With the change
of the lateral size, the domain structure evolves from a multidomain state for
larger bits to a single domain state for the smallest bits. Based on
spin-lattice simulations, we show that the physics of the domain pattern
formation in granular AFM bits is primarily determined by the energy
dissipation upon cooling, which results in motion and expelling of AFM domain
walls of the bit. Our results provide a way towards the fabrication of single
domain AFM-bit-patterned memory devices and the exploration of the interplay
between AFM nanostructures and their geometric shape.
