  Antiferromagnets have recently been propelled to the forefront of spintronics
by their high potential for revolutionizing memory technologies. For this,
understanding the formation and driving mechanisms of the domain structure is
paramount. In this work, we investigate the domain structure in a thin-film
canted antiferromagnet $\alpha$-Fe$_2$O$_3$. We find that the internal
destressing fields driving the formation of domains do not follow the crystal
symmetry of $\alpha$-Fe$_2$O$_3$, but fluctuate due to substrate clamping. This
leads to an overall isotropic distribution of the N\'eel order with locally
varying effective anisotropy in antiferromagnetic thin films. Furthermore, we
show that the weak ferromagnetic nature of $\alpha$-Fe$_2$O$_3$ leads to a
qualitatively different dependence on magnetic field compared to collinear
antiferromagnets such as NiO. The insights gained from our work serve as a
foundation for further studies of electrical and optical manipulation of the
domain structure of antiferromagnetic thin films.
