  We report the magnetostrictive length changes of CoTiO$_3$ studied by means
of high-resolution dilatometry in magnetic fields ($B$) up to 15~T. In the
long-range antiferromagnetically ordered phase below $T_N$ = 38~K, the
easy-plane type spin structure undergoes a spin-reorientation transition in the
$ab$ plane in magnetic fields $B || ab \approx 2$~T. We observe pronounced
length changes driven by external magnetic field in this field region
indicating significant magnetoelastic coupling in CoTiO$_3$. Specifically, we
observe anisotropic deformation of the lattice for fields applied in the $ab$
plane. While, for $B \lesssim 2$~T, in-plane magnetostriction shows that the
lattice expands (contracts) parallel (perpendicular) to the field direction,
the opposite behaviour appear at higher fields. Furthermore, there are
remarkable effects of slight changes in the applied uniaxial pressure on the
magnetostrictive response of CoTiO$_3$ persisting to temperatures well above
$T_N$. The data evidence the presence of magnetic domains below $T_N$ as well
as of structural ones in CoTiO$_3$. The presence of magnetic domains in the
spin ordered phase is further evidenced by an additional 3-fold magnetic
anisotropy appearing below $T_N$. We discuss the effects of rotational magnetic
domains on isothermal magnetization and magnetostriction and interpret our
results on the basis of a multi-domain phenomenological model.
