  Single crystal neutron diffraction reveals two distinct components to the
magnetic ordering in geometrically frustrated SrEr$_2$O$_4$. One component is a
long-range ordered ${\bf k}=0$ structure which appears below $T_N = 0.75$ K.
Another component is a short-range incommensurate structure which manifests
itself by the presence of a strong diffuse scattering signal. On cooling from
higher temperatures down to 0.06 K, the partially ordered component does not
undergo a pronounced phase transition. The magnetic moments in the long-range
commensurate and short-range incommensurate structures are predominantly
pointing along the [001] and [100] axes respectively. The unusual coexistence
of two magnetic structures is probed using both unpolarised and XYZ-polarised
neutron scattering techniques. The observed diffuse scattering pattern can be
satisfactorily reproduced with a classical Monte Carlo simulation by using a
simple model based on a ladder of triangles.
