Regular magnetic domain pattern in TbNi$_{2}$B$_{2}$C due to strong magneto-elastic coupling

$R$Ni$_{2}$B$_{2}$C compounds are of strong interest due to the competition between superconductivity and magnetism. The crystal electric field effects yield strong magnetoelastic effects. The strongest tetragonal-to-orthorhombic distortion is observed for TbNi$_{2}$B$_{2}$C with a relative distortion of 0.6 {\%} in the antiferromagnetic state at 1.5 K. The lowering of the symmetry forces the development of domains of two forms, in which the magnetic moment direction are align along the a or b axis, respectively. For both kind of domains, the lattice distortion is opposite in the ab plane. We investigated the resulting domain using scattering techniques. Temperature-dependent topographic x-ray images show that the domains are very large in (110) directions where as they are very narrow in the direction perpendicular in the ab plane. In X-ray and neutron diffraction sattelite reflections are found, which are produced by the regular pattern of domains with dimensions of 10 nm. A model describing this pattern and consequences for magnetic and superconducting properties will be discussed.