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We report a detailed single-crystal and powder neutron diffraction study of Co2TiO4 and Co2SnO4 between the temperatures 1.6 K and 80 K to probe their spin structures in the ground state. For both compounds the strongest magnetic intensity was observed for the (111)M reflection due to ferrimagnetic ordering, which sets in below TN = 48.6 K and 41 K for Co2TiO4 and Co2SnO4, respectively. An additional low intensity magnetic reflection (200)M was noticed in Co2TiO4 due to the presence of an additional weak antiferromagnetic component. Interestingly, from both the powder and the single-crystal neutron data of Co2TiO4 we noticed a significant broadening of the magnetic (111)M reflection, possibly results from the disordered character of the Ti and Co atoms on the B site. Practically, the same peak broadening was found for the neutron powder data of Co2SnO4. On the other hand, from our single-crystal neutron diffraction data of Co2TiO4 we found a spontaneous increase of particular nuclear Bragg reflections below the magnetic ordering temperature. Our data analysis showed that this unusual effect can be ascribed to the presence of anisotropic extinction, which is associated to a change of the mosaicity of the crystal. In this case it can be expected that competing Jahn-Teller effects act along different crystallographic axes can induce anisotropic local strain. In fact, for both ions Ti 3+ and Co 3+ the 2tg levels split into a lower dxy level and yields a higher two-fold degenerate dxz/dyz level. As a consequence, one can expect a tetragonal distortion in Co2TiO4 with c/a < 1, which could not significantly detected in the present work.

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