Spin Jahn-Teller antiferromagnetism in CoTi$_2$O$_5$

We have used neutron powder diffraction to solve the magnetic structure of orthorhombic CoTi$_2$O$_5$, showing that the long-range ordered state below 26 K identified in our muon-spin rotation experiments is antiferromagnetic with propagation vector ${\bf k}=(\pm \frac{1}{2}, \frac{1}{2}, 0)$ and moment of 2.72(1)$\mu_{\rm B}$ per Co$^{2+}$ ion. This long range magnetic order is incompatible with the experimentally determined crystal structure because the imposed symmetry completely frustrates the exchange coupling. We conclude that the magnetic transition must therefore be associated with a spin Jahn-Teller effect which lowers the structural symmetry and thereby relieves the frustration. These results show that CoTi$_2$O$_5$ is a highly unusual low symmetry material exhibiting a purely spin-driven lattice distortion critical to the establishment of an ordered magnetic ground state.