Research at the Laboratory of Crystallography
Incommensurate order in the low-dimensional quantum magnets TiOCl and TiOBr
TiOCl and TiOBr are isostructural compounds that exhibit quasi-one-dimensional (1D) magnetic behavior with S = 1/2 magnetic moments on the Ti atoms. Below Tc1 = 67 K (TiOCl) or Tc1 = 27 K (TiOBr) both compounds are in a spin-Peierls state . The spin-Peierls state is characterised by a pairing of the spins of electrons on neighbouring atoms, accompanied by a dimerisation of the crystal lattice. The result is a state with complete magnetic order (zero value for the magnetic susceptibility).
At the Laboratory of Crystallography we have measured temperature dependent X-ray diffraction with synchrotron X-ray radiation at Hasylab in Hamburg. The known room-temperature structure could be confirmed (Fig. 1), but below Tc1 superlattice reflections have been discovered, that indicate a twofold superstructure. Refinements of the superstructures at T = 20 K show both compounds to be isostructural at low temperatures. Atomic displacements (arrows in Fig. 2) have been found to indicate a spin-Peierls state, that is the result of direct exchange interactions between electrons on the chains of Ti atoms parallel the crystallographic b axis [2,3].
Fig. 1: Perspective view of one layer of the crystal structure of TiOBr. Crystallographically independent atoms are indicated by numbers. Different but symmetry equivalent atoms are indicated by superscripts i and ii. The unit cell axes a and c are indicated.
Fig. 2: One ribbon of TiOBr parallel b and c, containing a chain of Ti atoms; The displacements in the superstructure are given by arrows (20 x the true values).
For temperatures between Tc1 = 27 K and Tc2 = 47 K we have discovered incommensurate satellite reflections in the diffraction of TiOBr (Fig. 3). The existence of an incommensurately modulated crystal structure provides an explanation for the first-order character of the phase transition at Tc1. Refinements of the incommensurate crystal structure show that the transition at Tc1 is the result of a competition between the spin-Peierls state (1D interactions) and a state of 2D magnetic order, thus resulting in an incommensurate superstructure .
Fig. 3: Q-scans along a* centered on (-2, -3.5, -1). Open circles (data at T=17.5 K) indicate a twofold superstructure. Full circles (data at T = 37 K) show a pair of incommensurate satellite reflections. Lines are a guide for the eye.
Fig. 4: Incommensurately modulated structure of TiOBr at T = 37 K. One double layer of Ti atoms parallel to the a,b-plane is shown for the 2D modulation with orthorhombic symmetry. Atoms are depicted at their basic positions, with shifts towards their true position indicated by arrows with a length of 20 times the true displacements. Dark and light circles represent Ti atoms at -z and z, respectively. 5x11 unit cells of the basic structure are displayed.
Participating researchers at the Laboratory of Crystallography in Bayreuth: Andreas Schönleber, Lukas Palatinus#, Mohammad Shaz and Sander van Smaalen.
Part of this research has been done in collaboration with M. Hoinkis, M. Klemm, S. Horn and R. Claessen (Dept. of Physics, University of Augsburg; present address: University of Wurzburg).
Literature and Publications:
 A. Seidel, C.A. Marianetti, F.C. Chou, G. Ceder and P.A. Lee: S = 1/2 chains and spin-Peierls transition in TiOCl, Phys. Rev. B 67, 020405(R) (2003).
 M. Shaz, S. van Smaalen, L. Palatinus, M. Hoinkis, M. Klemm, S. Horn and R. Claessen: The Spin-Peierls transition in TiOCl, Phys. Rev. B 71, 100405(R) (2005).
 L. Palatinus, A. Schönleber and S. van Smaalen: Two-fold superstructure of titanium(III)-oxybromide at T = 17.5 K, Acta Crystallogr. C 61, i48-i49 (2005).
 S. van Smaalen, L. Palatinus and A. Schönleber: Incommensurate interactions and non-conventional spin-Peierls transition in TiOBr, Phys. Rev. B 72, 020105(R) (2005).
#Permanent address: Institute of Physics of the Academy of Sciences in Prague, Czech Republic.