Theoretical study of the magnetism in the incommensurate phase of TiOCl
  Going beyond a recently proposed microscopic model for the incommensurate transition in the spin-Peierls TiOX (X=Cl, Br) compounds, in the present work we start by studying the thermodynamics of the model with XY spins and adiabatic phonons. We find that the system enters in an incommensurate phase by a first order transition at a low temperature $T_{c1}$. At a higher temperature $T_{c2}$ a continuous transition to a uniform phase is found. Furthermore, we study the magnetism in the incommensurate phase by Density Matrix Renormalization Group (DMRG) calculations on a 1D Heisenberg model where the exchange is modulated by the incommensurate atomic position pattern. When the wave vector $q$ of the modulation is near $\pi$, we find local magnetized zones (LMZ) in which spins get free from their singlets as a result of the domain walls induced by the modulated distortion. When $q$ moves away enough from $\pi$, the LMZ disappear and the system develops incommensurate magnetic correlations induced by the structure. We discuss the relevance of this result regarding to previous and future experiments in TiOCl. 
D.M. Mastrogiuseppe, M.E. Torio, C.J. Gazza, A.O. Dobry