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In the present work we aim to characterize the lattice configurations and themagnetic behavior in the incommensurate phase of spin-Peierls systems. Thisphase emerges when the magnetic exchange interaction is coupled to thedistortions of an underlying triangular lattice and has its experimentalrealization in the quasi-one dimensional compound family TiOX (X = Cl, Br).With a simple model of spin-1/2 chains inserted in a planar triangular geometrywhich couples them elastically, we are able to obtain theuniform-incommensurate and incommensurate-dimerized phase transitions seen inthese compounds. Moreover, we follow the evolution of the wave-vector of thedistortions with temperature inside the incommensurate phase. Finally, wepredict gapless spin excitations for the intermediate phase of TiOX compoundsalong with incommensurate spin-spin correlations. This exotic Luttingerliquid-like behavior could be observed in future experiments.

Incommensurate spin Luttinger liquid phase in a model for the spin-Peierls materials TiOBr and TiOCl