KTi(SO$_{4}$)$_{2}$ .H$_{2}$O - a possible candidate for a new spin-Pierles system

Recently a large number of compounds belonging to the family of J$_{1}$-J$_{2}$ chain models with competing ferromagnetic (FM) and antiferromag- netic (AFM) interactions have been discovered. In most cases, FM-J$_{1}$ and AFM-J$_{2}$ is observed, leading to helical order with no spin gap (for frustration ratio $\alpha$ = $\frac{J_{1}}{J_{2}}$ $\geq$ -0.25). Systems with both J$_{1}$ and J$_{2}$ being AFM causing a spin gap are rather rare. The thermodynamic data of the recently prepared KTi(SO$_{4}$)$_{2}$.H$_{2}$O reveal that this system is a quasi 1D spin 1/2 chain compound with both J$_{1}$ and J$_{2}$ being AFM, and a frustration ratio $\alpha$ $\approx$ 0.29. Here we report the results of electronic structure calculations within the LSDA+$U$ method along with tight-binding models. Our calculations confirm that both J$_{1}$ and J$_{2}$ are AFM. In contrast to the experiments we obtain a larger $\alpha$, slightly depending on the choice of the Coulomb repulsion $U$ . Therefore KTi(SO$_{4}$)$_{2}$.H$_{2}$O might be a new candidate for a spin-Pierles ground state. A brief comparison with other systems belonging to the class of frustrated chain materials is given with respect to their position in the general phase diagram of the 1D J$_{1}$ - J$_{2}$ model.