Abstract
On the basis of single-crystal x-ray diffraction we show that TiPO${}_{4}$ undergoes a spin-Peierls distortion below 74.5(5) K, with a dimerization of the Ti chains along the $\mathbf{c}$ axis. Between 74.5(5) and 111.6(3) K, TiPO${}_{4}$ develops an incommensurate (IC) phase with temperature-dependent $\mathbf{q}$ vector (${\ensuremath{\sigma}}_{1}$,0,0). Density functional calculations strongly suggest that the IC phase results from a frustration of the lock-in spin-Peierls transition due to the competition of three energetically almost degenerate crystal structures and elastic coupling of the Ti chains via the bridging PO${}_{4}$ units. The phase transition into the IC phase is of second order, but the lock-in transition into the spin-Peierls distortion below 74.5 K is of weak first order in nature.
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