Orbital Dimerization and Dynamic Jahn-Teller Effect in NaTiSi$_2$O$_6$

We study with the Raman scattering technique two types of phase transitions in the pyroxene compounds NaMSi$_2$O$_6$ (with M=Ti, V, and Cr). In the quasi one-dimensional S=1/2 system NaTiSi$_2$O$_6$ we observe anomalous high-temperature phonon broadening and large changes of the phonon energies and line-widths across the phase transition at 210 K. The phonon anomalies originate from an orbital order-disorder phase transition and these results --combined with theoretical considerations-- indicate that the high temperature dynamical Jahn-Teller phase of NaTiSi$_2$O$_6$ exhibits a spontaneous breaking of translational symmetry into a dimerized, Jahn-Teller distorted, orbital ordered state under the formation of spin valence bonds. In S=1 NaVSi$_2$O$_6$ orbital degrees of freedom are strongly suppressed and the magnetic excitations are well described within a Heisenberg model, indicating that at T$_N$=19K this system orders antiferromagnetically.