Orbital ordering and magnetic dimensionalities in the p-orbital spin-1/2 CsO$_{2}$ and Cs$_{4}$O$_{6}$

The materials containing magnetic O$_{2}^{-}$ anions, i.e., alkali superoxides, $A$O$_{2}$ (A $=$ Na, K, Rb, Cs), and alkali sesquioxides, $A_{4}$O$_{6}$ ($A = $ Rb, Cs), exhibit two key features that make them appealing for investigation of the coupling between lattice, orbital and spin physics as an alternative to the more established $d$-orbital materials. First, the O$_{2}^{-}$ dumbbells can easily reorient down to the low temperatures, thereby modulating the overlaps of $p$ orbitals. And second, as the $S = $ 1/2 spin is localized in a pair of $p$-derived $\pi \ast $ orbitals, their original degeneracy can be removed by the cooperative tilting of O$_{2}^{-}$ dumbbells. Here we report on our studies of CsO$_{2}$ and Cs$_{4}$O$_{6}$ using $^{133}$Cs nuclear magnetic resonance and electron paramagnetic resonance techniques. In CsO$_{2}$ we find the structural phase transition occurring at 61 K on cooling associated with the freezing out of the O$_{2}^{-}$ librations. The transition also includes $\pi \ast $ orbital ordering that is responsible for the quasi-one-dimensional low-temperature magnetism. Clear signs of the spin Tomonaga-Luttinger liquid state are found from the spin-lattice relaxation and spin susceptibility data. On the other hand, the mixed valence Cs$_{4}$O$_{6}$ shows much more complex phase diagram with several transitions depending on the exact cooling protocol.