Successive Orbital Ordering Transitions inNaVO2

Physical property measurements on samples of triangular-lattice ${\mathrm{NaVO}}_2$ reveal two successive orbital ordering transitions. At 300 K, the structure is rhombohedral. At 98 K, the system undergoes a second-order transition to a monoclinic phase in which the in-plane V-V distances separate into four short and two long bonds, corresponding to orbital ordering of one electron per ${\mathrm{V}}^{3+}$. Below 93 K, there is a first-order transition to a second monoclinic phase with four long and two short V-V bonds, consistent with orbital ordering of two electrons per ${\mathrm{V}}^{3+}$. Long range magnetic ordering of $0.98(2){\mu }_B$ per ${\mathrm{V}}^{3+}$ ($3d^2$) sets in at the 93 K structural transition. The orbital ordering relieves the geometric frustration and leads to a magnetically ordered ground state.