Spin Order due to Orbital Fluctuations: Cubic Vanadates

We investigate the highly frustrated spin and orbital superexchange interactions in cubic vanadates. The fluctuations of $t_{2g}$ orbitals trigger a novel mechanism of ferromagnetic interactions between spins $S=1\mathrm{}$ of ${\mathrm{V}}^{3+}$ ions along one of the cubic directions which operates already in the absence of Hund's rule exchange $J_H$, and leads to the $C$-type antiferromagnetic phase in ${\mathrm{LaVO}}_3$. The Jahn-Teller effect can stabilize the orbital ordering and the $G$-type antiferromagnetic phase at low temperatures, but large entropy due to orbital fluctuations favors again the $C$ phase at higher temperatures, as observed in $\mathrm{YVO}{}_3$.