One-dimensional orbital fluctuations and the exotic magnetic properties ofYVO3

Abstract

Starting from the Mott insulator picture for cubic vanadates, we derive and investigate the model of superexchange interactions between ${\mathrm{V}}^{3+}$ ions, with nearly degenerate ${t}_{2g}$ orbitals occupied by two electrons each. The superexchange interactions are strongly frustrated and demonstrate a strong interrelation between possible types of magnetic and orbital orders. We elucidate the prominent role played by fluctuations of $yz$ and $xz$ orbitals which generate ferromagnetic superexchange interactions even in the absence of Hund's exchange. In this limit, we find orbital valence bond state which is replaced either by $C$-type antiferromagnetic order with weak $G$-type orbital order at increasing Hund's exchange, or instead by $G$-type antiferromagnetic order when the lattice distortions stabilize $C$-type orbital order. Both phases are observed in $\mathrm{Y}\mathrm{V}{\mathrm{O}}_{3}$, and we argue that a dimerized $C$-type antiferromagnetic phase with stronger and weaker ferromagnetic bonds alternating along the $c$ axis may be stabilized by large spin-orbital entropy at finite temperature. This suggests a scenario which explains the origin of the exotic $C$-type antiferromagnetic order observed in $\mathrm{Y}\mathrm{V}{\mathrm{O}}_{3}$ in the regime of intermediate temperatures and allows one to specify the necessary ingredients of a more complete future theory.