One-dimensional orbital fluctuations and the exotic magnetic properties of YVO$_3$

TL;DR

This paper models the superexchange interactions in YVO$_3$, revealing how orbital fluctuations influence magnetic order and proposing a scenario for the observed exotic magnetic phases.

Contribution

It introduces a detailed superexchange model considering orbital fluctuations, explaining the origin of exotic magnetic orders in YVO$_3$.

Findings

Orbital fluctuations generate ferromagnetic interactions without Hund's exchange.

Identification of an orbital valence bond state and its transition to different magnetic orders.

Proposal of a temperature-dependent dimerized C-AF phase in YVO$_3$.

Abstract

Starting from the Mott insulator picture for cubic vanadates, we derive and investigate the model of superexchange interactions between 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 order. 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 YVO$_3$ and we argue that a dimerized $C$-type antiferromagnetic phase with stronger and weaker FM 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 $C$-AF order observed in YVO$_3$ in the regime of intermediate temperatures and allows one to specify the necessary ingredients of a more complete future theory.