Spin-orbital exchange as a route to intertwined dipole-quadrupole orbital order in MnV$_2$O$_4$ under strong trigonal crystal field

TL;DR

This paper investigates how strong trigonal crystal fields influence spin-orbital interactions in MnV₂O₄, revealing a novel intertwined dipole-quadrupole orbital order and complex magnetic configurations.

Contribution

It combines first-principles calculations with an effective model to show the significant role of trigonal crystal fields and subdominant hopping in stabilizing new orbital and magnetic orders.

Findings

Trigonal crystal field is significant in high-temperature phase.

Subdominant hopping processes alter spin-orbital exchange interactions.

System stabilizes a two-in/two-out magnetic configuration with intertwined orbital order.

Abstract

Orbitally degenerate systems provide a promising platform for realizing novel quantum phases driven by spin-orbital exchange interactions, as described by the Kugel-Khomskii model. Spinel vanadates, in which orbital degrees of freedom remain active, exhibit structural and magnetic transitions accompanied by orbital ordering, but the nature of the orbital state in MnV$_2$O$_4$ remains under debate. Here, we combine first-principles calculations with an effective spin-orbital model to address this problem. We show that a significant trigonal crystal field is present in high-temperature cubic phase and plays an essential role in determining the low-energy degrees of freedom. Based on the resulting parameters, we construct an effective Hamiltonian beyond the conventional dominant-hopping approximation and demonstrate that subdominant hopping processes strongly modify the spin-orbital exchange interactions. As a result, the system stabilizes a two-in/two-out magnetic configuration featuring spin canting and intertwined dipole-quadrupole orbital order.