Is orbital ordering in crystals a magnetic phase transition?

TL;DR

This paper demonstrates that orbital ordering in crystals with Jahn-Teller ions involves breaking time-reversal symmetry, classifying these phase transitions as magnetic, and analyzes the symmetry and mechanisms behind these phenomena.

Contribution

It introduces a group-theoretical framework linking orbital and spin ordering transitions, showing orbital ordering as a magnetic phase transition due to symmetry breaking.

Findings

Orbital ordering breaks time-reversal symmetry, indicating a magnetic phase transition.

Symmetry groups for orbital and spin phases are derived from the parent phase.

Orbital ordering is driven by superexchange, while spin ordering results from spin-orbital interactions.

Abstract

It is shown that the time-reversal symmetry is broken during the phase transition causing orbital ordering in a crystal with Jahn-Teller (J-T) ions. This means that such phase transitions are magnetic ones. As an example we have considered the spinel crystals containing $T_{2g}$ ions: $NiCr_2O_4$ ($T_{orb}=310$ K, $T_c=70$ K) and $CuCr_2O_4$ ($T_{orb}=860$ K, $T_c=135$ K), where the orbital ordering precedes the spin ordering, which occurs at lower temperatures. The spin-ordering transition is naturally included into our general group-theoretical scheme of the phase transition. Based on the symmetry group of the parent phase, the symmetry groups for possible orbital- and spin-ordered phases are found. We present arguments in favor of the idea that the orbital ordering occurs due to the superexchange between J-T ions, and the spin ordering is caused by the spin-orbital interaction. At the same time, the displacements of atoms of the coordination polyhedron do not lead to the removal of the orbital degeneracy, and they are merely an accompanying effect.