Ferrimagnetism from quantum fluctuations in Kitaev materials

TL;DR

This paper uses symmetry analysis and spin-wave theory to explain ferrimagnetism in Kitaev materials, showing it arises from noncollinear multi-q states and quantum fluctuations, not collinear zigzag states.

Contribution

It demonstrates that ferrimagnetism in Kitaev materials is compatible with noncollinear multi-q states, providing a symmetry-based explanation and computational evidence using an extended Heisenberg-Kitaev-Gamma model.

Findings

Ferrimagnetism cannot originate from collinear zigzag states due to symmetry constraints.

Triple-q states can produce a finite zero-temperature magnetization consistent with experiments.

Quantum fluctuations induce finite magnetization in triple-q states even with identical g-factors.

Abstract

Ferrimagnetism appears in the temperature-field phase diagrams of several candidate Kitaev materials, such as the honeycomb cobaltates Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$. In a number of instances, however, the exact nature of the corresponding ground states remains the subject of ongoing debate. We show that general symmetry considerations can rule out candidate states that are incompatible with the observed ferrimagnetic behavior. In particular, we demonstrate that a ferrimagnetic response cannot be reconciled with a collinear zigzag ground state, owing to the combined time-reversal and translational symmetry inherent to that configuration. Instead, the observed behavior is fully compatible with the symmetries of noncollinear multi-$\mathbf q$ states, such as the triple-$\mathbf q$ discussed in the context of Na$_2$Co$_2$TeO$_6$. We exemplify this general result by computing the ferrimagnetic response of an extended Heisenberg-Kitaev-Gamma model with explicit sublattice symmetry breaking within linear spin-wave theory. If the model realizes a triple-$\mathbf q$ ground state, the calculated magnetization curve is well consistent with the low-temperature behavior observed in Na$_2$Co$_2$TeO$_6$. In this case, a finite magnetization remains in the zero-temperature limit as a consequence of quantum fluctuations, even if the $g$-factors on the different sublattices are identical. For a zigzag ground state, by contrast, the total magnetization vanishes both at zero and finite temperatures, independent of possible sublattice-dependent $g$-factors, as expected from the symmetry analysis. The implications of our general result for other Kitaev materials exhibiting ferrimagnetic behavior are also briefly discussed.