Counterroating incommensurate magnetic order and strong quantum fluctuations in the honeycomb layers of $\rm NaNi_2BiO_6$

Abstract

We report the magnetic structure and electronic properties of the honeycomb antiferromagnet $\rm NaNi_2BiO_{5.66}$. We find magnetic order with moments along the $c$ axis for temperatures below $T_{c1}=6.3(1)\>{\rm K}$ and then in the honeycomb plane for $T < T_{c2}=4.8(1)\>{\rm K}$ with a counterrotating pattern and an ordering wave vector ${\bf q}=(\frac{1}{3},\> \frac{1}{3},\> 0.15(1))$. Density functional theory and electron spin resonance indicate this is high-spin Ni$^{3+}$ magnetism near a high to low spin transition. The ordering wave vector, in-plane magnetic correlations, missing entropy, spin state, and superexchange pathways are all consistent with bond-dependent Kitaev-$\Gamma$-Heisenberg exchange interactions in $\rm NaNi_2BiO_{6-\delta}$.