# Sodium layer chiral distribution and spin structure of Na$_2$Ni$_2$TeO$_6$ with a honeycomb network

## TL;DR

This study uncovers the 2D chiral distribution of Na ions and the complex spin ordering in Na$_2$Ni$_2$TeO$_6$, revealing insights into its ion diffusion and magnetic properties using advanced neutron diffraction and various measurement techniques.

## Contribution

It introduces a novel inverse Fourier transform neutron diffraction method to visualize Na ion distribution and elucidates the coexistence of incommensurate and commensurate antiferromagnetic spin orderings.

## Key findings

- Na ions form a 2D chiral pattern without breaking crystal symmetry.
- Na diffusion follows a chiral mechanism consistent with BVS calculations.
- Both strong incommensurate and weak commensurate AFM spin orderings are observed.

## Abstract

The nature of Na ion distribution, diffusion path, and the spin structure of $P2$-type Na$_2$Ni$_2$TeO$_6$ with a Ni honeycomb network has been explored. The nuclear density distribution of Na ions reveals a 2D chiral pattern within Na layers without breaking the original 3D crystal symmetry, which has been achieved uniquely via an inverse Fourier transform (iFT)-assisted neutron diffraction technique. The Na diffusion pathway described by the calculated iso-surface of Na ion bond valence sum (BVS) map is found consistent to a chiral diffusion mechanism. The Na site occupancy and Ni$^{2+}$ spin ordering were examined in detail with the electron density mapping, neutron diffraction, magnetic susceptibility, specific heat, thermal conductivity and transport measurements. Signatures of both strong incommensurate (ICM) and weak commensurate (CM) antiferromagnetic (AFM) spin ordering were identified in the polycrystalline sample studied, and the CM-AFM spin ordering was confirmed by using a single crystal sample through the $k$-scan in the momentum space corresponding to the AFM peak of ($\frac{1}{2}$, 0, 1).