Revealing the microscopic origin of the magnetization plateau in Na$_3$Ni$_2$BiO$_6$

TL;DR

This study establishes a microscopic, first-principles description of Na$_3$Ni$_2$BiO$_6$ by combining DFT, projED, and a multi-orbital Hubbard framework to extract exchange interactions. It shows that the magnetism is dominated by ferromagnetic $J_1$ and antiferromagnetic $J_3$ Heisenberg couplings, with a substantial out-of-plane single-ion anisotropy (SIA), while Kitaev terms are comparatively small. The observed $1/3$ magnetization plateau arises from the interplay of $J_1$ and $J_3$ under strong SIA, realized as a \

Abstract

Recent experimental studies of the spin-1 honeycomb antiferromagnet Na$_3$Ni$_2$BiO$_6$ have revealed a pronounced one-third magnetization plateau under applied magnetic fields, highlighting the presence of strong magnetic frustration and anisotropy in this material. Such behavior has been attributed to substantial bond-dependent Kitaev interactions in combination with single-ion anisotropy, placing Na$_3$Ni$_2$BiO$_6$ among honeycomb compounds of interest for unconventional magnetic phases. Motivated by these observations, we present a first-principles-based analysis of the magnetic interactions in Na$_3$Ni$_2$BiO$_6$. By combining density-functional calculations with microscopic modeling, we extract the relevant exchange parameters and construct an effective spin model that quantitatively reproduces both the elastic neutron-scattering spectra and the magnetization curve. The model captures the experimentally observed zero-field zigzag magnetic order, and proposes a $\textit{double-zigzag}$ state at intermediate magnetic fields, realizing the 1/3-magnetization plateau in a simpler way than suggested in previous works. Crucially, we show that the one-third magnetization plateau does not require Kitaev interactions; instead, it arises from the interplay of strong out-of-plane single-ion anisotropy and competing ferromagnetic nearest-neighbor ($J_1$) and antiferromagnetic third-neighbor ($J_3$) Heisenberg couplings. These results establish a consistent microscopic description of Na$_3$Ni$_2$BiO$_6$ and clarify the origin of its field-induced plateau phase.

Figures (8)

• Figure 1: Projection on the $ab$ plane of the crystal structure of Na$_3$Ni$_2$BiO$_6$. Each honeycomb layer consists of Ni atoms surrounded by oxygen octahedra. The center of each honeycomb is occupied by a single Bi atom. The axes of the local Wannierization coordinate system x, y and z are oriented along the bonds between Ni and O atoms. The X (red), Y (green) and Z (blue) Ni-Ni bonds are depicted inside the octahedral structure.
• Figure 2: Ground state spin configuration in zero-field (a-c) and $\mu_0H=5.5$T, $H\vert\vert c^*$ (d-f). In the zero-field environment, three distinct zigzag phases in close energetic proximity (c higher in energy by $\sim0.1$meV) to one another coexist in different honeycomb layers and domains. Similarly, for $\mu_0H=5.5$T three distinct 1/3-magnetization phases in close energetic proximity coexist (f higher in energy by $\sim0.03$meV)
• Figure 3: Static structure factor $S(\textbf{q})$ at zero magnetic field corresponding to the three possible ground state spin configurations (see \ref{['fig:SpinConfiguration']}a-c). Data is presented for the $(H,0,0)$, $(0,K,0)$ momentum space plane with $H$ and $K$ in terms of fractional k-space lattice units. The displayed spectrum consists of the averaged sum of three spectra that each result from one of the three different ground state spin configurations. The data for the individual configurations is visible in Supplementary Note 3, \ref{['Supp:fig:ENS_NoField']}.
• Figure 4: Static structure factor $S(\textbf{q})$ at a magnetic field $\mu_0H=5.5$T, $H\vert\vert c^*$ for the three possible ground state spin configurations (see \ref{['fig:SpinConfiguration']}d-f). Data is presented for the $(H,0,0)$, $(0,K,0)$ momentum space plane with $H$ and $K$ in terms of fractional k-space lattice units. The displayed spectrum consists of the averaged sum of three spectra that each result from one of the three different ground state spin configurations. The data for the individual configurations is visible in Supplementary Note 3, \ref{['Supp:fig:ENS_Field']}.
• Figure 5: Magnetization curve of NNBO, representing the magnetization parallel to $c*$ per Ni$^{2+}$, for different values of temperature T, for fixed $\gamma=0.28$. The 1/3-plateau phase is observed for $0$, $2$ and $4$K, while at $7$K the intermediate phase disappears.