High-resolution neutron diffraction determination of noncollinear antiferromagnetic order in the honeycomb magnetoelectric Fe$_{4}$Nb$_{2}$O$_{9}$

TL;DR

Fe4Nb2O9 exhibits a strong magnetoelectric response but its magnetic ground state has been disputed. The authors combine high-resolution powder neutron diffraction, complementary x-ray, magnetic, dielectric, and magnetodielectric measurements, and group-theory refinements to reveal a noncollinear antiferromagnetic order with a substantial c-axis moment, emerging below $T_N ≈ 97.5$ K and accompanied by a structural transition near $T_S ≈ 87.5$ K that evolves into a monoclinic phase. Their analysis shows that all nine magnetoelectric tensor components are symmetry-allowed in the lowest magnetic symmetry $P\bar{1}'$, and that configurations with out-of-plane spin components are energetically favorable, consistent with ab initio results. This work resolves the magnetic structure and symmetry of Fe4Nb2O9, providing a framework for understanding its unconventional magnetoelectric properties and guiding studies of related A4B2O9 honeycomb oxides.

Abstract

Magnetoelectric systems offer potential for device applications exploiting coupled states between electric and magnetic properties. Among magnetoelectric materials, \FNO has attracted special attention because of its pronounced dielectric signal at high magnetic transition temperatures. However, the magnetic ground state, which is essential information for understanding its unusual magnetoelectricity, remains unclarified. Here, we report a noncollinear magnetic ground state of Fe$_{4}$Nb$_{2}$O$_{9}$. To examine the magnetoelectric effect associated with sequential magnetic and structural transitions upon cooling, we conducted combined x-ray diffraction, magnetic susceptibility, magnetization, dielectric constant, and magnetodielectric experiments. Powder neutron diffraction experiments revealed a series of magnetic Bragg peaks and clear splitting of peaks via structural transition. Magnetic Rietveld refinements, combined with group theory analysis, determined a noncollinear antiferromagnetic structure including a significant $c$-axis moment component at 1.5 K. This study provides insights into the understanding of its magnetoelectric properties.

Figures (8)

• Figure 1: Crystal structure of Fe$_{4}$Nb$_{2}$O$_{9}$. (a) The crystallographically distinct Fe1 and Fe2 sites in a unit cell (black solid lines, 0 $\leqslant$z$\leqslant$ 1). (b) and (c) The buckled (0.15 $\leqslant$$z$$\leqslant$ 0.35) and flat ($-$0.1 $\leqslant$$z$$\leqslant$ 0.1) honeycomb layers.
• Figure 2: Sample characterizations. (a) Rietveld refinement results obtained from x-ray diffraction patterns collected at room temperature. Impurity peaks are minimal. (b) ZFC and FC magnetic susceptibilities at 0.05 T. The solid magenta line indicates the CW fit (see text). (c) Magnetic isotherm at 2.5 K. The solid magenta line is a linear fit. The dashed cyan lines denote the critical magnetic field for the spin-flop transition. (d) Dielectric constant at 0.05 T. (e) Magnetodielectric data for the magnetic field at 2 K. The dashed red, blue, and green lines are the $T_{\rm N}$, $T_{\rm S}$, and $T_{\rm 0}$ values determined from the neutron diffraction data (Fig. \ref{['fig:Block 3']}).
• Figure 3: Evolution of magnetic and nuclear Bragg peaks upon cooling. (a), (c), (e), (g), and (i) Contour plots for representative magnetic and nuclear Bragg peaks. (b), (d), (f), (g) and (h), and (j) Corresponding diffraction patterns from 100 to 70 K, highlighting two transitions. Red, blue, and green lines represent $T_{\rm N}$, $T_{\rm S}$, and $T_{\rm 0}$. The $T_{\rm 0}$ is the temperature where the low-temperature peaks are only observed. Data from bank 3 are displayed. Peak indexing above the top panel is based on the parent trigonal lattice. Top vertical ticks for peak indexing in (b), (d), (f), (h), and (j) correspond to 100 K in the trigonal lattice, while those in the lower section are from 70 K in the triclinic lattice.
• Figure 4: Group-subgroup diagram. A hierarchy of MSGs from $C2/c'$ and $C2'/c$ to the lowest possible group, $P1$, is shown. Three potential MSGs are highlighted by the green and blue rectangles.
• Figure 5: Magnetic and nuclear refinements at 1.5 K. (a) Model A: collinear antiferromagnetic order without $M_{c}$Jana2019. (b) Model B: noncollinear antiferromagnetic order without $M_{c}$Ding2020. (c) Model C: noncollinear antiferromagnetic order with $M_{c}$ using $C2/c'$. (d) Model F: noncollinear antiferromagnetic order with $M_{c}$ using $P\bar{1}'$. Bank3 data are presented. The wR$_{\mathrm{p}}$ values shown are for all banks (see Tables \ref{['1p5K_magnetic_results_right_part']} and \ref{['table:1p5K:magnetic:results']} for detailed information). Bragg peaks for impurity phases are omitted for brevity and to facilitate clearer matching of the main peaks with the data.