Large spin-driven dielectric response and magnetoelectric coupling in the buckled honeycomb ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$

We present the significant spin-driven dielectric anomaly ($\sim 40\%$ drop) and magnetoelectric coupling near the magnetic ordering temperature in single crystal ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$. By combining neutron and x-ray single crystal diffraction techniques, we unambiguously determined its magnetic symmetry and studied the structural phase transition at $T_S$ = 70 K. The temperature-dependent static dielectric constant is strongly anisotropic, rendering two dielectric anomalies along the $a$ axis in the hexagonal lattice with the first one coupled to the magnetic ordering around $T_N$ = 97 K and the second one accompanying with a first-order structural transition around $T_S$ = 70 K. Below $T_N$, we found that the anomalous dielectric constant is practically proportional to the square of the magnetic moment from neutron diffraction data, indicating that the exchange striction is likely responsible for the strong spin-lattice coupling. Magnetic-field-induced magnetoelectric coupling was observed and is compatible with the determined magnetic structure that is characteristic of antiferromagnetically arranged ferromagnetic chains in the honeycomb plane. We propose that such magnetic symmetry should be immune to external magnetic fields to some extent favored by the freedom of rotation of moments in the honeycomb plane, laying out a promising system to control the magnetoelectric properties by magnetic fields.

Figure 1

(a) Schematic drawing of the crystal structure of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ at room temperature viewing along the [110] direction. (b) The slightly buckled honeycomb layer is formed by Fe1 atoms. (c) Observed and calculated single crystal x-ray diffraction data at room temperature with the goodness-of-fit ${\chi }^2$ = 0.94 and $R$ factor $R_{F^2}$ = 3.15%.

Figure 2

Temperature dependence of the magnetic susceptibility of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ with a magnetic field ${\mu }_0\mathrm{H}$ = 0.2 T parallel to the $a$ and $c$ axes under both ZFC and FC protocols.

Figure 3

The temperature-dependent dielectric constant at various frequencies with the electric field $E$ parallel to the $a$ and $c$ axes, respectively.

Figure 4

Magnetic field dependence of the dielectric constant of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ with magnetic and electric fields applied to different configurations. Inset shows the magnified view of the the magnetoelectric coupling.

Figure 5

Temperature dependence of the pyroelectric current (top panel) and the corresponding polarization (bottom panel) under various magnetic fields. The observable magnetoelectric coupling occurs below 96 K, close to the magnetic transition temperature of 97 K. Inset shows the linear behavior of the polarization as a function of magnetic field.

Figure 6

(a, b) Crystal structure of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ projected along the $b$ and $c$ directions. (c) Observed structure factor squared values of diffraction peaks compared to those calculated by fitting the $C2/c$ monoclinic structural model at 40 K with the goodness-of-fit ${\chi }^2$ = 1.45 and $R$ factor $R_{F^2}$ = 5.86%. (d) Visualization of the atomic displacements of the primary $\mathrm{GM}3+$ irrep (amplitude: 0.1124 Å) from the symmetry adapted mode analysis projected into the $ab$ plane, accounting for the $P\overline{3}c1$ to $C2/c$ transition. Arrows denote the polarization vectors of the symmetry modes of the O atomic displacements with moduli proportional to the amplitude.

Figure 7

(a)–(c) Contour plots of the neutron diffraction reflections (0 1 0), (0 2 0), and (0 0 4) as a function of temperature. (d) Temperature dependence of the (0 0 4) peak intensity. The solid lines stand for the power-law fits in different temperature regimes.

Figure 8

(a) Observed intensity of all magnetic peaks at 5 K compared to those calculated by fitting the magnetic structural model. (b,c) The ground-state magnetic structure of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ in the hexagonal lattice setting. The solid yellow line marks the nearest-neighboring exchange interaction while the solid blue line represents the next-nearest-neighboring exchange interaction $J2$.

Figure 9

The dielectric change below $T_N$ due to spin ordering in representative antiferromagnetic materials. Note that the dielectric change was evaluated using (${\varepsilon }_{T_N}^{\prime }-{\varepsilon }_L^{\prime }$)/${\varepsilon }_{T_N}^{\prime }$ where ${\varepsilon }_L^{\prime }$ is the static dielectric constant at the lowest measured temperature for each case.

Figure 10

Comparison between the dielectric constant ${\varepsilon }_a{}^{\prime }$($T$) and the magnetic reflection (0 0 4) as a function of temperature. Note the peak intensity is proportional to the square of the magnetic moment in ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$.