Electric polarization reversal and nonlinear magnetoelectric coupling in the honeycomb antiferromagnet ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ single crystal

As a new magnetoelectric material, honeycomb-based antiferromagnet ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ has attracted a great deal of attention due to its prominent magnetoelectric (ME) coupling and high Néel temperature, while the physics of magnetoelectricity is far from understood. In the present study, we present our systematic investigations of the anisotropic ME effect, electric polarization reversal, and nonlinear ME effect of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ single crystals, thus highlighting the phase diagram extended down to 10 K. Our results provide clear evidence for electric polarization reversal driven by magnetic field ($H$) along the [110] and [1-10] directions, respectively, while no such polarization reversal occurs as $H$ is applied along the [001] direction. The nonlinear ME effects and electric control of magnetism are unambiguously demonstrated. In addition, the angular-dependent probing reveals a 2θ rotation of the induced electric polarization around the $c$ axis upon the rotation of magnetic field by an angle θ. The electric polarization responses and concomitant ME coupling are well explained by means of the metal-ligand hybridization $p\text{−}d$ mechanism. This work represents an essential step forward in the understanding of ME coupling not only in this $A_4{M}_2{\mathrm{O}}_9$ honeycomb magnet.

Figure 1

(a) Schematic illustration of crystal structure of $P\text{−}3c1$ phase in ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$. Green and black dashed lines denote the ferromagnetic and antiferromagnetic exchange interactions. Top view of magnetic structures of Fe1 layer and Fe2 layer in (b), (c) $P\text{−}3c1$ phase and (d), (e) $C2/c$ phase, respectively. Red arrows denote the magnetic moments of ${\mathrm{Fe}}^{2+}$ ions. The symbol of “×” denotes the space inversion center, and red triangle presents the threefold symmetry along the $c$ axis. Solid black line in (b) denotes the twofold rotation symmetry and the dashed black line denotes the mirror symmetry.

Figure 2

(a). XRD pattern of as-grown single crystal at room temperature. The inset shows the photograph of the single crystal and the Laue diffraction spots obtained along the [001] direction. (b) XRD diffraction pattern and the Rietveld refinement of the crushed single crystal measured at room temperature.

Figure 3

(a) Magnetic susceptibility $\chi \left(T\right)$ curves measured under ZFC mode with magnetic field $H=0.1$ T applied along the [001], [110], and [1-10] directions. The inset shows the Curie-Weiss fitting in the paramagnetic region. (b) $T$-dependent $C_p/T, {\chi }_{\left[1\text{−}10\right]}$, and ${\chi }_{\left[110\right]}$ curves. (c) $H$-dependent magnetization ($M$) measured at different $T$ under the magnetic field along [1-10] and (d) [001] directions. Green dashed lines in (c) and (d) as guide to the eye indicate the linear relationship.

Figure 4

Pyroelectric current $I_{\left[110\right]}$ as a function of temperature under different magnetic fields applied along (a) [110], (b) [1-10], and (c) [001] direction. (d)–(l) $T$ dependence of polarization in the magnetic field and poling electric field applied along the [110], [1-10], and [001], alternatively. Green dashed lines indicate the magnetic transition points $T_1$ and $T_N$.

Figure 5

(a) Magnetoelectric current $I_H$ and (b) modulated field-induced polarization $\mathrm{\Delta }{P}_H$ along [110] direction as a function of time with respect to linearly varying magnetic field between −9 and 9 T along [110] direction, respectively. (c) Corresponding $H$ dependence of $\mathrm{\Delta }{P}_{\left[110\right]}$ under $H$//[110] and (d) [001] direction, respectively. (e) $H$ dependence of $\mathrm{\Delta }{P}_{\left[110\right]}$ under different poling electric fields $E$ at 10 K. (f) Modulated magnetization of $M_{\left[110\right]}$ as a function of external electric field $E$ applied along [110] direction. Dashed lines are used to show the linear relationship.

Figure 6

Dependence of $\mathrm{\Delta }{P}_H$ on angle θ defined by the relative direction of magnetic field $H$ and the [1-10] axis at 10 K under $H=9$ and 2.5 T as well as 85 K with $H=9$ T.

Figure 7

(a) H-T phase diagrams of ${\mathrm{Fe}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$ with magnetic field applied along [1-10], and (b) [001] direction.

Figure 8

Directions of the magnetic moment at the $S_1$ and $S_2$ sites in the Fe1 and Fe2 layer under the external magnetic field applied in (a) $H$//[110], (b) $H$//[1-10] and $H<H_c$, (c) $H$//[1-10] and $H>H_c$, and (d) $H$//[001]. Red arrows indicate the magnetic moments on each site. Blue and black dashed lines represent the x- and $y$ directions. $S_1$ and $S_2$ represent the two Fe sites in each Fe1 and Fe2 layer.

Figure 9

Correlation among the magnetic field direction, the magnetic structure, and the induced polarization of Fe1 and Fe2 layer under a magnetic field applied in the $ab$ plane rotation at 85 K. ${\phi }_1\left({\phi }_2\right)$ is the canting angle of the magnetic moments for Fe1(Fe2) layer under $H$//[1-10]. θ is the angle of $H$ measured from [1-10] direction. Blue dashed lines denote the $x$ direction and the black solid lines denote the original location of moments for $H$//[1-10].