Ferroelectric order associated with ordered occupancy at the octahedral site of the inverse spinel structure of multiferroic ${\mathrm{NiFe}}_2{\mathrm{O}}_4$

We report a ferroelectric order at $\sim 98$ K for ${\mathrm{NiFe}}_2{\mathrm{O}}_4$, which carries an inverse spinel structure with a centrosymmetric $Fd\overline{3}m$ structure at room temperature. The value of spontaneous electric polarization is considerably high as $\sim 0.29 \mu \mathrm{C}/{\mathrm{cm}}^2$ for 5 kV/cm poling field. The electric polarization decreases considerably ($\sim 17\%$) around the liquid-nitrogen temperature upon application of 50 kOe field, proposing a significant magnetoelectric coupling. The synchrotron diffraction studies confirm a structural transition at $\sim 98$ K to a noncentrosymmetric structure of $P{4}_{1}22$ space group. The occurrence of polar order is associated with an ordered occupancy of Ni and Fe atoms at the octahedral sites of the $P{4}_{1}22$ structure, instead of random occupancies at the octahedral site of the inverse spinel structure. The results propose that ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ is a member in the type-II multiferroics.

Figure 1

Atomic positions in the inverse spinel structure of NFO. A portion of connecting (Fe,$\mathrm{Ni}){\mathrm{O}}_6$ octahedra around a ${\mathrm{FeO}}_4$ tetrahedron is also depicted, where “Oc” and “Te” in the suffix indicate the octahedron and tetrahedron.

Figure 2

Fe $2p$ core-level XPS of NFO. Deconvolution of the curves along with the fit are shown by the solid curves.

Figure 3

(a) Temperature ($T$) variation of dc-biased current ($I_{\mathrm{DC}}$) with a 5 kV/cm bias field. The inset highlights the “dip” in $I_{\mathrm{DC}}\left(T\right)$ at 98 K. $T$ variations of (b) pyroelectric current ($I_P$) for different poling temperatures ($T_{\mathrm{pole}}$) at poling field ($E$) of 5 kV/cm, (c) $I_P$ for different $E$ and $T_{\mathrm{pole}}$ = 150 K, (d) $I_P$ for different temperature sweep rates and $E$ = 5 kV/cm, (e) $I_P$ for different $E$ and $T_{\mathrm{pole}}$ = 150 K after subtracting the extrinsic thermally stimulated depolarization currents, (f) electric polarization ($P$) at different $E$, (g) $I_P$, and (h) $P$ at $E$ = 5 kV/cm in zero magnetic field and 50 kOe using both the ZFC and FC modes. The inset of (b) highlights the peaks at the FE transition ($T_C$). Vertical broken lines used in the inset of (b), (e), and (g) indicate the temperature at $T_{\mathrm{FE}}$.

Figure 4

Thermal variations of (a) ZFC magnetization ($M$) (left axis) and real part (${\epsilon }^{\prime }$) of dielectric permittivity at frequency, $f$ = 707 Hz, (right axis) around $T_{\mathrm{FE}}$. Vertical broken line used in (a) indicates the temperature of $T_{\mathrm{FE}}$. Magnetic field ($H$) dependence of (b) $M$ (left axis) and ${\epsilon }^{\prime }$ (right axis) at 10 K. (c) Plot of $M^2$ with [1-${\epsilon }^{\prime }\left(H\right)/{\epsilon }^{\prime }$(0)](%) at 10 K. Straight line depicts the linear fit below 900 Oe.

Figure 5

Synchrotron diffraction patterns at (a) 300 K for NFO. Solid curve represents the fit using Rietveld refinement. (b) Selected diffraction peaks at different temperatures around $T_{\mathrm{FE}}$. $T$ dependence of (c) integrated intensities and (d) FWHM of the (216) peak. Vertical broken lines used in (c) and (d) indicate the temperature of $T_{\mathrm{FE}}$.

Figure 6

Synchrotron diffraction patterns at (a) 90 K for NFO. Solid curve represents the fit using Rietveld refinement. Rietveld refinements are compared with (b) tetragonal $P{4}_{1}22$ and cubic $Fd\overline{3}m$ space groups at 90 K. $T$ dependence of (c) lattice constants and (d) unit-cell volume ($V$). Vertical broken lines used in (c) and (d) indicate the temperature of $T_{\mathrm{FE}}$.

Figure 7

Thermal variations of the bond lengths of (a) Fe tetrahedra (${\mathrm{Fe}}_{\mathrm{Te}}-\mathrm{O}$), (b) Fe octahedra (${\mathrm{Fe}}_{\mathrm{Oc}}-\mathrm{O}$), and (c) Ni octahedra (${\mathrm{Ni}}_{\mathrm{Oc}}-\mathrm{O}$). Vertical broken lines used in (a)–(c) indicate the temperature of $T_{\mathrm{FE}}$. Schematic representations of the distortions of the (d) Fe tetrahedron, (e) Fe octahedron, and (f) Ni octahedron.