Coupled magnetic and ferroelectric states in the distorted honeycomb system ${\mathrm{Fe}}_4{\mathrm{Ta}}_2{\mathrm{O}}_9$

We report on the magnetic, thermodynamic, dielectric, and pyroelectric measurements on the hitherto unreported $\mathrm{Fe}{}_4\mathrm{Ta}{}_2{\mathrm{O}}_9$. This system is seen to exhibit a series of magnetic transitions, many of which are coupled to the emergence of ferroelectric order, making $\mathrm{Fe}{}_4\mathrm{Ta}{}_2{\mathrm{O}}_9$ the only genuine multiferroic in its material class. We suggest that the observed properties arise as a consequence of an effective reduction in the dimensionality of the magnetic lattice, with the magnetically active $\mathrm{Fe}{}^{2+}$ ions preferentially occupying a quasi-two-dimensional buckled honeycomb structure. The low-temperature $H\text{−}T$ phase diagram of $\mathrm{Fe}{}_4\mathrm{Ta}{}_2{\mathrm{O}}_9$ reveals a rich variety of coupled magnetic and ferroelectric phases similar to that observed in the distorted kagome systems.

Figure 1

(a) The Rietveld refinement of room-temperature x-ray diffraction data of $\mathrm{Fe}{}_4\mathrm{Ta}{}_2{\mathrm{O}}_9$. This corresponds to a fit with $R$ parameters of $R{}_{wp}=9.13,R{}_e=5.55$, and $\chi {}^2=2.7$. (b) The structure of this system, which can be viewed as a stack of alternating $A$ and $B$ layers along the crystallographic $c$ axis.

Figure 2

(a) Temperature dependence of the dc magnetic susceptibility $M/H$ as measured in ZFC and FC protocols at an applied magnetic field of 100 Oe. The inset shows a Curie-Weiss fit to the data in the high-temperature regime. (b) The inset of depicts $d\chi /dT$ vs $T$, clearly indicating the presence of transitions at $T_1$ (80 K) and $T_2$ (60 K). The main panel depicts the temperature dependence of specific heat $C_P$ as measured at 0 and 7 T. (c) The temperature dependence of the magnetic contribution to the specific heat $C{}_{\mathrm{mag}}/T$. The inset shows the evolution of the magnetic entropy $S{}_{\mathrm{mag}}$ as a function of temperature.

Figure 3

(a) The dielectric constant ${\epsilon }^{\prime }$ and the pyrocurrent in the vicinity of the transitions at $T_1$ (80 K) and $T_2$ (60 K). (b) The flipping of the polarization associated with these transitions on reversal of the poling electric field, indicating that they correspond to robust independent ferroelectric states.

Figure 4

(a) The variation of the Fe1-O and Fe2-O bond lengths across the magnetic transition. (b) The variation in the lattice parameters as a function of temperature. (c) The crystallographic structure of $\mathrm{Fe}{}_4\mathrm{Ta}{}_2{\mathrm{O}}_9$ below the magnetic transition, where the buckling of the FeO polyhedra is observed.

Figure 5

(a) The buckled honeycomb lattice formed by the Fe1 ions separated by the nonmagnetic $\mathrm{TaO}{}_6$ octahedra and (b) the zigzag chain of the nonmagnetic Fe2 ions. Considering the fact that the Fe1-O bond length is larger than the Fe2-O one, we speculate that the magnetic $\left(S=2\right)\mathrm{Fe}{}^{2+}$ ions preferentially occupy the buckled honeycomb lattice and the nonmagnetic $\left(S=0\right)\mathrm{Fe}{}^{2+}$ ions preferentially occupy the zigzag chain.

Figure 6

(a) The inset depicts the dc magnetic susceptibility as measured at 5 kOe and 3 T, indicating the presence of a magnetic-field-induced transition. This is seen more clearly in the plots of the derivative $\left[d\right(1/\chi )/dt]$ vs $T$ shown in the main panel. (b) The inset shows the temperature dependence of the dielectric constant ${\epsilon }^{{}^{\prime }}$ as measured at different magnetic fields, with sharp downturns being observed at the field-induced transition. This is also seen as a peak in the magnetic-field-dependent pyroelectric current measurements shown in the main panel. (c) Polarization obtained after integrating the pyrocurrent as measured in different electromagnetic poling conditions. A subtle signature corresponding to this magnetic-field-induced transition is also observed in the specific-heat data, as depicted in the inset.

Figure 7

(a) The dc magnetic susceptibility measured at 5 kOe and 7-T fields, indicating a cusp in the magnetization corresponding to a possible transition at 5 K. (b) Measurements of the dielectric constant in the same temperature range, as measured at different magnetic fields.

Figure 8

(a) The low-temperature $MH$ isotherms as measured at different temperatures. (b) The $dM/dH$ of these isotherms to clearly identify the metamagnetic transition. The inset depicts the temperature evolution of the critical field $H_C$ of the metamagnetic transition, with the solid line being a fit of the form $AT{}^2+BT+C$.

Figure 9

The $H\text{−}T$ phase diagram of ${\mathrm{Fe}}_4{\mathrm{Ta}}_2{\mathrm{O}}_9$ as determined from magnetic $(\square )$, specific-heat $(\times )$, dielectric $(\circ )$, and pyroelectric $(△)$ investigations. The dotted lines do not represent experimentally determined phase boundaries and are only meant as a guide to the eye.