Highly nonlinear magnetoelectric effect in buckled-honeycomb antiferromagnetic Co4Ta2O9

Strongly correlated materials with multiple order parameters provide unique insights into the fundamental interactions in condensed matter systems and present opportunities for innovative technological applications. A class of antiferromagnetic honeycomb lattices compounds, A4B2O9 (A = Co, Fe, Mn; B = Nb, Ta), have been explored owing to the occurrence of linear magnetoelectricity. From our investigation of magnetoelectricity on single crystalline Co4Ta2O9, we discovered strongly nonlinear and antisymmetric magnetoelectric behavior above the spin-flop transition for magnetic fields applied along two orthogonal in-plane directions. This observation suggests that two types of inequivalent Co2+ sublattices generate magnetic-field-dependent ferroelectric polarization with opposite signs. The results motivate fundamental and applied research on the intriguing magnetoelectric characteristics of these buckled-honeycomb lattice materials.

www.nature.com/scientificreports/ lattices, similar to the magnetic structure of Co 4 Nb 2 O 9 21 , the single crystalline CTO reveals strongly nonlinear magnetoelectric effect which is unique among A 4 B 2 O 9 (A = Co, Fe, Mn and B = Nb, Ta) compounds 20,30,[33][34][35][36] . This suggests the existence of two different polarization components originating from inequivalent Co 2+ sublattices. Our nontrivial discovery calls for further experimental and theoretical studies to reveal the underlying microscopic mechanism.

Results and discussion
CTO crystallizes in a trigonal P3c1 structure with unit cell dimensions of a = 0.517 nm, and c = 1.413 nm, obtained from the single crystal X-ray diffraction experiment (see Supplementary Information S1 for details). The crystallographic structures viewed from the top and side are depicted in Fig. 1a,b, respectively. Two dissimilar types of honeycomb layers are stacked alternatingly along the c axis. One layer consists of six edge-shared CoO 6 octahedra in the same plane, while the other consists of corner-shared octahedra buckled in a zig-zag arrangement around the ring 20 . Recent neutron diffraction measurements on single crystals of CTO 37 reveal a consistent result with the magnetic order shown in Fig. 1a,b when assuming a collinear arrangement of Co 2+ moments. Considering the centrosymmetric trigonal structure with three-fold rotational symmetry about the c axis combined with two types of 180°-oriented antiferromagnetic domains leads to the possible formation of six types of 60°-oriented antiferromagnetic domains.
To examine the magnetic properties of CTO, the T dependence of the magnetic susceptibility, χ = M/H, was measured at H = 0.1 T upon warming after zero-field-cooling. The anisotropic χ, obtained for the H along the three distinguishable axes a, b*, and c, are shown in Fig. 1c. For the two orthogonal in-plane orientations, a and b*, the χ exhibits a sharp anomaly at T N ≈ 20.5 K, indicating the emergence of antiferromagnetic order. The T dependence of C/T measured at zero H also shows a distinct anomaly at T N (Fig. 1d). Above T N , the χ for the two in-plane orientations decreases smoothly with T with nearly identical shapes. On the other hand, a weak anomaly at T N is observed in the χ for the c axis.
The overall T dependence of χ, compared between in-plane and out-of-plane orientations, shows strong magnetic anisotropy, suggesting the in-plane antiferromagnetic alignment of Co 2+ spins. The shape of χ curve for a and b* axes are different below T N and the faster decrease of χ for the a axis upon lowering T is observed because the spins in two types of the antiferromagnetic domains align along this axis. As T is further decreased, a sudden increase of χ occurs at T C = 6.5 K. The characteristics of this transition were investigated in detail by AC χ measurement, which indicates the formation of a new phase such as a weakly ferromagnetic or/and glass state (see Supplementary Information S2 for details).
The isothermal M for the three inequivalent orientations was measured up to ± 9 T at T = 2 K, as shown in Fig. 2a. The M along the a direction (M a ) shows a broad bending at a low H regime. Upon increasing H further, the M a increases monotonously and reaches 3.7 μ B /f.u. at 9 T. The M b* exhibits a similar H dependence to the M a ; however, the magnetic moment at 9 T is found to be ~ 3.9 μ B /f.u., which is slightly larger than that of the M a . As manifested as the change in slope shown in the magnified plot of the M a (Fig. 2b), the spin-flop transition occurs  31 . On the other hand, the M c increases almost linearly up to 9 T resulting in a magnetic moment of ~ 2.1 μ B /f.u. at 9 T, consistent with the strong magnetic anisotropy observed in the T dependence of anisotropic χ (Fig. 1c). The anisotropic characteristics of magnetoelectric properties were examined through the T dependence of P for the a, b*, and c axes. The magnitude of P was obtained by integrating the pyroelectric current density measured after poling in an electric field along the direction of P and H up to 9 T for the three different orientations, as shown in Fig. 3. Interestingly, the P emerges dominantly along the a axis below T N (P a , Fig. 3a-c) with an unusual T dependence upon increasing H. The other components of P do not vanish (P b* and P c , Fig. 3d-i) similar to the T dependence of P in Co 4 Nb 2 O 9 21 . In detail, Fig. 3b shows the T-dependence of P a at H = 1, 3, 5, 7, and 9 T along the b* axis (H b* ). The P a at H b* = 1 T starts from a negative value of − 13.2 μC/m 2 at 2 K, increases monotonously to zero upon increasing T, and disappears at T N. At H b* = 3 T, P a exhibits the largest negative value of − 32.2 μC/m 2 at 2 K and crosses zero P a at approximately 15 K. A similar trend of change in the sign of P a is observed at H b* = 5 T with an upward shift in the overall magnitude of P a . The P a at H b* = 7 and 9 T retains positive values throughout the whole T range below T N , and shows its maximum magnitude of 55.9 μC/m 2 at 2 K and H b* = 9 T. This strongly nonlinear magnetoelectric behavior is also observed in P a at different values of H a (Fig. 3a). At H a = 1 T, the P a is very small in magnitude and shows the negligible T dependence. The values of P a at H a = 3, 5, and 7 T are all negative at low temperatures. In contrast to the case of an in-plane H, the P a under an applied H c tends to increase gradually as H c is increased, maintaining a positive value throughout the entire range of T below T N (Fig. 3c). The P a at H c = 9 T and 2 K is found to be 78.7 μC/m 2 (Fig. 3c), which is approximately twice that of P a = 34.9 μC/m 2 at H a = 9 T and 2 K (Fig. 3a). Figure 4a shows the T-dependence of dielectric constant for E//a (ε a '), measured at H b* = 9 T and f = 100 kHz. The ε a ' at 9 T exhibits a very sharp peak at 20.02 K with a 2.8% change in its magnitude (at the peak maximum). The sharpness of the peak at 9 T is characterized by the very small full width at half maximum (FWHM) estimated to be only 0.08 K, which indicates a good crystal quality. As H is decreased, the peak of ε a ' shifts progressively to a higher T with a gradual reduction of the peak height (Fig. 4b) and almost disappears at 4 T. At 5 T, a tiny peak in ε a ', with only 0.27% change in the overall magnitude, occurs at 20.37 K.
The nonlinear behavior of P and the intricate relationship between magnetic and electric properties in CTO were examined in detail by comparing the H dependence of P, M, and ε' at 2 K. The isothermal P a was obtained by integrating the magnetoelectric current density, measured by sweeping the H b* between 9 and − 9 T at 2 K after poling in H b* = 9 T and E a = 4.72 kV/cm, as shown in Fig. 5a. Starting from the maximum value of P a = 52.5 μC/m 2 at 9 T, the P a decreases upon decreasing H b* and becomes zero at 6.3 T. As H b* is decreased further, the P a shows a broad minimum at 3.2 T with P a = − 27.5 μC/m 2 . Below H C ≈ 0.3 T, P a disappears. Further decrease in H in the negative direction leads to the antisymmetric H dependence of the P a . The sweeping of H b* from − 9 to + 9 T completes the isothermal P a curve, showing negligible magnetic hysteresis. In Fig. 5b, the magnetodielectric (MD) effect, described by the variation of ε a ' by applying H b* and defined as MD a (%) = ε ′ (H)−ε ′ (0T) ε ′ (0T) × 100 , was measured up to ± 9 T at f = 100 kHz and T = 2 K. The initial curve of MD a exhibits a slight curvature at low H b* regime and the maximum slope at H C ≈ 0.3 T. Above H C , the MD a reduces more gradually which becomes almost www.nature.com/scientificreports/ linear above H b* = 1.5 T. The maximum variation of MD a is found to be approximately − 0.36% at 9 T. The full MD a curve appears to be symmetric because the direction of P a is indistinguishable in the AC excitation of E a for the ε a ' measurement. For a precise comparison with the MD a , the H b* derivative of isothermal M b* , dM b* /dH b* at 2 K is also plotted in Fig. 5c. The dM b* /dH b* increases linearly up to H C and reveals a kink at H C , after which it begins to decrease. To elucidate the H a and H c dependences of P a (Fig. 3a,c), the detailed field dependent behaviors as Fig. 5 are also included in the Supplementary Information S3. The T evolution of strongly nonlinear magnetoelectric effect in CTO is presented, which shows that the major features are preserved at 10 K above T C = 6.5 K. Figure 6 shows the comparison among isothermal P a , M b* , and dM b* /dH b* at M b* up to ± 9 T and T = 5, 10, 15, and 20 K below T N . At 5 K, the overall H b* dependences of P a and   www.nature.com/scientificreports/ M b* tend to behave akin to those at 2 K (Figs. 2a, 5a). In comparison with the P a at 2 K, the maximum value of P a at 5 K and 9 T reduces slightly to 45.1 μC/m 2 (Fig. 6a) and the M b* at 9 T also decreases to ~ 3.72 μ B /f.u. (Fig. 6e). Upon decreasing H b* , a broad minimum of the P a (= − 31.8 μC/m 2 ) occurs at 3.1 T (Fig. 6a) and the dM b* /dH b* at 5 K reveals kinks at H C = ± 0.3 T (Fig. 6i), consistent with the plateau region within H C in the P a curve (Fig. 6a). At 10 K, the broad minimum of P a occurs at 2.9 T with a significantly reduced value of − 8.1 μC/m 2 (Fig. 6b). However, the maximum value of P a = 58.9 μC/m 2 at 9 T is found to be the largest despite the slight decrease of M b* (~ 3.64 μ B /f.u., Fig. 6f). At 15 K, the regime of nearly zero P a extends up to ± 3.0 T with the absence of the broad minimum (Fig. 6c). At 20 K, the P a almost disappears (Fig. 6d) throughout the measurement region of H b* while the M b* shows a linear increase upon increasing H b* and finally becomes ~ 3.50 μ B /f.u. at 9 T (Fig. 6h). Distinctive from the linear magnetoelectric behavior in the isostructural Co 4 Nb 2 O 9 , the electric polarization in CTO arises at the spin-flop transition above which strongly nonlinear and antisymmetric field dependence was observed. The linear magnetoelectric response and controllable electric polarization by rotating magnetic fields 38 in Co 4 Nb 2 O 9 have recently been explained by several theoretical works such as the orbital model incorporating local spin-orbit coupling at the site of Co 2+ ion 39 and symmetry interpretation considering local C 3 point group 40 . In such theoretical analyses, the contributions from two types of magnetic sublattices, which are associated with two dissimilar types of honeycomb layers, to the net electric polarization are not distinguishable. Another theoretical work based on the Hartree-Fock calculations presents a noticeable consequence that each magnetic sublattice produces electric polarization with a different magnitude and direction, each of which varies linearly with the applied magnetic field strength 6 . The superposition of two different contributions leads to a linear behavior in the total polarization. However, the highly-nonlinear magnetoelectric effect of our CTO in the P a under H a and H b* implies the more intricate contribution of each sublattice to the magnetic-field dependent polarization. In particular, above the spin-flop transition, the dominant negative-polarization arising from one sublattice gives rise to the negative net P a , but the gradual increase of the positive-polarization from the other sublattice results in the broad minimum and further increase of the net P a upon increasing the field. Therefore, our results motivate more elaborate theoretical calculations comprising other factors such as additional lattice and magnetic domain contributions, and possible change of magnetic structure driven by electric field poling, which have not been considered in the previous studies.

Conclusion
In summary, we have synthesized single crystals of magnetoelectric Co 4 Ta 2 O 9 and explored magnetic and magnetoelectric properties along different crystallographic orientations. Despite the presence of several off-diagonal components, the dominant magnetic-field-driven change of polarization occurs for the a axis. More importantly, an antiferromagnetic order below T N = 20.5 K leads to a highly nonlinear magnetoelectric effect above the spinflop transition for in-plane magnetic fields. This is clearly different from the linear magnetoelectricity in other isostructural compounds, and indicates the complex evolution of polarization components with opposite signs originating from two different Co 2+ sublattices. Our results provide insights into fundamental magnetoelectric interactions in the family of the buckled-honeycomb magnetoelectric magnets, paving way for the discovery of novel materials for magnetoelectric functional applications.

Methods
Hexagonal plate-like single crystals of CTO were grown by the conventional flux method with NaF, Na 2 CO 3 , and V 2 O 5 fluxes in air 32 . Co 3 O 4 , and Ta 2 O 5 powders were mixed in the stoichiometric ratio and ground in a mortar, followed by pelletizing and calcining at 900 °C for 10 h in a box furnace. The calcined pellet was finely reground and sintered at 1,000 °C for 15 h. After regrinding, the same sintering procedure was carried out at 1,100 °C for 24 h. A mixture of pre-sintered polycrystalline powder and fluxes was heated to 1,280 °C in a Pt crucible. It was melted at the soaking T, slowly cooled to 800 °C at a rate of 1 °C/h, and cooled to room T at a rate of 100 °C/h. The temperature (T) and magnetic-field (H) dependences of the DC magnetization (M) were measured using a vibrating sample magnetometer at T = 2-300 K and H = -9 to 9 T in a physical properties measurement system (PPMS, Quantum Design, Inc.). The specific heat (C) was measured with the standard relaxation method in the PPMS. The T and H dependences of dielectric constant (ε') were observed at f = 100 kHz using an LCR meter (E4980, Agilent). The T and H dependences of electric polarization (P) was obtained by integrating pyro-and magneto-electric currents, respectively, measured after poling in a static electric field (E).