One of the major breakthroughs associated with multiferroicity in recent years is the discovery of ferroelectricity generated by specific magnetic structures in some magnetic insulating oxides such as rare-earth manganites RMnO3 and RMn2O5. An unresolved issue is the small electric polarization. Relatively large electric polarization and strong magnetoelectric coupling have been found in those manganites of double magnetic ions: magnetic rare-earth R ion and Mn ion, due to the strong R-Mn (4f-3d) interactions. DyMn2O5 is a representative example. We unveil in this work the ferrielectric nature of DyMn2O5, in which the two ferroelectric sublattices with opposite electric polarizations constitute the ferrielectric state. One sublattice has its polarization generated by the symmetric exchange striction from the Mn-Mn interactions, while the polarization of the other sublattice is attributed to the symmetric exchange striction from the Dy-Mn interactions. We present detailed measurements on the electric polarization as a function of temperature, magnetic field and measuring paths. The present experiments may be helpful for clarifying the puzzling issues on the multiferroicity in DyMn2O5 and other RMn2O5 multiferroics.
Multiferroics have been intensively investigated for ten years since the pioneer works on BiFeO31 and TbMnO3 in 20032. In particular, the discovery of magnetically induced ferroelectrics (the so-called type-II multiferroics) has comprehended our understanding of multiferroicity2,3,4. In these materials, electric polarization P is believed to be correlated with particular magnetic orderings below certain temperatures and thus the cross-coupling between ferroelectricity and magnetism is significant, allowing possible magnetic control of ferroelectricity or/and electric control of magnetism5,6,7,8,9,10,11. To dates, what keeps the research interest alive is the possibility of unveiling microscopic physics which is substantially different from our earlier knowledge and even general principles for guiding the design and synthesis of multiferroics of promising practical applications5,12,13,14,15. It is noted that most discovered type-II multiferroics so far either have low ferroelectric and magnetic transition temperatures or exhibit small electric polarization/weak magnetization.
While conventional ferroelectrics exhibit the electric polarization via the structural symmetry-breaking transitions from high symmetric paraelectric (PE) phase16, for those type-II multiferroics the primary order parameter is magnetic rather than structural. Two major magnetic mechanisms for the ferroelectricity generation have been proposed. One is the asymmetric exchange striction, in which the inverse Dzyaloshinskii-Moriya (DM) interaction associated with the non-collinear spin ordering drives the structural symmetry-breaking6,17,18. The other is the symmetric exchange striction, in which specific collinear spin ordering, such as the E-type antiferromagnetic (AFM) ordering19,20 and ↑↑↓↓ ordering21, drives the structural symmetry-breaking.
Interestingly, another class of multiferroics, in which the symmetric exchange striction is believed to play major roles, is rare-earth manganites RMn2O5 family22. The RMn2O5 family shows complicated lattice distortions and spin structures and exhibits multifold competing interactions, large electric polarization and remarkable magnetoelectric (ME) responses5,16,23. Nevertheless, partially due to the multifold competing interactions, the multiferroic transitions and underlying mechanisms in RMn2O5 are not yet well understood8,9. All members of this RMn2O5 family have similar structural ingredients16. The lattice structure projected on the ab-plane is shown in Fig. 1. The Mn ions are partitioned into Mn3+ and Mn4+, which are coordinated respectively in square pyramid Mn-O units and octahedral Mn-O units. On the ab-plane, the octahedra and pyramids are corner-sharing by either the pyramid bases or pyramid apex and the adjacent pyramids are connected with their bases. Along the c-axis, the octahedral sharing edges constitute linear chains. Each Mn3+ ion is located in between two Mn4+ ions and the R3+ ions are located on the alternative layers between two Mn4+ ions.
In RMn2O5, the Mn spin interactions are characterized by the three dominant components J3, J4 and J5, plus additional long-range components16,24. Their competitions lead to consecutive commensurate antiferromagnetic (C-AFM) and incommensurate AFM (IC-AFM) ordering sequence25,26. Also, the 3d-4f interactions can't be neglected if the R ion has big moment and the strong R-Mn coupling allows even more fascinating spin structure evolution. The ferroelectricity and its magnetic origins are thus far from understanding. Here, we choose DyMn2O5 as a representative example for illustration8,9,24. The paramagnetic phase above temperature T ~ 43 K transits into an IC-AFM phase, followed by a C-AFM phase below TN1 = ~40 K and then by the coexistence of an IC-AFM phase and a C-AFM phase below TN2 ~ 28 K. This coexistence is again replaced by two coexisting IC-AFM phases below TN3 ~ 20 K. At T < TDy ~ 8 K, the Dy3+ spins order independently. The structural and interaction origins for these magnetic transitions were discussed extensively, while no full consistency has been reached8,9,25.
With respect to the magnetic structures, our understanding of the ferroelectricity is even in the earlier stage. While it is believed that the C-AFM phase is ferroelectric and the IC-AFM phase is not, the measured results are not always consistent with this prediction8,9. Basically, the measured P most likely aligns along the b-axis. However, the measured data in experiment by Hur et al show that the P appears below TN1 (TFE1) and changes its sign from negative value to positive one at a certain T lower than TN2 ~ 27 K, giving a feature of ferrielectric (FI) state8. However, in experiment by Higashiyama et al9, the measured P(T) experiences several transitions which correspond one-to-one to the magnetic transitions and the system becomes non-ferroelectric below TDy ~ 8 K (the so-called X-phase) while the ferroelectric nature of this X-phase remains unclear. Besides, the magnetic origins for these transitions were discussed in details16. So far available data on the ME effect of RMn2O5 family are also materials-dependent. Remarkable ME response was observed in the low-T range for those materials with big 4f magnetic moments, where the 3d-4f (R-Mn) coupling is strong enough in determining the magnetic structure8,9,12,26,27.
The inconsistencies and insufficient data, as partially highlighted above, suggest a critical appealing for revisiting the electric polarization and its response to magnetic field in RMn2O5 (here DyMn2O5). On the basis that DyMn2O5 has strong Dy-Mn interactions in addition to the dominant Mn-Mn interactions28, one has reasons to expect a ferrielectric state with more than one polarization component. With no doubt, convincing evidences with this ferrielectric state become primarily critical for understanding the multiferroicity of DyMn2O5 and more generally the RMn2O5 family. In this work, it will be suggested that DyMn2O5 is a ferrielectric composed of two anti-parallel ferroelectric sublattices. The electric polarizations of the two sublattices have different microscopic origins, with one arising from the Mn-Mn symmetric exchange striction and the other from the Dy-Mn symmetric exchange striction. It is noted that the ME effect can be reasonably explained by this ferrielectric model. We employ a modified pyroelectric current (mPyro) method to track the evolution of the electric polarization upon various paths, while a detailed discussion on the methodology for measuring the polarization and a description of this mPyro method can be found in the Supplementary document.
Multiferroic phase transitions
We first look at the phase transition sequence in terms of specific heat CP, magnetization M and dielectric constant ε as a function of T, as shown in Fig. 2. For reference, the released current Itot(T) (i.e. Ipyro(T)) using the mPyro method at a warming rate of 2 K/min is shown in Fig. 2(d), while a demonstration of the mPyro method in precisely measuring the pyroelectric current released from polarized charges is given in the Supplementary document. The CP(T) curve shows clear anomalies roughly at TN1 ~ 40 K, TN2 ~ 27 K and TDy ~ 8 K, while the peak at TN3 ~ 20 K, if any, is weak. These anomalies reflect the sequent magnetic transitions from the paramagnetic phase to the C-AFM phase, to the coexisting IC-AFM phase plus C-AFM phase, then to the two IC-AFM coexisting phases and eventually to the independent Dy3+ spin order plus IC-AFM phase, consistent with earlier reports26. However, no features corresponding to these transitions, except the independent Dy3+ spin ordering at TDy, were observed in the measured M-T data, mainly due to the fact that the Dy3+ moment is much bigger than the Mn3+/Mn4+ moments. The anomalies in the ε-T curve at these phase transitions reflect the magneto-dielectric response, as revealed earlier8. Interestingly, a series of anomalies in the Ipyro-T curve at these transition points are available, as shown in Fig. 2(d), consistent with earlier report8 too, evidencing the strong ME effect. In addition, these magnetic transitions may be path-dependent and the features in the cooling run are different from those in the warming run. Our data on the electric polarization below also illustrate this dependence.
Nonzero polarization of the X-phase
The measured Ipyro-T curves and as-evaluated P-T curves under Epole = 10 kV/cm are plotted in Fig. 3, given different starting temperatures (Tend), where the Tend is the temperature to which the sample is cooled down from high-T paramagnetic state under Epole = 10 kV/cm. It is seen that the Ipyro-T curves exhibit clear anomalies at the magnetic transition points (TN1, TN2, TN3 and TDy) and the P-T curve at Tend = 2 K is similar in shape to that reported in Ref. 8.
We suggest that the X-phase is ferrielectric (i.e. ferroelectric in general sense). First, the measured data in Fig. 3(a) and (b) indicate that the X-phase has nonzero electric polarization. The pyroelectric current in both the X-phase region and the other three ferroelectric regions is much bigger than 0.3 pA, the background level in the present experiment. It is also observed that the pyroelectric current depends on the poling field, the bigger the current the higher the field. The mPyro method used in the present experiment is different from the Pole method used in Ref. 9 for the electric polarization measurement (see the Supplementary document). In the Pole method, the current flowing across the sample under a relatively low electric field is measured during the sample cooling. In this case, by assuming that the leakage current at low T is much lower than the polarization current, one may evaluate the electric polarization from the polarization current data directly. As seen in Ref. 9, the measured polarization in the X-phase region was indeed negligible, suggesting that the X-phase is non-ferroelectric. Clearly, if the X-phase is antiferroelectric, or ferrielectric with two comparable antiparallel polarization components, the polarization current can be small and even comparable with the leakage current. In this sense, the Pole method may not be applicable for identifying the ferrielectric or antiferroelectric state.
Second, each measured P(T) curve shown in Fig. 3(a) ~ (d) indicates a negative-positive sign change with decreasing T, suggesting immediately that DyMn2O5 is a ferrielectric (FI) rather than a normal ferroelectric8. The sign change would be the consequence of competition between the two ferroelectric sublattices whose polarization components should exhibit different T-dependences. In this case, careful measurement using the mPyro method can provide critical data on details of the ferrielectric state and the different T-dependences.
Given a fixed Epole, the Ipyro(T) and thus the P(T) show remarkable Tend-dependent behaviors, i.e. path-dependent. To see clearly this path-dependence, the Ipyro-T curve with Tend = 2 K is shown by a thin dashed line in each plot of Fig. 3. The temperature TP= 0, at which the P(T) changes its sign, is plotted as a function of Tend in Fig. 4(a). The TP= 0 shifts ~9 K when Tend increases for ~10 K, implying that the ferrielectric state is not robust against thermal fluctuations (T) or external field (Epole). Supposing that the ferrielectric state is composed of two sublattices, one expects that at least one of them is strongly T-dependent or Epole-dependent. What surprising us is the Ipyro-T curves as Tend > 12 K, some of which are plotted in the right column of Fig. 3. In spite of positive Epole, the measured P data below TN1 are negative. The negative Ipyro peak at TN1 remains nearly unchanged even with Tend = 38 K, very close to TN1 = 40 K. Such a negative P can't be possible in a normal ferroelectric, unless the P has two components which are anti-parallel to each other.
The Tend-dependences of the Ipyro(T) and P(T) curves are strange at the first glance. It is reflected that the electric polarization has the magnetic origin, since no structural phase transitions occur below TN1. We present in Fig. 4(b) the measured P value at Tend, i.e. P(Tend), where the P(T) curve with Tend = 2 K is inserted for comparison. For a normal ferroelectric, the P(Tend) should overlap with the P(T) by setting Tend = T. Here, the overlapping only occurs below TDy, noting that the P(Tend) is always larger than the P(T). The difference between them maximizes at Tend = T ~ 10 K and ~24 K and becomes negligible as Tend → TN1, suggesting that the magnetic transitions below TN1 have the path-dependent characteristic, while the first-order or second-order nature of these transitions deserves for additional clarification. In fact, combining the P(Tend) and P(T) data generates a double-loop like hysteresis, as shown in Fig. 4(b).
For DyMn2O5, the symmetric exchange striction effect arising from the specific Mn/Dy spin alignment is the main mechanism for the electric polarization16. For a simplification consideration, we don't take into account the contributions from the noncollinear spin orders. However, the effect of the independent Dy spin ordering at TDy imposes significant effect on the electric polarization, due to the strong Dy-Mn interactions and thus will be considered.
Referring to relevant literature on DyMn2O524, we present in Fig. 5(a) the spin structure projected on the ab-plane over the T-range between TN1 and TDy. The square pyramidal and octahedral structural units surrounding the Dy3+, Mn3+ and Mn4+ spins are drawn for a better view in Fig. 5(b). The light gray and gray structural units shift 1/4 lattice unit from each other along the c-axis16. Along the b-axis, one finds two types of three-spin blocks each centered on a Mn4+ spin, as shown in Fig. 5(c) and (d), respectively. One is block A, consisting of one Mn4+-O octahedron connected with two pyramid units each with one Mn3+ spin inside (Fig. 5(c)). The other is block B, consisting of one Mn4+-O octahedron connected with two Dy3+ spins located in the space surrounded by the MnO6 and MnO5 units (Fig. 5(d)). Because of the symmetric exchange striction, the two Mn3+ ions in the block A shift roughly up and the two Dy3+ ions in the block B shift down with respect to the Mn4+ ions. Therefore, one electric polarization component (PMM) in the block A and one polarization component (PDM) in the block B are generated. They are roughly anti-parallel to each other but align along the b-axis. The whole lattice as the consequence of the alternating stacking of the two types of blocks is therefore a ferrielectric lattice composed of two FE sublattices.
Different from the PMM, the PDM originates from the Dy-Mn interactions and thus depends on the Dy3+ spin order. Above TDy, the Dy3+ spins may order in coherence with the Mn spin ordering around TN1 or TN2, due to the strong Dy-Mn interactions. At T < TDy, this induced Dy3+ spin ordering is partially and gradually replaced by the independent Dy3+ spin ordering, although the details of the Dy3+ spin ordering sequence has not been well understood. To this stage, one has reason to argue that the PDM will show much more significant T-dependence than the PMM. The reason can be discussed considering the weak ordering of the Dy3+ spins themselves. This ordering is sensitive to the 3d-4f interactions and external field. We discuss this issue below from various aspects.
First, the 4f interactions in some transition metal oxides are quite localized and the R3+ spins alone can't order unless the temperature is very low (the ordering point TR is less than ~2 K), as identified in oxides without 3d moments but only the 4f moments, as seen in R2Ti2O7 etc with R = Gd, Tb, Ho and Er etc29, where the Ti4+ has no magnetic moment and thus no 4f-3d interaction is available. In some other oxides, the R3+ spins can't order even at extremely low temperature, leading to spin liquid or spin ice states due to the crystal fields and quantum fluctuations30,31. In these oxides, a magnetic field of ~1.0Tesla is sufficient to break the original spin orders and enforce the parallel spin alignment.
Second, for DyMn2O5 and other RMn2O5/RMnO3 with R = Gd, Ho, Er etc, the situation can be different since the R3+ spins coexist with the Mn spins. The independent R3+ spin ordering can occur at a TR as high as 6 ~ 10 K (here TDy ~ 8 K). Furthermore, if the Mn spin ordering occurs well above TR, an additional R3+ spin ordering at a temperature higher than TR will be induced by the Mn spin orders due to the 4f-3d interactions. These observations suggest that the 4f-3d interactions can enhance the TR value if the sign of interaction is consistent with that of the 4f-4f exchange interaction16,32,33. A typical case is seen in DyMnO3, where the Mn3+ spins order antiferromagnetically at ~38 K and are locked in the noncollinear spiral order at ~20 K. Slightly below this locking point, the Dy3+ spins order in a coherent manner with the Mn3+ spin order. This induced Dy3+ spins order sustains until TDy ~ 7 K at which the independent Dy3+ spin ordering enters34. In addition, a magnetic field of 1.0 ~ 2.0Tesla is sufficient to break the coherent and independent Dy3+ spin orders, while much higher field is needed to melt the Mn spin orders.
The above discussion suggests that the Dy3+ and other rare-earth moments have relatively weak 4f-4f exchange-coupling with respect to the 3d moments such as Mn spins here. This discussion thus serves as the model basis on which the PDM and PMM as a function of T are evaluated, respectively. For simplification, the effect of independent Dy3+ spin ordering below TDy on the Mn spin order is assumed to be weak if any. It can be reasonably assumed that the PMM initiating at TN1 increases rapidly in magnitude with decreasing T and becomes saturated in the low T range, because the Mn spin order is already well developed below TN1. Consequently, the PDM as a function of T can be extracted. Take the data with Tend = 8 K ~ TDy as an example. The measured P(T) data are plotted in Fig. 6(a). The PMM(T) curve is extracted based on the above assumption and then PDM(T) = P(T) − PMM(T) is evaluated. For a clear illustration, the two ferroelectric sublattices on the ab-plane are schematically drawn in Fig. 6(c) and (d) and a combination of them constitutes the ferrielectric lattice in Fig. 6(b). As expected, the PDM increases gradually with decreasing T until T ~ 20 K, below which a much more significant T-dependence than that for the PMM is then exhibited.
As Tend = 2 K ≪ TDy, the effect of the independent Dy3+ spin ordering on the PDM takes effect. At T = Tend, some Dy3+ spins are on the track of the independent ordering, leading to disappearance of PDM at some lattice sites. The PDM sublattice is thus partially melted away, giving rise to a smaller PDM. This is the reason for the low TP = 0 and small |P| below TP = 0, with respect to the case of Tend = 8 K. Here it should be mentioned that the difference in the PDM(T) curve between the case of Tend = 8 K and that of Tend = 2 K reflects the difference in the magnetic structures between the two cases. The origin lies in the fact that the magnetic transition at TDy is path-dependent.
Given the ferrielectric model shown in Fig. 5 and the different PDM(T) and PMM(T) behaviors, a puzzling issue appears: why does the measured PMM (or P) remain negative even though Tend is higher than TN2? For Tend > TN2, the PDM should be much smaller than the PMM and thus a poling by a positive Epole would generate a positive PMM. In this case, the measured Ipyro and P should be positive, contradicting with the measured data. At this stage, we have no convincing explanation of this anomalous phenomenon. One possible reason is that the PDM(T) is sensitive to the Epole. Considering the fact that the Dy3+ spins have weak exchange coupling, as addressed above, one expects that the electric field driven alignment of the Dy3+ spins coherently with the Mn spins would be energetically easy. Therefore, the PDM can be remarkably enhanced by the Epole. If it is the case, the electric poling during the cooling sequence can enhance the PDM remarkably while the PMM is roughly unchanged, so that the PDM around Tend is larger than the PMM in magnitude. This results in the alignment of the PMM opposite to both the Epole and PDM. After the removal of the Epole at Tend, the PDM shrinks back to a value smaller than the PMM. Consequently, the pyroelectric current remains negative. Another possible explanation for this strange phenomenon is the ferroelastic effect in DyMn2O535, which makes the PMM domains be clamped along a direction opposite to the Epole during the poling process. However, this assumption remains to be confirmed.
Obviously, referring to the ferrielectric model, one immediately predicts that the ME parameter ΔP(H) = [P(H) − P(H = 0)] is negative and also remarkably T-dependent, since a magnetic field as big as 1.0–2.0Tesla is sufficient to align the R3+ spins even at an extremely low T9. For DyMn2O5 here, this effect suggests that a magnetic field of 1.0–2.0 Tesla re-aligns the Dy3+ spins along the field direction, while the Mn spins remain robust. Therefore, the ↑↑↓ or ↓↓↑ pattern in the block B is broken, as shown in Fig. 7, leading to the PDM ~ 0. The spin structure in the block A remains roughly unchanged and thus does the PMM. The experimental data conform this prediction, as presented in Fig. 8. In Fig. 8(a) are plotted the P-T data at Tend = 2 K, where the PDM(T) and PMM(T) under H = 0 are presented too. The ΔP(H > 2 T) should not be much less than the PDM in magnitude although their signs are opposite. Our data also support this prediction. The ferrielectric state as a basis for this ME effect is then confirmed. Here, it should be mentioned that the model shown in Fig. 7 assumes that magnetic field H is parallel to the b-axis. Nevertheless, our samples are polycrystalline and the grains/magnetic domains are randomly oriented. Taking into account of the polycrystalline nature, one still can expect that the ↑↑↓ and ↓↓↑ patterns of most block B units in the sample will be broken. This model explanation is thus qualitatively reasonable.
To this stage, we have presented a qualitative explanation of the major features associated with the electric polarization and ME effect in DyMn2O5, based on the proposed ferrielectric model. Nevertheless, several issues remain yet unclear or unsolved: (1) No detailed discussion on the possible ferroelectric phase transitions at the magnetic transition points TN2, TN3 and even TDy, respectively, has been given. (2) The path-dependence of the electric polarization is attributed to the magnetic transitions which are path-dependent. The first-order ot second-order nature of these magnetic transitions remains to be clarified. (3) An uncertain point regarding the present ferrielectric model is the response of the PDM to electric field which is assumed to be remarkable in order to account for the experimental observations. Searching for convincing evidence on this assumption is challenging although the assumption itself is physically reasonable. A careful characterization of the Dy3+ spin structures at various T is critical for dealing with these issues. It was reported that the element specific X-ray resonant magnetic scattering (XRMS) is a powerful tool although neutron scattering may face the problem of large absorption by Dy nuclei36.
In summary, extensive multiferroic measurements on DyMn2O5 have been carried out and the complicated electric polarization behaviors have been characterized. It is revealed that the electric polarization in DyMn2O5 does consist of two antiparallel components, demonstrating the ferrielectric state at low temperature. The two electric polarization components are believed to originate from the symmetric exchange striction. One is generated from the Mn3+-Mn4+-Mn3+ blocks with the ↓↑↑ and ↑↓↓ spin alignments, which is robust against temperature and magnetic field. The other is generated from the Dy3+-Mn3+-Dy3+ blocks with the ↓↓↑ and ↑↑↓ spin alignments, which is sensitive to temperature and magnetic field. The present work represents a substantial step towards a full-scale understanding of the electric polarization in DyMn2O5 and probably other RMn2O5 family members.
Polycrystalline DyMn2O5 samples were used for the present experiments. The samples were prepared by standard solid state sintering. Stoichiometric amount of Dy2O3(99.99%) and Mn2O3(99%) was thoroughly mixed, compressed into pellets and sintered at 1200°C for 24 h in an oxygen atmosphere with several cycles of intermediate grindings. For every sintering cycle, the samples were cooled down to room temperature at 100°C per hour. The as-prepared samples were cut into various shapes for subsequent microstructural and property characterizations. The sample crystallinity was checked using X-ray diffraction (XRD) with Cu Kα radiation at room temperature.
Measurements on the specific heat (CP), magnetization (M) and dc magnetic susceptibility (χ), dielectric susceptibility (ε) and electric polarization (P) of the samples were carried out. All the data presented in this work were obtained from the polycrystalline samples. The M and χ were measured using the Quantum Design Superconducting Quantum Interference Device (SQUID) in the zero-field cooled (ZFC) mode and field-cooling (FC) mode, respectively. The cooling field and measuring field are both 1000 Oe. The Cp was measured using the Quantum Design Physical Properties Measurement System (PPMS) in the standard procedure.
The polarization P was measured using the modified pyroelectric current (mPyro) method with different starting temperature Tend = 2 K − 38 K, respectively. Each sample was polished into a thin disk of 0.2 mm in thickness and 10 mm in in-plane dimension and then sandwich-coated with Au layers as top and bottom electrodes. The measurement was performed using the Keithley 6514 A and 6517 electrometers connected to the PPMS. In details, each sample was submitted to the PPMS and cooled down to ~100 K. Then a poling field Epole ~ 10 kV/cm was applied to the sample until the sample was further cooled down to Tend, at which the sample was then short-circuited for sufficient time (>30 min) in order to release any charges accumulated on the sample surfaces or inside the sample. The recorded background current noise amplitude was ~0.3 pA. Then the sample was heated slowly at a warming rate up to a given temperature T0 = 60 K > TN, during which the released current Itot was collected. Similar measurements were performed with different warming rates from 1 K/min to 6 K/min and the collected Itot data are compared to insure no contribution other than pyroelectric current Ipyro. Finally, polarization P(T) was obtained by integrating the collected Ipyro(T) data from T0 down to Tend. The validity of this procedure was confirmed repeatedly in earlier works15 and the data presented in the Supplementary document.
In addition, the ε data at various frequencies as a function of T were collected using the HP4294A impedance analyzer with an ac-bias field of ~50 mV. Besides the ε-T data and P-T and data, we also measured the response of P to magnetic field H in two modes. One is the isothermal mode with which the variation in P in response to the scanning of H was detected and the other is the iso-field mode with which the P-T data under a fixed H were collected. By such measurements, one can evaluate the ME coupling of the samples. We define ΔP(H) = P(H) − P(H = 0) as the ME parameter.
We also employed the PUND method to obtain the P-E loops at various temperatures, using the identical procedure as reported in literature e.g. Ref. 37. Our data are quite similar to reported ones from other groups (see the Supplementary document).
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This work was supported by the National 973 Projects of China (Grants No. 2011CB922101), the Natural Science Foundation of China (Grants Nos. 11234005, 11374147, 51332006, 51322206) and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.
The authors declare no competing financial interests.
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Zhao, Z., Liu, M., Li, X. et al. Experimental observation of ferrielectricity in multiferroic DyMn2O5. Sci Rep 4, 3984 (2014). https://doi.org/10.1038/srep03984
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