Molecular ferroelectric with low-magnetic-field magnetoelectricity at room temperature

Magnetoelectric materials, which encompass coupled magnetic and electric polarizabilities within a single phase, hold great promises for magnetic controlled electronic components or electric-field controlled spintronics. However, the realization of ideal magnetoelectric materials remains tough due to the inborn competion between ferroelectricity and magnetism in both levels of symmetry and electronic structure. Herein, we introduce a methodology for constructing single phase paramagnetic ferroelectric molecule [TMCM][FeCl4], which shows low-magnetic-field magnetoelectricity at room temperature. By applying a low magnetic field (≤1 kOe), the halogen Cl‧‧‧Cl distance and the volume of [FeCl4]− anions could be manipulated. This structural change causes a characteristic magnetostriction hysteresis, resulting in a substantial deformation of ~10−4 along the a-axis under an in-plane magnetic field of 2 kOe. The magnetostrictive effect is further qualitatively simulated by density functional theory calculations. Furthermore, this mechanical deformation significantly dampens the ferroelectric polarization by directly influencing the overall dipole configuration. As a result, it induces a remarkable α31 component (~89 mV Oe−1 cm−1) of the magnetoelectric tensor. And the magnetoelectric coupling, characterized by the change of polarization, reaches ~12% under 40 kOe magnetic field. Our results exemplify a design methodology that enables the creation of room-temperature magnetoelectrics by leveraging the potent effects of magnetostriction.

1.From Fig. S2, the authors claimed that the phase transition with a pair of thermal anomaly peaks was observed at temperatures of 321.5/338.1 K on cooling and heating, suggesting a discontinuous first-order phase transition.Nevertheless, from Fig. 1(b) and Fig. 3(f), one could find that the SHG intensity and ferroelctric polarization droped to zero continuously, respectively, indicating the second-order phase transition.Could the authors provide clarification on this? 2.Along c-axis, the polarization-electric field (P-E) hysteresis loop with saturated polarization (PS) reaching up to 6 μC cm-2, which was mentioned in the text, was not found in Fig. 1(c).
3.In Fig. S5, it was shown that the χMT value was 4.79 cm3 mol−1 K, slightly higher than the expected value of 4.375 cm3 mol−1 K for single Fe(III) ions (S = 5/2 and g = 2.0).The authors claimed that this difference in susceptibility was primarily attributed to orbital contributions resulting from spin-orbit coupling.If the dissociative [FeCl4]− anion as magnetic impurity existed in single crystal, it maybe also result in slightly higher paramagnetic value of susceptibility.Thus, the purity of single crystal and effective moment should be further tested to identify the orbital contributions resulting from spin-orbit coupling.
4.In Fig. S5, the curve of χMT versus T increases with temperature ascending, and then keeps a constant, implying the low-temperature antiferromagnetism crossover into hightemperature paramagnetism.The antiferromagnetism has been further identified by the DFT calculation.Around 323K, the authors claimed the occurence of paramagnetic phase transition.It may be a ferroelectric transition accompanied by structural transition rather than a magnetic phase transition.May the authors please clarify?Furthermore, at low temperatures, the antiferromagnetic order and ferrolectric order coexist, i.e., multiferroics.Is there any intrinsic ME coupling at low temperatures, compared to the room temperature paramagnetic ME coupling induced by low magnetic fields?5.Fig.1(d) was still labelled as Fig. 1(c).It should be revised.

Reviewer #2 (Remarks to the Author):
MANUSCRIPT Molecular ferroelectric with low-magnetic-field magnetoelectricity at room temperature The authors investigated the paramagnetic ferroelectric molecule i.e. [TMCM][FeCl4] shows the coupled magnetic and electric polarizabilities, providing multiple high quality experimental evidence to support the claim along with theoretical results obtained from DFT calculations.Highlighting the stretching of the Cl-Cl bonds and change sphericity of the molecules leads to the robust ME coupling effect.It is commendable to see these exotic properties at the room temperature coupled with a low-magnetic-field in this type of molecule different from the traditional inorganic ferroelectric materials.However, at few points adding more DFT or theoretical evidence will highly elevate the impact of the current work, this manuscript could be considered for publication once the following issues has been addressed.[1] Author had evidence from the DFT calculations that support the experimental results such as lattice parameters and magnetic moment.However, it would be highly recommended to calculate the ferroelectric polarization value for this molecule using DFT.It won't be as trivial in comparison to the paramagnetic states.
[2] Fig. 1 labels were not in order, also the information such as on line 107 "6 μC cm−2 along c-axis" not shown anywhere in the plots.[3] Author should consider some good color scheme to plot the molecule, difficult to distinguish H atoms.
[4] "The ferroelectric domains manifest as spike-like patterns that reflect distinct polarization orientations", author should acknowledge the prior theoretical work citing the Carbon Trends 11 (2023): 100264, showing the significance of the domain wall roughness associated with the FE-domains in the traditional ABO3 material.
[5] On line 133, author mentioned "This transition can be associated with changes in orbital contributions related to the structural phase transition experienced by the material", please provide the appropriate evidence or prior work to support this claim.
[6] Similarly, on line 164, please provide the supporting evidence (theoretical or experimental) for the claim "could also lead to a decrease in the energy barrier of cationic motion, which may decrease the ferroelectric polarization."[7] Author should consider rewriting this sentence on line 211 "volume occupancy of [FeCl4]− anions", what happens to volume occupancy?[8] Author should specify the meaning or reason showing different colors in the Supplementary Figure 6? [9] Author should rewrite the explanation of figure 1d on line 115-116

Reviewer #3 (Remarks to the Author):
In this work, the authors claim proposing a methodology for constructing single phase roomtemperature ME ferroelectrics by harnessing magnetostriction via spin-orbit coupling.Although the subject of magnetoelectricity is intriguing, most of the conclusions of the different techniques remain vague, the outcomes of the manuscript are in my opinion seems contradictory I can not recommend the acceptance due to following reasons.
--The overall presentation is poor, falls short of the high standards expected by Nature Communications.The text is marred by numerous errors, such as an incorrect icon in fig. 1 and a misalignment between the content depicted in fig.1c and its corresponding text description in the main text.Several images are typically not standardized.
--The authors claim proposing a methodology for constructing single phase roomtemperature ME ferroelectrics by leveraging magnetostriction via spin-orbit coupling.While magnetostrictive mechanisms in magnetoelectric materials have been documented, it is important to note that such mechanisms likely exist in various ME materials with differing contributions.Consequently, the claims regarding the methodology have been significantly overstated.
--The compound under investigation does not seem to be a new material.Without diving too deep into the literature, also found that significant overlap with characterization data found in reference 27 provided by the authors.
--The paper contains numerous instances of contradictory data, such as: -In fig.1c, a substantial polarization value is detected at 323 K, while DSC data contradicts this observation by indicating the compound is in the paraelectric phase at this temperature.the authors demonstrate a significant polarization value detected at 323 K.Even more confusing, the data in fig.3f indicates that the polarization value at 323 K is inexplicably 0.
-The magnetostriction results obtained by In-situ single-crystal X-ray diffraction also appear inconsistent with theoretical calculation results.
--Many data provided by the author appear Inconsistencies.For instance, in fig.1f, the display indicates 70 V, yet the accompanying icons suggest 20 V. Supplementary Table 1 present the values along axis 'a' with clear elongation, in contrast to the author's values, which appear shortened.In summary, the dataset appears messy and inconsistent.
Considering these issues, this manuscript fails to meet the standards required for publication in a prestigious journal such as Nature Communications.coupling was demonstrated at low magnetic fields.They revealed that the magnetostriction effect induced by the in-plane magnetic field was responsible for the robust ME coupling.This magnetostriction effect manifested the structural deformation with the stretching of halogen Cl‧‧‧Cl contactings and the change in volume occupancy of [FeCl4]-anions at low magnetic fields.Furthermore, the magnetostriction effect is qualitatively simulated by density functional theory (DFT) calculations.The methodology seems to be sound.The findings presented in the manuscript are overall scientifically sound and supported by the data and detailed analysis, I recommend publication of the work in Nature communications after the below concerns are addressed.

Response:
We thank the reviewer for his/her careful reading, precise summary, and recommendation.
Comment 1: From Fig. S2, the authors claimed that the phase transition with a pair of thermal anomaly peaks was observed at temperatures of 321.5/338.1 K on cooling and heating, suggesting a discontinuous first-order phase transition.Nevertheless, from Fig. 1(b) and Fig. 3(f), one could find that the SHG intensity and ferroelctric polarization droped to zero continuously, respectively, indicating the second-order phase transition.Could the authors provide clarification on this?
Response: Many thanks for this suggestion.In general, the type of phase transition (first-order or second-order) for ferroelectric materials can be determined by DSC, SHG, and pyroelectric curves.There are obvious differences in DSC curves between the first-order and second-order transitions.The first-order phase transition has larger thermal entropy change and thermal hysteresis (e.g.Fig. R1a) compared with those of second-order phase transition (e.g.Fig. R1c).The DSC curve of (TMCM)[FeCl4] is close to the first-order phase transition (see Fig. R2a).Moreover, the temperature dependent SHG strength are also significantly different.For the first-order phase transition, the SHG strength changes less with temperature below TC and presents a discontinuous sharp decrease to 0 at (near) TC, as shown in Fig. R1b.For the second-order phase transition, the SHG intensity presents a continuous decrease with temperature, as shown in Fig. R1d.The temperature dependence of SHG intensity of our (TMCM)[FeCl4] sample tends to be a first-order phase transition (Fig. R2b).Furthermore, the temperature-dependent pyroelectric curves for the first-order and second-order transitions are also significantly different.The polarization (P) varies less with temperature for the first-order phase transition before a discontinuous sharp decrease of polarization to 0 near TC, as shown in Fig. R1b.For the second-order phase transition, the P-T curve presents relatively uniform and continuous decrease over a large temperature range (e.g.~50 K) till TC, as shown in Fig. R1e.
The polarization of (TMCM)[FeCl4] decreases sharply from a large value to 0 in a very narrow T-range (~5 K) under different magnetic fields (Fig. 3(f)).Therefore, all these results indicate that the phase transition of (TMCM)[FeCl4] is likely to be a first-order one.
Corresponding revision: Lines 92-95 are revised as "The SHG signal changes sharply around 320 K and becomes less-changed below 315 K.Such a behavior, with a pair of thermal anomaly peaks (321.5 K and 338.1 K) in the DSC curves on cooling and heating (Supplementary Fig. 2), suggesting a discontinuous first-order phase transition." Comment 2: Along c-axis, the polarization-electric field (P-E) hysteresis loop with saturated polarization (PS) reaching up to 6 μC cm -2 , which was mentioned in the text, was not found in Fig. 1(c).
Response: Thank you very much for the reviewer's reminder.We have corrected it and added the P-E curve in the revised Supporting Information (Fig. S3).
Comment 3: In Fig. S5, it was shown that the χMT value was 4.79 cm 3 mol −1 K, slightly higher than the expected value of 4.375 cm 3 mol −1 K for single Fe(III) ions (S = 5/2 and g = 2.0).The authors claimed that this difference in susceptibility was primarily attributed to orbital contributions resulting from spin-orbit coupling.If the dissociative [FeCl4] − anion as magnetic impurity existed in single crystal, it maybe also result in slightly higher paramagnetic value of susceptibility.Thus, the purity of single crystal and effective moment should be further tested to identify the orbital contributions resulting from spin-orbit coupling.
Response: It is a good question.We have again collected direct-current magnetic data of complex 1.
To ensure the purity of the sample, we measured the magnetic properties of powder sample from a big crystal.This process can exclude possible magnetic impurity attached at the surfaces of multiple crystals.
The result has been added in the revised Supporting Information (Fig. S6).Now the deviation between the experimental value and expected value has been reduced from 9.5% to 0.6%, implying a very nice agreement.
The corresponding revision: "At room temperature, the χMT value is 4.401 cm 3 mol −1 K, very close to (slightly higher than) the expected value of 4.375 cm 3 mol −1 K for single Fe(III) ions (S = 5/2 and g = 2.0)."Comment 4: In Fig. S5, the curve of χMT versus T increases with temperature ascending, and then keeps a constant, implying the low-temperature antiferromagnetism crossover into high-temperature paramagnetism.The antiferromagnetism has been further identified by the DFT calculation.Around 323K, the authors claimed the occurence of paramagnetic phase transition.It may be a ferroelectric transition accompanied by structural transition rather than a magnetic phase transition.May the authors please clarify?Furthermore, at low temperatures, the antiferromagnetic order and ferrolectric order coexist, i.e., multiferroics.Is there any intrinsic ME coupling at low temperatures, compared to the room temperature paramagnetic ME coupling induced by low magnetic fields?
Response: The reviewer's opinion is correct.It is paramagnetic at high temperature.The anomaly of χMT at 323 K was owing to the structural transition.Indeed, there are intrinsic ME couplings at low temperatures.Unluckily, in our laboratory, we do not have instruments to characterize the ME coupling at low temperatures, therefore we did not discuss it in this work.If suitable characterization methods are available in the future, we will try to study multiferroics behavior at low temperatures.Even though, it does not affect our conclusion on room-temperature ME behavior, which is even more interesting for potential applications than the low-temperature one.
Response: Thanks for pointing out this typo.We have corrected it.

Response to Reviewer #2
General Comment: The authors investigated the paramagnetic ferroelectric molecule i.e.
[TMCM][FeCl4] shows the coupled magnetic and electric polarizabilities, providing multiple high quality experimental evidence to support the claim along with theoretical results obtained from DFT calculations.
Highlighting the stretching of the Cl-Cl bonds and change sphericity of the molecules leads to the robust ME coupling effect.It is commendable to see these exotic properties at the room temperature coupled with a low-magnetic-field in this type of molecule different from the traditional inorganic ferroelectric materials.However, at few points adding more DFT or theoretical evidence will highly elevate the impact of the current work, this manuscript could be considered for publication once the following issues has been addressed.

Response:
We thank the reviewer for his/her careful reading, precise summary, and recommendation.
Comment 1: Author had evidence from the DFT calculations that support the experimental results such as lattice parameters and magnetic moment.However, it would be highly recommended to calculate the ferroelectric polarization value for this molecule using DFT.It won't be as trivial in comparison to the paramagnetic states.
Response: Thanks for this suggestion.In the revised manuscript, we have calculated the ferroelectric polarization for this molecule based on the structure of ground state (G-AFM) for reference, since the room-temperature paramagnetic state can not be directly simulated in the DFT calculation.According to our calculation, the polarization is 0.31 μC cm -2 along the a-axis and 8.23 μC cm −2 along the c-axis, very close to (and slightly higher than) the experimental values at room temperature (0.32 μC cm −2 along the a-axis (Fig. 1c) and 6.1 μC cm −2 along the c-axis (Fig. S3)).
The corresponding revision: "Since the room-temperature paramagnetic state can not be directly simulated in the DFT calculation, the theoretical value of polarization are estimated based on the structure of ground state (G-AFM), which leads to 0.31 μC cm -2 along the a-axis and 8.23 μC cm -2 along the c-axis, very close to (and slightly higher than) the experimental values at room temperature (0.32 μC cm -2 along the a-axis (Fig. 1c) and 6.1 μC cm -2 along the c-axis (Fig. S3)." Comment 2: Fig. 1 labels were not in order, also the information such as on line 107 "6 μC cm −2 along c-axis" not shown anywhere in the plots.

Response:
We have fixed the labels in Fig. 1 and added Fig. S3 in the revised Supporting information.
Comment 3: Author should consider some good color scheme to plot the molecule, difficult to distinguish H atoms.
Response: Following this suggestion, we have changed the color scheme, as follows.these data do not touch the core issue of present work, i.e. the room-temperature magnetoelectricity.In fact, even the ferroelectricity itself had not been confirmed in Ref. 27, without the ferroelectric hysteresis loops.
In contrast, our work (especially Fig. 3) unambiguously demonstrates that it is a molecular ferroelectric material, and own significant ME coupling at room temperature at low magnetic field.Thus, our work is very important for ME coupling studying.Response: Thanks for this comment.As shown in Fig. S2a, the phase transition temperature of compound 1 was 338.1 K. Thus, it is ferroelectric at 323 K according to the DSC data.In our previous measurements of SHG curves, the temperature sensing probe was placed on the top of sample, and the heating/cooling temperature scan rate was relatively fast (15 K/min) as shown in Fig. R4c, resulting in an inconsistent phase transition temperature compared to DSC measurements shown in Fig. R4a.
Therefore, we adjusted the temperature sensing probe to the surface of sample and set the scan rate of 5 K/min, as shown in Fig. R4d, the new result is basically consistent with the result of DSC measurement, as shown in Fig. R4b.We have re-measured the pyroelectricity of compound 1 under different magnetic fields (Fig. 3f).The phase change temperature is 335 K, which is same with DSC resulting.Besides, the P-E curve of compound 1 were re-measured at 310 K (Fig. 1c and S3).

Comment 5:
The magnetostriction results obtained by In-situ single-crystal X-ray diffraction also appear inconsistent with theoretical calculation results.
Response: Thanks for this comment.Considering the paramagnetic state can not be directly mimicked in the DFT calculation, instead the lattice constants (a, b, c) of ground state (G-AFM) are used to qualitatively simulate the magnetostrictive effect.Although the G-AFM state is not exactly equal to the paramagnetic state in experiment, the change of lattice constants between G-AFM and FM can also reveal that there is a moderate magnetostrictive effect at zero temperature.A quantitative agreement is impossible for current computational techniques.
Comment 6: Many data provided by the author appear Inconsistencies.For instance, in fig.1f, the display indicates 70 V, yet the accompanying icons suggest 20 V. Supplementary Table 1 present the values along axis 'a' with clear elongation, in contrast to the author's values, which appear shortened.In summary, the dataset appears messy and inconsistent.

Response:
We sincerely apologize for these mistakes and improper statements.We have carefully checked full manuscript and corrected all mistakes in revised manuscript.

REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): In the revised manuscript, the authors have made critical improvements and also made a further comparison with theoretical (DFT) calculation, all my questions and comments have been taken care of.On this basis, I think the present version now is suitable for the publication in Nature Communications.

Reviewer #2 (Remarks to the Author):
Remarks to the Author: In the second revision of the manuscript, authors addressed all the comments raised in the earlier version.Performing DFT calculations for ferroelectric polarization confirms the credability of the experiments as well as elevate the impact of the paper.Furthermore, refering additional suppporting refereces increases the readability of the manuscript.
I would suggest this manuscript should be accepted.

Reviewer #3 (Remarks to the Author):
Hu et al.'s paper entitled, "Molecular ferroelectric with low-magnetic-field magnetoelectricity at room Temperature: Despite the authors' diligent efforts to address many of the concerns raised during the initial review process, while the subject matter of the manuscript remains intriguing, numerous unclear and even erroneous elements persist, preventing it from meeting the high standards expected by Nature Communications.For example, the compound belongs to a C2 point group, Cm space group, I believe that's not correct.the intrinsic piezoelectricity in two direction can be seen in Supplementary fig. 4 ?, what are the two directions ?There is a distinct inconsistency between the image and the text content.The icon in Supplementary fig. 4 refers to fig.3a, which, in reality, does not exist.
The main text described the topography and reversible domain along the c-axis in Supplementary fig.Once again, the revised manuscript still contains many issues, and publication is not recommended.

Fig. R2 .
Fig. R2.Characteristics of our ferroelectric transition, which is obviously the first-order one.

Comment 4 :
The paper contains numerous instances of contradictory data, such as: In fig.1c, asubstantial polarization value is detected at 323 K, while DSC data contradicts this observation by indicating the compound is in the paraelectric phase at this temperature.the authors demonstrate a significant polarization value detected at 323 K.Even more confusing, the data in fig.3findicates that the polarization value at 323 K is inexplicably 0.

Fig. R4 .
Fig. R4.Comparison of SHG measurements with different configurations of temperature sensing.
5. However, none of these actually exist in Supplementary parts.During estimating the ME coupling: fig.3f in main text used the UCS diagram, the value is difficult to be distinguished.Supplementary fig.11 mentioned fig.4e, however, this also doesn't present.What is doop ?Supplementary fig.11 reveals the peak at +1kOe is almost the same as the one at 0 Oe, this clearly contradicts the main text description.