Understanding the multiferroicity in TmMn₂O₅ by a magnetically induced ferrielectric model

Abstract

The magnetically induced electric polarization behaviors in multiferroic TmMn₂O₅ in response to varying temperature and magnetic field are carefully investigated by means of a series of characterizations including the high precision pyroelectric current technique. Here polycrystalline rather than single crystal samples are used for avoiding the strong electrically self-polarized effect in single crystals, and various parallel experiments on excluding the thermally excited current contributions are performed. The temperature-dependent electric polarization flop as a major character is identified for different measuring paths. The magneto-current measurements indicate that the electric polarization in the low temperature magnetic phase region has different origin from that in the high temperature magnetic phase. It is suggested that the electric polarization does have multiple components which align along different orientations, including the Mn³⁺-Mn⁴⁺-Mn³⁺ exchange striction induced polarization P_MM, the Tm³⁺-Mn⁴⁺-Tm³⁺ exchange striction induced polarization P_TM, and the low temperature polarization P_LT probably associated with the Tm³⁺ commensurate phase. The observed electric polarization flop can be reasonably explained by the ferrielectric model proposed earlier for DyMn₂O₅, where P_MM and P_TM are the two antiparallel components both along the b-axis and P_LT may align along the a-axis. Finally, several issues on the unusual temperature dependence of ferroelectric polarizations are discussed.

Introduction

The discovery of magnetically induced ferroelectric (FE) polarization in a number of transition metal oxides which usually have the strong electronic correlation characters represents a milestone for multiferroic physics and materials sciences^1,2,3,4,5,6. Taking perovskite ABO₃ manganites (RMnO₃) as the most extensively investigated multiferroic systems where R is Y or rare-earth^7,8, two major microscopic mechanisms for magnetically induced ferroelectricity have been well accepted. The first mechanism is the collective ionic displacement generated by the Dzyaloshinskii-Moriya (DM) interaction (asymmetric exchange striction) associated with the spin-orbit coupling in non-collinear spin systems such as orthorhombic RMnO₃ with R = Ga, Tb, Dy, and so on^3,9,10,11. The second one is the collective ionic displacement generated by the spin-lattice (symmetric exchange striction) in specific collinear spin systems (e.g. ↑↑↓↓ spin order) such as orthorhombic RMnO₃ with R = Ho, Y, Tm, Lu, and so on^12,13,14,15. While some other mechanisms have also been proposed for individual systems^16,17, the two mechanisms represent the main pillars for the physics of magnetically induced ferroelectricity in the so-called type-II multiferroics⁴.

Nevertheless, besides RMnO₃, another class of manganites, RMn₂O₅, which are also orthorhombic in structure and identified as the type-II multiferroics, are believed to have different physics of multiferroicity but not yet well-understood^{18,19,20,21,22,23,24,25,26,27}. The FE polarizations in most RMn₂O₅ are much larger than those in RMnO₃ and the multiferroic phase transitions are more complicated^23,27,28. The possible reason for such big difference is associated with the stronger spin frustration due to the coexistence of Mn³⁺ and Mn⁴⁺ spins and more seriously distorted lattice structure²⁹. These characters may enable more than three, four, or even more magnetic phase transitions within a narrow range of temperature (T) below 40 K. We take DyMn₂O₅ as an example, which is a representative one of this RMn₂O₅ family of complicated magnetic structure evolution³⁰. Upon cooling from the paramagnetic (PM) state above T = T_N0 ~ 43 K, a series of incommensurate (IC) antiferromagnetic (ICM) and commensurate (C) antiferromagnetic (CM) ordering events are identified, where the moments are believed to be from the Mn spins. It is suggested that DyMn₂O₅ transits into a non-FE ICM phase below T_N0 and then enters a FE CM phase below T_N1 ~ 40 K. The magnetic phase transitions at T_N2 ~ 28 K mark the gradual transition from the FE CM phase to the non-FE ICM phase until T_Dy ~ 9 K below the Dy³⁺ spins form the independent CM order.

Based on the magnetic scenario highlighted above, the FE behaviors of RMn₂O₅ members have been discussed in details^{18,19,20,29,30,31}. The common characters in terms of ferroelectricity, excluding those individual features for respective members, can be summarized from several aspects^11,31. First, an electric polarization P (denoted as P_C) appears in the CM phase below T_N1 and above T_N2, which is quite large. The measured P drops rapidly down to another P (denoted as P_IC) once the CM phase is gradually and partially replaced by the ICM phase below T_N2. The P_IC can possibly be negative in some cases and positive in others. For reference, the measured P(T) data below T_N1, taken from literature for several compounds using the conventional pyroelectric current technique are schematically drawn in Fig. 1(a)^31,32. Second, the two components P_C and P_IC can be separated by assuming various mechanisms for them. The two cases, taking R = Tm and R = Y, are plotted in Fig. 1(b,c) for a guide of eyes^31,33. It has been suggested that component P_C is related to the symmetric exchange striction, i.e. P_C ~ (S_i·S_j) with S_i and S_j the spin moments at two neighboring sites i and j, while component P_IC is ascribed to the asymmetric exchange striction, i.e. P_IC ~ (S_i×S_j). Both P_C and P_IC align along the b-axis. It should be mentioned here that for TmMn₂O₅, third electric polarization P_LT along the a-axis is believed below T ~ T_Tm ~ 5–6 K, which is associated with a long-range commensurate (LCM) ordering of Tm³⁺ spins^34,35. Third, it was revealed that the response of polarization below T_N2, i.e. P_IC, against magnetic field H, is much more remarkable than that of polarization P_C between T_N1 and T_N2. This effect fits the scenario of P_IC ~ (S_i×S_j), noting that the noncollinear spin structure is usually more sensitive to varying H than the collinear structure^36,38.

Figure 1

Schematic presentations of ferroelectric polarization P(T) for several members of RMn₂O₅ for a guide of eyes.

(a) The P(T) curves for R = Y, Dy, Eu, and Tm. (b) The proposed polarization components as a function of T respectively for R = Tm, where the claimed origins for P_C, P_IC, and P_LT are described in text. (c) The proposed polarization components as a function of T respectively for R = Y. These curves are sketched from the data reported in ref. 31.

Nevertheless, one has several reasons to question the above highlighted scenario on the multiferroicity of RMn₂O₅. First, it is seen that the P(T) dependences of these compounds above T_N2, i.e. P_C(T), are roughly similar for different compounds, but the P(T) dependences below T_N2, i.e. P_IC(T), are very different from each other with no rational correlation between the P_IC(T) behavior and the R site ionic size or magnetic moment^22,24. This suggests that the measured P_IC contain some unknown contributions other than P_IC ~ (S_i×S_j). Second, it is noted that all these data were obtained in single crystal samples grown by flux method. These single crystals are claimed to have strong self-polarized effect which would self-polarize the FE domains^32,33, leading to the strong path-relevance of the measured data. This consequence was often mentioned in literature on RMn₂O₅^33,35 to account for those anomalous data on polarization below T_N2. In this sense, the proposed relation P_IC ~ (S_i×S_j) should be questioned too. To avoid this self-polarized effect and its impact on the pyroelectric current data, polycrystalline sample may be even a better choice than single crystal since the small grain size in polycrystalline samples allows a sufficient cancellation of this self-polarized effect if any. Third, the so-called double-wave method (DWM) associated with the Sawyer-Tower circuit was used to measure the polarization-electric field hysteresis loop of these materials³¹. The obtained second hysteresis loops exhibit clear double-loop shape, suggesting possible ferrielectric (FIE) or antiferroelectric (AFE) characters for YMn₂O₅ around T_N2, reviving the earlier proposed FIE model although a number of unclear issues on this model remains to be identified.

In fact, systematic investigations on the behaviors of P(T, H) in polycrystalline DyMn₂O₅ were performed recently using the highly sensitive pyroelectric current technique^29,38,39. The main polarization can be illustrated by a FIE model, in which consists of two roughly antiparallel polarization components. This FIE model reasonably explains the main features of the measured multiferroic behaviors of DyMn₂O₅ below T_N1^29,40. However, this FIE model relies on the R-Mn coupling and it becomes questionable if R is non-magnetic such as R = Y, which remains to be an issue so far. Furthermore and more importantly, additional check of this FIE model with other RMn₂O₅ would be necessary for a consideration of generality. In this work, we intend to investigate the multiferroicity of TmMn₂O₅. Earlier neutron scattering analysis of the magnetic structure and electric polarization of TmMn₂O₅ suggested a qualitatively similar magnetic structure and FE behaviors to those of DyMn₂O₅^21,34. The T-phase diagram in terms of dielectric permeability and IC/C-AFM phase on single crystal TmMn₂O₅ is indeed similar to DyMn₂O₅ although the values of T_N0, T_N1, T_N2 are slightly different³⁴. This allows us an opportunity to revisit this FIE model for understanding the complicated magnetism-induced ferroelectric behaviors of TmMn₂O₅.

Results

Multiferroic phase transitions

Before presenting the Multiferroic phase transitions data, we first give a set of microstructural characterizations results. The lattice structure of orthorhombic TmMn₂O₅ is schematically shown in Fig. 2(a), which clearly indicates the ordered Mn³⁺ and Mn⁴⁺ occupation in the lattice. The occupancy of Tm³⁺ ions can be also seen clearly. In Fig. 2(b), the measured and refinement-evaluated data X-ray diffraction (XRD) θ–2θ patterns at room temperature for a sample is presented. Pure orthorhombic structure with space group of Pbam is clearly identified, as confirmed by the high refinement quality factors shown in the inset of Fig. 2(b). The refined lattice parameters are a = 0.7216 nm, b = 0.8436 nm, and c = 0.5654 nm, well consistent with earlier reported results²¹. Furthermore, the scanning electron microscopy (SEM) images of the broken surface of the sample at several scales are shown in Fig. 3(a~c). It is seen that the grains are short-bar like in shape and very dense. The spatial distributions of the species Tm, Mn, and O on an area shown in Fig. 3(d) are presented in Fig. 3(e–o) respectively, revealing the high element homogeneity. The evaluated chemical composition is close to the nominal one within uncertainty of less than 5%.

Figure 2

(a) A schematic drawing of lattice structure of TmMn₂O₅. (b) Measured XRD θ-2θ spectrum of polycrystalline TmMn₂O₅ sample and the Rietveld method refined data for comparison. The reliability factors R_wp, R_p, and χ² of the refinement are labeled.

Figure 3

SEM images of the polycrystalline sample (a–d). The planar composition distributions of Tm, Mn, and O are presented in (e–g) respectively, as obtained by the EDS imaging with the SEM.

We discuss the measured specific heat (C_P), magnetization (M), and dielectric constant (ε) as a function of T respectively, and the results are summarized in Fig. 4(a~c). In order to exaggerate the features in the C_P ~ T curve, the evaluated d(C_P/T)/dT ~ T curve is inserted in Fig. 4(a) for a comparison. Given the measuring uncertainties from various research groups, the proposed magnetic transition points are nicely reproduced in the present work, with an error of ~ ±1 K, i.e. T_N0 ~ 44 K, T_N1 ~ 35 K, T_N2 ~ 24 K, and T_Tm ~ 6 K^21,34,35. As stated earlier^21,35, T_N0 marks the transition from the PM phase to the high-temperature ICM phase (probably mixed with small amount of CM phase), and T_N1 labels the transition from the ICM phase to the CM phase, followed by the transition from the CM phase to the low temperature ICM phase at T_N2. The anomaly at T_Tm indicates the so-called LCM phase associated with the Tm³⁺ spin order and the nature of this LCM ordering remains elusive.

Figure 4

Measured specific heat C_P and its derivative d(C_P/T)/dT (a) magnetization M under the FC and ZFC modes, and dielectric constant at f = 1 MHz (b) and pyroelectric current I_pyro(T) at T_end = 2 K, E_P = 10 kV/cm, and a warming rate of 2 K/min (c) as a function of T respectively.

It should be mentioned that the anomaly in the d(C_P/T)/dT ~ T curve around T_N2 is not remarkable, while some other weak anomalies between T_N1 and T_Tm have not yet been properly assigned. The weak feature around T_N2 seems to suggest that the CM-ICM transition may not be typical and the CM and ICM coexistence in this T-range is highly possible. On the other hand, the Tm-Mn coupling should be strong although no specific indication in the d(C_P/T)/dT ~ T curve can be found. The well-ordered magnetic structure including the R³⁺ spin ordering in the high-T range for TmMn₂O₅, similar to the cases of DyMn₂O₅ and GdMn₂O₅ for instance^19,27, confirms the strong Tm-Mn coupling.

Nevertheless, different from the C_P data, the measured M(T) curve does not show non-trivial feature but a smooth and monotonous increasing with decreasing T over the whole T-range, as shown in Fig. 4(b). No separation between the ZFC and FC curves and no remarkable anomaly at T_N0, T_N1, T_N2, and even T_Tm can be identified. Obviously the magnetization signals are mainly from Tm³⁺ moment since it is much larger than the Mn³⁺/Mn⁴⁺ moment. The smooth M ~ T curve over the whole T-range also suggests that the Tm³⁺ spin ordering is already gradually developed far above T_Tm ~ 6 K, most likely induced by the strong Tm-Mn coupling. Otherwise, an anomaly around T_Tm should be observable if the Tm³⁺ spin structure is paramagnetic above T_Tm.

The measured ε(T) data provide additional indication of the multiferroic phase transitions and one set of data at f = 1.0 MHz are plotted in Fig. 4(b), while the ε(T) curves at different f show similar features. Besides the relatively sharp peak around T_N1 and small peak right around T_Tm, a smeared and broad shoulder around T_N2 can be found. The sharp peak at ~T_N1 certainly marks the FE transition corresponding to the ICM-CM transition. The small peak at ~T_Tm indicates another FE transition which should be related with the LCM ordering at T_Tm. The intermediate shoulder (bump) seems to characterize the gradual or diffusive FE transition covering the broad T-range around T_N2. It was reported that the single-crystal samples do show a weak jump around T_N2^34,41, which becomes a shoulder here.

Before discussing the magnetically induced ferroelectricity data in details, we present one representative pyroelectric current I_pyro(T) curve as shown in Fig. 4(c) measured at T_end = 2 K with a warming rate of 2 K/min. The data reliability will be identified later. First, one sharp valley at ~T_N1 and one sharp peak at ~T_Tm are observed, consistent with the anomalies in the ε(T) curve. The sharp valley indicates the appearance of electric polarization at T_N1. The peak at ~T_Tm indicates another FE transition and the generated electric polarization should be assigned as P_LT along the a-axis (shown in Fig. 1(b))^31,34. Second, a broad peak between T_N1 and T_N2 is identified, suggesting the existence of third electric polarization which ensues gradually with decreasing T. Here, the most important feature is the negative current valley at ~T_N1 and broad positive peak at T_N2 < T < T_N1, intimating the existence of two antiparallel polarizations, distinctly different from the reported data on single crystal samples^32,33. This behavior is however similar to earlier data on polycrystalline DyMn₂O₅^29,39. It may come to us immediately that the two polarizations are the components of a FIE state, giving rise to the polarization flop with decreasing T at certain temperature. Below T_N2, the two polarizations compete with each other, leading to the flat grade between T_N2 and T_Tm. A detailed discussion on this FIE model will be performed later.

Pyroelectric current and electric polarization

The issue of top priority here is the reliability of measured I_pyro(T) data, and this issue is critical for a growing understanding of the underlying physics. The pyroelectric current method is sometime questioned since the measured “pyroelectric” current has been often questioned to include other current contributions such as trapped charges^29,30,42. A careful clarification of these contributions if any should be made. We have performed the following measurements for this clarification.

First, we checked the I_pyro(T) data at different warming rates given the fixed electric poling field E_P = 10 kV/cm and T_end = 2 K, as shown in Fig. 5(a). The three peaks/valleys against varying warming rate are non-shifted from one and another, and the under-curve area is roughly proportional to the warming rate, revealing that the measured current signals have no contribution from the de-trapped charges during the sample warming. Otherwise one will observe the shifting of these peaks/valleys towards the high-T side with increasing rate. Second, the nearly symmetric I_pyro(T) curves with respect to axis I_pyro = 0 under E_P = ±10 kV/cm respectively, as plotted in Fig. 5(b), also evidence the reversible electric polarization. The as-evaluated P(T) curve is presented in Fig. 5(c), indicating clearly the appearance of a negative polarization around T_N1, the polarization flop from negative value to positive one around T_N2, and another FE transition around T_Tm, respectively. This polarization flop is the character of a typical FIE system^29,38.

Figure 5

Measured I_pyro(T) curves at three warming rates at E_P = 10 kV/cm (a) I_pyro(T) curves at E_P = ±10 kV/cm and warming rate of 2 K/min (b) evaluated P(T) curve at E_P = 10 kV/cm (c). T_end = 2 K for all the cases.

For further checking the pyroelectric origin for the I_pyro(T) data, we plot the I_pyro(T) curves measured at different E_P in Fig. 6(a). We first look at the data at E_P = 0 which are indeed very weak and can’t be identified unless the data are magnified for 30 times. The repeated measuring cycling shows the similar features: weak valley around T_N1, weak bump right above T_N2, and another weak valley or bump (history-dependent) around T_Tm, respectively. Given the fact that the sample was not pre-poled electrically, these weak features suggest the existence of FE phase transitions around T_N1, T_N2, and T_Tm respectively. The electric pre-poling treatments under increasing E_P enable a set of I_pyro(T) curves with non-shifted valleys/peaks but increasing valley/peak magnitudes. This fact also suggests no remarkable contribution from the de-trapped charges which otherwise would shift the valleys/peaks with increasing E_P. The corresponding P(T) curves evaluated from the I_pyro(T) data are plotted in Fig. 6(b), giving rise results consistent with the above discussion.

Figure 6

Measured I_pyro(T) curves at different poling fields E_P as labeled (a). Evaluated P(T) curves from these I_pyro(T) curves (b). T_end = 2 K for all the cases. Measured dielectric constant ε(T) curves at several different frequencies (c).

The measured ε(T) curves under an ac-field of 0.1 V/cm and different frequencies f are also plotted in Fig. 6(c) for checking the FE phase transitions. All these curves have the anomalies at T_N1 and T_Tm, while weak shoulders around T_N2 appear only in the high-f curves. It is noted that the highest frequency used for the ε(T) measurements is 1.0 MHz which is sufficient to suppress any charge de-trapping under such a weak electric field. In the other word, these anomalies would be absent if the I_pyro(T) signals are from the non-pyroelectric contributions. Furthermore, it is found that the dielectric peak at T_N1 is quite broad, suggesting that the FE phase transition is not sharp. However, this phase transition would not be diffusive since no remarkable frequency dispersion can be identified^34,42. The another possible reason is that the broad peak may come from a superposition of more than one FE phase transitions such as the consecutive appearance of the two electric polarizations of the FIE system, as to be proposed below. On the other hand, it is understandable that the polarization flop as proposed at T_N2 may not necessarily produce significant dielectric response. Anyhow, to this end, one may trust that the measured I_pyro(T) data are indeed contributed from the pyroelectric current and the FE phase transitions do appear at T_N1 and T_Tm, while a polarization flop at T_N2 is argued.

Path-dependent electric polarization

In order to understand the nature of the observed P(T) dependence, we have performed a set of I_pyro(T) measurements given a fixed E_P = 10 kV/cm but different T_end. The measured I_pyro(T) curves and evaluated P(T) curves are plotted in Fig. 7(a,b) respectively where the curves are shifted vertically for clarification. Several critical features deserve for highlighting here. First, the major features of the I_pyro(T) curves above T_end remain essentially unchanged, showing that the data are path-independent. In other words, this set of experiments demonstrates that the pyroelectric current is only T-dependent and has nothing to do with the measurement sequences (e.g. different T_end). Second, the peaks around T_Tm and T_N2 and the valley at T_N1 are seemingly irrelevant with each other and the disappearance of one feature does not affect the others. Third, the polarization flop occurring around T_N2 remains unaffected until T_end > T_N2. What surprises us is that the negative polarization remains as T approaches T_N1, noting that the sample is positively poled. This unusual behavior will also be discussed later.

Figure 7

Measured I_pyro(T) curves (a) and evaluated P(T) curves (b) for different values of T_end as marked. The warming rate is 2 K/min and E_P = 10 kV/cm. For data clarification, these curves are shifted from one and another vertically.

Discussion

We would like to address that all these features support the argument that the observed P(T) dependence is the consequence of a FIE system. Before we discuss this FIE scenario, it is noted that the I_pyro(T) peak around T_Tm is contributed from the LCM phase generated polarization P_LT aligned along the a-axis^31,34,35. Due to the polycrystalline nature of the samples, its contribution can be detected here. Similar to the FIE model in DyMn₂O₅, see Fig. 8, Fig. 8(a) shows the ionic and spin configurations on the ab-plane of DyMn₂O₅, which consist of ordered Mn⁴⁺, Mn³⁺, and Dy³⁺ occupations in the lattice. Clearly, the ab-plane spin configuration can be divided into four sub-groups as shown in Fig. 8(b,c)³⁹. If the weak noncollinear components of these spins are not considered, these sub-groups actually are the ↑↑↓ or ↓↓↑ blocks. Each of these blocks contributes one local electric dipole due to the ionic displacement, consulting to the symmetric exchange striction for ferroelectricity generation. Immediately, one recalls that the ab-plane constitutes a FIE lattice of two roughly antiparallel polarization components: One component can be generated by the symmetric exchange striction in the Mn³⁺-Mn⁴⁺-Mn³⁺ blocks, denoted as P_MM, and the other can be generated by the symmetric exchange striction in the Tm³⁺-Mn⁴⁺-Tm³⁺ blocks, denoted as P_TM which is antiparallel to P_MM. Here, we applies it to the present case of TmMn₂O₅ for explaining the observed P(T) behaviors. The only revision to Fig. 8(a~c) is to replace the Dy³⁺ ions with the Tm³⁺ ions. In principle, it is believed that the strong Tm-Mn coupling enables the gradual ordering of Tm³⁺ spins in coherence with the Mn³⁺/Mn⁴⁺ spin ordering below T_N1. The independent Tm³⁺ ordering occurs at T_Tm due to the competition of the Tm-Tm exchange over the Tm-Mn coupling, contributing to the LCM phase around T_Tm.

Figure 8

(a) The ab-plane projected ionic and spin configurations of DyMn₂O₅ and TmMn₂O₅ is assumed to have similar configurations, where the arrows indicate the spins, open circles mark the original ionic sites without inclusion of the magnetic interactions, and solid circles the final ionic sites with the magnetic interactions. (b,c) The four blocks each of which consists of three neighboring magnetic cation ions. The symmetric exchange striction in each block leads to shifting of the ions, generating a local electric polarization as indicated by the long arrow, and the as-generated polarizations P_MM and P_DM (P_TM) are roughly antiparallel, forming a ferrielectric lattice.

The proposed physical sequence upon decreasing T is as the following. As T falls down to T_N1, the Mn spins begin to order into the CM phase which generates polarization P_MM. In spite of the claimed CM-ICM phase transition at T_N2, no sufficient evidence with the absence of ferroelectricity in the CM phase is available. Therefore, it can be argued that this CM-ICM phase transition does not affect the P_MM very much. Since the Mn-Mn exchange is strong, suggesting that the spin ordering at T_N1 is sharp and the FE phase transition finishes in a narrow T-range. On the other hand, the Tm-Mn coupling enables the coherent Tm³⁺ spin ordering with the Mn spin ordering, leading to polarization P_TM which is roughly antiparallel to P_MM. This phase transition would be relatively diffusive since the Tm³⁺ spin ordering is induced by the Tm-Mn coupling as the second-order exchange. Consequently, the total polarization P = P_MM + P_TM as a function of T can be complex and a polarization flop event may occur.

The observed P(T) curve suggests that inequality |P_TM| > |P_MM| should be satisfied below T_N1. The proposed two components as a function of T in a qualitative sense, are plotted in Fig. 9(a). The two FE sublattices coherently constitute the FIE lattice and the two polarization components as a function of T respectively are schematically drawn just for a guide of eyes. When the low-T polarization component P_LT is summed to the total P = P_MM + P_TM + P_LT, the observed P(T) curve (blue) can be nicely reproduced, as shown in Fig. 9(a) too. The three polarization components at different T can be schematically mapped by arrows in Fig. 9(b).

Figure 9

(a) Measured P(T) curve at the warming rate of 2 K/min and E_P = 10 K/min, and the assumed polarization components P_MM(T), P_TM(T), and P_LT(T), as a function of T respectively. (b) A schematic drawings of the three polarization components (arrows in colors) at different T.

It has been repeatedly confirmed that the Mn spin orders in RMn₂O₅ systems are highly robust against external magnetic field^38,39,40. A magnetic field of several Tesla seems not to shake much the Mn spin orders. Different from this property, one is aware of the much soft Tm³⁺ spin orders against magnetic field, due to the fact that the 4f-4f exchange is weak with respect to the Mn-Mn exchange^43,44. The Tm-Mn coupling is much stronger than the 4f-4f exchange although it is relatively weaker than the Mn-Mn exchange. Therefore, both P_TM and P_MM are robust against H but P_MM is the highest robust. This difference allows an opportunity to check this FIE model by measuring the magnetoelectric response of TmMn₂O₅. Given a fixed T, applying a magnetic field certainly destabilizes the Tm³⁺ spin orders and thus completely suppresses polarization component P_LT, while component P_TM may be also partially suppressed but P_MM remain less affected.

The above discussion is confirmed by the measured data, as shown in Fig. 10(a~d) respectively. On one hand, the I_pyro(T) peak and the P_LT component in the P(T) curves around T_Tm are indeed suppressed by a field of ~5.0 T, while P_MM and P_TM remain less affected, as shown in Fig. 10(a,b). On the other hand, Fig. 10(c,d) show the magnetically induced current (I_H) loops in response to the H-cycling at T = 2 K and 10 K. The I_H ~ H loop at 2 K clearly indicates the suppression of P_LT by increasing and decreasing H cycle. This feature becomes seriously weakened at T = 10 K where the weak I_H response is from the partially H-suppressed P_TM, consistent with the above discussed FIE scenario too.

Figure 10

Measured I_pyro(T) curves (a) and evaluated P(T) curves (b) under different magnetic fields H as labeled, with T_end = 2 K and E_P = 10 kV/cm. The iso-thermal I_pyro(H) hysteresis loops at T = 2 K and 10 K are plotted in (c,d) respectively. The polarization components at various stages are drawn for a guide of eyes.

It should be noted that our proposed FIE model seems to reasonably explain our experimental results. However, the ceramic samples exhibit some intrinsic defects such as grain boundaries and voids, which have an influence on the polarization properties, although the use of polycrystalline may avoid the impact of self-polarized effect on polarization behaviors in our samples. Therefore, we felt that more research by testing of single crystal samples is needed to further support our claims.

Furthermore, an unsolved and puzzling issue regarding this FIE model is the appearance of negative P right below T_N1 for both DyMn₂O₅ discussed earlier and TmMn₂O₅ here. In fact, the appearance of negative P right below T_N1 is understandable if T_end≪ T_N1, because of |P_TM| > |P_MM| at T ≪ T_N1 and E_P > 0. However, as shown in Fig. 7, for T_end ~ 32 K at which |P_TM| < |P_MM| and thus the positive E_P would drive a positive P instead of negative P under a positive poling field. An understanding of this unusual feature is detrimental to the FIE model, which otherwise could be totally wrong.

So far, almost all of the literature discussing the multiferroicity of RMn₂O₅ has concentrated on the magnetically induced ferroelectricity below T_N1 (T_N0)^{18,19,20,21,22,23,24,25,26,27}. This fact leaves a somehow misleading impression that RMn₂O₅ would be paraelectric above T_N1. The only exceptional experiment was from V. Baledent et al. who demonstrated that RMn₂O₅ is actually a family of room ferroelectricity whose microscopic origin has nothing to do with magnetism, and it was argued that this room temperature ferroelectricity is structurally driven⁴⁵. The magnetically induced FE polarization is simply an additional component to the room ferroelectricity. Unfortunately, due to the extremely large conductivity of single crystal RMn₂O₅ at T > 150 K, the FE polarization at high T can’t be measured. In the present work, our polycrystalline samples show better insulating property than single crystals, allowing a relatively sufficient electric poling at T up to ~300 K by a field of ~8 kV/cm, although the electrical insulativity of the samples are still far from sufficient to obtain reliable P-E hysteresis. The high-T FE phase transition temperature has not yet been determined.

Nevertheless, the claimed room ferroelectricity for TmMn₂O₅ allows us an opportunity to explore the origin for the negative P right below T_N1. We perform the following experiments: an electric field E_P(T), which is gradually increased with decreasing T, is imposed to the sample during the sample cooling. The value of E_P is increased to 10 kV/cm (or −10 kV/cm) at 260 K down to T ~ 45 K which is slightly higher than T_N0 = 44 K. Then the poling field is removed and the sample is further cooled down to 32 K which is below T_N1. Subsequently, the sample is sufficiently short-circuited electrically and then the sample is warmed at a rate of 2 K/min up to 50 K, during which the I_pyro(T) is measured. The measured data are presented in Fig. 11(a,b) respectively, where the E_P(T) data are also inserted for reference.

Figure 11

Measured I_pyro(T) curve and evaluated P(T) curve for two specific cases.

The sample was cooled down from room temperature with an electric poling down to 45 K, and then further down to 32 K with zero electric bias, followed by warming at a rate of 2 K/min during I_pyro(T) data are is probed: (a) E_P < 0 and (b) E_P > 0. The poling sequences for the two cases are marked.

Surprisingly, one observes the positive I_pyro peak (positive P) around T_N1 when E_P < 0 above T_N0 (Fig. 11(a)), and the negative I_pyro peak (negative P) around T_N1 when E_P > 0 above T_N0 (Fig. 11(b)), noting that no electrical bias is imposed on the sample between T_N0 and T = 32 K. This implies that the negative P valley just below T_N1 in our whole package of measurements is induced by the electric poling process far above T_N0. This is the reason for the observed negative P valley in Fig. 7 at T_end = 32 K and below.

Assuming that TmMn₂O₅ is already a ferroelectric at room temperature and its polarization is P₀, which is positive if E_P > 0 and negative if E_P < 0. This structurally induced P₀ may align the magnetically induced polarization P_MM in opposite direction via e.g. the ferroelastic effect or so far unknown magneto-lattice coupling mechanism^46,47. In the other words, P_MM is always antiparallel to P₀ which is however aligned by the electric poling. Although such a coupling or ferroelastic effect has not yet been understood and will be further investigated, all of the observed phenomena in our experiments can be well explained, given this P_MM↓↑P₀ assumption.

Conclusion

In conclusion, we have performed extensive measurements of the magnetically induced ferroelectricity of TmMn₂O₅ in polycrystalline form, focusing on the ferrielectric nature and its magnetic origins. It is revealed that the ferroelectric polarization contains several components which appear respectively in various temperature ranges and is suggested to be generated by different microscopic mechanisms. These components include the polarization P_MM generated by the Mn³⁺-Mn⁴⁺-Mn³⁺ collinear spin block via the symmetric exchange striction, the polarization P_TM generated by the Tm³⁺-Mn⁴⁺-Tm³⁺ collinear spin block via the symmetric exchange striction, and the polarization P_LT generated by long-range noncollinear Tm³⁺ spin ordering via the asymmetric exchange striction. The Tm³⁺-Mn⁴⁺-Tm³⁺ collinear spin ordering is driven by the strong Mn-Tm coupling. The two components P_MM and P_TM are antiparallel, constituting two ferroelectric sublattices of a ferrielectric system. The polarization flop with decreasing temperature is observed as a representative character of the ferrielectricity. It is suggested that this magnetically induced ferrielectricity of TmMn₂O₅ is likely an additional ingredient to the high-temperature ferroelectricity which is structurally driven. The present work represents a growing understanding of the complicated multiferroic behaviors in RMn₂O₅ compounds.

Methods

In our experiments, polycrystalline TmMn₂O₅ samples were prepared by the standard solid-state reaction method. Stoichiometric amounts of Tm₂O₃ (99.99%) and Mn₂O₃ (99%) powder were thoroughly ground and then fired at 980 °C for 24 h in a flowing oxygen atmosphere. The resultant powder was re-ground and granulated using 4 wt% poly vinyl alcohol (PVA) solution and then pelletized under a pressure of 9 MPa into disks of 11.5 mm in diameter. The disk samples were sintered at 1080 °C for 48 h in a flowing oxygen atmosphere in prior to natural cooling down to room temperature. The as-prepared samples were submitted to a set of microstructural characterizations. The crystallinity and lattice structure were checked using the X-ray diffraction (XRD) (PANalytical X’Pert PRO diffractometer) with the Cu-K_α radiation at room temperature. The data were refined using the Rietveld method. The scanning electron microscopy (SEM, Ultra 5, Zeiss) and the associated EDS mapping were used to check the grain morphology and chemical distribution.

The isometric specific heat (C_P) of the sample as a function of T was measured in the standard procedure using a physical properties measurement system (PPMS, Quantum Design Inc.) installed inside a well-shielded space to insure extremely low electrical and thermal noise (background). The electrical noise can be as low as 0.02 pA as probed by the Keithley 6430 electrometer. The evaluated d(C_P/T)/dT ~ T data are used to mark these phase transition points. The dc magnetization M(T) data at the field-cooling (FC) and zero-field-cooled (ZFC) modes were obtained using the vibrating sample magnetometer (VSM) integrated with the PPMS system. The cooling and measuring fields were both 100 Oe, sufficiently low so that the magnetic field driven side-effects if any are as weak as possible.

For the electrical measurements, disk-like samples of 11.5 mm in diameter and 0.17 mm in thickness were deposited with Au electrodes on each side. The dielectric constant ε as a function of T at various frequencies (f) covering six orders of magnitude was measured using the E4980A precision LCR meter. The electric polarization P as a function of T was evaluated from the pyroelectric current I_pyro-T data. The measurement was carried out following the procedure below. First, the sample in the plate capacitor geometry was cooled down to 150 K without electrical bias and then an electric poling field E_P = ± 10 kV/cm was applied to the sample during further cooling at a rate of 2 K/min down to a given end temperature T_end. Then the sample capacitor was electrically short-circuited for sufficient time at T_end, followed by a slow sample heating until a temperature higher than T_N0, during which the electric current (I_tot) released from the capacitor was recorded using the Keithley 6430 electrometer.

A set of additional experiments were performed to check whether the probed current I_tot from the capacitor is solely from the pyroelectric current I_pyro or not. These experiments include the measurement of dependence ε(f, T), released current curves I_tot(T) at several heating rates, and isothermal magneto-current I_H in the H-cycling at a rate of 150 Oe/s. The I_pyro(T) data under various magnetic fields H were also collected. The T_end was varied from 2 K to T < T_N1. Furthermore, the polarization current method was also employed to qualitatively the sample’s ferroelectricity. The current passing through the sample under an electric field of 10 kV/cm, which should contain both the leaky current (I_E) and polarization current (I_P), was measured too. Assuming that I_E(T) decreases monotonously with decreasing T, the I_P can be extracted although it may not be quantitatively accurate. Unfortunately, for TmMn₂O₅, the current passing across the samples was too big to be possible for extracting the polarization current of tens of pA, suggesting the incapability of this method in the present case.