Abnormal dependence of multiferroicity on high-temperature electro-poling in GdMn 2 O 5
Cite as: J. Appl. Phys.126, 174104 (2019);doi: 10.1063/1.5120971
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Submitted: 22 July 2019 · Accepted: 15 October 2019 · Published Online: 1 November 2019
S. H. Zheng,1 J. J. Gong,1Y. Q. Li,1 C. F. Li,1Y. S. Tang,1J. H. Zhang,1 L. Lin,1Z. B. Yan,1X. P. Jiang,2 S. W. Cheong,3and J.-M. Liu1,4,a)
AFFILIATIONS
1Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
2School of Materials Sciences, Jingdezhen University of Ceramics, Jingdezhen 333403, China
3Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
4Institute for Advanced Materials, South China Normal University, Guangzhou 510006, China
a)Author to whom correspondence should be addressed:[email protected]
ABSTRACT
Magnetically induced ferroelectric polarization in rare-earth RMn2O5 manganites is believed to originate from the symmetric exchange striction associated with a specific antiferromagnetic phase in the low temperature (T) region and would be irrelevant with electropoling in the high-Tparamagnetic-paraelectric phase region. In this work, we demonstrate that low-Tpyroelectric polarization of GdMn2O5single crystals along thebaxis in the antiferromagnetic phase exhibits remarkable dependence on the electropoling history imposed in the high-T paramagnetic-paraelectric phase. In particular, the high-Telectropoling results in a reversal of ferroelectric polarization in the low-Tregion, which can beflopped back by the electropoling being sustained in the low-Tferroelectric region. The existence of an electrically polarizable magnetic cluster state in the high-Tparamagnetic-paraelectric region is proposed based on a combination of experimental observations and first-principles calculations. An intrinsic correlation between the low-T antiferromagnetic ordering and the high-T polarizable state is discussed. The present experiments unveil the emergent phenomena on multiferroicity of RMn2O5and suggest an alternative scenario for electrocontrol of magnetism.
Published under license by AIP Publishing.https://doi.org/10.1063/1.5120971
I. INTRODUCTION
In the past decade, studies on multiferroics and underlying physics have experienced rapid progress,1–7with a number of mate- rials with remarkable magnetoelectric (ME) coupling.8–12Current challenges include both the weak ME coupling in spite of high fer- roelectric (FE) Curie temperatureTCand large electric polarization P, as found in type-I multiferroics such as BiFeO3,13–16and the low TCand smallPin spite of strong ME coupling, as found in type-II multiferroics such as RMnO3 and RMn2O5 where R is small rare-earth species or Y.8,9,17–21It is understood that the lowTCand smallPin type-II multiferroics are due to the microscopic mecha- nisms for polarization generation that are essentially the second- order or higher-order effects associated with specific magnetic order. The most-concerned mechanisms are: (1) the asymmetric exchange striction in noncollinear magnetic compounds where the
Dzyaloshinskii-Moriya (DM) interaction is non-negligible and3,4 (2) the symmetric exchange striction in some collinear systems where spin-lattice coupling breaks the spatial inversion symmetry.22
The orthorhombic RMn2O5 compounds are a representative family fitting to the second case.23,24 Nevertheless, it is puzzling that these compounds exhibit different FE and ME behaviors although they have highly similar lattice structures.8,11,25–30 First, R-Mn coupling can be different depending on the A-site ion R, which is strong in DyMn2O5 but negligible in GdMn2O5, making the P(T) dependence strongly material-related.11,31,32 Second, the magneticfield (H) dependence of polarizationPcan be distinctly different. It was found that polarization P is enhanced with increasing magnetic fieldHfor compounds with R = Ho and Dy and suppressed for compounds with R = Tb, as well as sign reversed for compounds with R = Er and Gd.8,11,33,34 Third and unusually, the reported P(T) data for the same compound are
sample-dependent.11,35In some cases, the role of 4f electron and R-Mn coupling, that are believed to be responsible for these differ- ences, was discussed.33,34
It comes to our attention that all the multiferroic measure- ments on this family of compounds were based on the scenario that the high-Tlattice structure of RMn2O5is nonpolar and ideally paramagnetic–paraelectric (PM–PE), and a nonpolar (Pbam) to polar (Pb21m) transition does not occur until the magnetic order- ing from the high-T paramagnetic (PM) state. Therefore, it is believed that the system is in the ideally paramagnetic–paraelectric (PM–PE) state above the magnetic ordering point. The whole physics of multiferroicity is thus discussed in the low-Tmagneti- cally ordered region and has nothing to do with the high-T process. Nevertheless, for theP(T) data measured using the pyro- electric current method (so-called the pyroelectric polarization), one observes the distinctly differentP(T) curves for R = Dy (P< 0) and for R = Ho and Tb (P> 0) while these samples were sufficiently electropoled in similar conditions.36 To avoid these confusing results, thefield-cooling method was once utilized to measure the polarization and the possible uncertainties and deficiencies of this method were discussed.29 Nevertheless, these inconsistencies remain.
Furthermore, a recent work in 2015 claimed that the lattice structure of RMn2O5at room temperature belongs to the polarPm space group rather than nonpolarPbamspace group.37Although several subsequent works followed this claim, the reliability of data on the structure and polarization is doubtable38–41and the room temperature structure shouldfit the nonpolar Pbamspace group.
In spite of these disputes, possible high-Tpolarizablefluctuations in the high-Tregion and subsequent impact on the low-Tmultifer- roicity may be an issue. In the other words, the high-T state may not be an ideal PM–PE state. This issue was initially discussed in an earlier work on TmMn2O5with complicated Mn spin ordering and R-Mn coupling.42In proceeding, it would be more promising if one takes GdMn2O5as an alternative object for investigation. In this RMn2O5 family, GdMn2O5 shows a polarization as large as 0.1μC/cm2 along the b axis (T <30 K). Besides, a giant P-flop driven by magnetic field H, generating a change of ∼0.5μC/cm2 was found, evidencing the large ME response.11It is also noted that GdMn2O5has non-negligible but relatively weak Gd–Mn coupling and the Mn spin ordering sequence from the PM–PE state is simpler than other systems.43Our preliminary work on polycrystal- line GdMn2O5did reveal a high-Tpolarizable state that influences the low-T P(T) behaviors,44based on which the present work on single crystals was stimulated.
The lattice structure of GdMn2O5 is schematically drawn in Fig. 1, where the major Mn-Mn exchanges are marked. One may refer to earlier literature on the structure.45,46For the magnetic and dielectric properties, earlier works on GdMn2O5 single crystals reported the PM-PE state aboveTN1∼40 K, and an incommensu- rate (ICM) phase below TN1 followed by a commensurate (CM) ordering below TN2∼34 K at which a FE phase (FE1) is gener- ated.35,43This CM + FE1 phase region is narrow and replaced by another CM and FE phase (CM + FE2) belowTC∼29 K which is usually defined as the FE Curie point although the CM + FE1 phase belowTN2is also ferroelectric. Further cooling fromTCdoes not induce more remarkable spin reordering although a peak of
specific heat normalized byT,Cp/T, can be identified atTGd∼10 K.
This peak marks the reordering of Gd spins. The system enters the third FE phase (CM + FE3) belowTGdalthough actually no distinct difference between FE3 and FE2 can be seen. This sequence of magnetic and FE ordering is schematically shown inFig. 2(a)and one sees the complicated phase transition sequence.
Earlier works on GdMn2O5 suggested the existence of two local polarization components.11,47One is componentPMM, gener- ated by the symmetric exchange striction associated with the Mn3+–Mn4+–Mn3+ blocks and the other is component PGM, generated by the symmetric exchange striction associated with the Gd3+–Mn4+–Gd3+ blocks. The Gd–Mn coupling is insufficiently strong to strictly align the Gd spin antiparallel to the Mn spins, allowing rotation of Gd spins by magneticfield.11These local com- ponents each deviate slightly from theb axis but the sum of these components is aligned along thebaxis, making the total polariza- tion Ptot=PMM+PGM much larger than that of other RMn2O5
members. ThePMM(T) andPGM(T) dependences can be schemati- cally drawn in Fig. 2(b) where PMM emerges at T∼TC and PGM appears slightly below TC. Therefore, the Ptot(T) curve would exhibit a two-steplike pattern, as observed in earlier reports and also plotted in Fig. 2(b). More discussion on Fig. 2(b) will be shown later and in the caption.
In this work, we address the effect of electropoling in the high-T PM–PE phase on the low-T multiferroic behaviors of GdMn2O5single crystals. This is no doubt an emergent phenome- non deserved but not yet for investigation.48We obtain the high- quality data from single crystal samples, and propose a specific FIG. 1. A schematic of GdMn2O5orthorhombic lattice structure where the three major exchangesJ3,J4, andJ5are marked.
roadmap for probing the pyroelectric currentIas a function ofT.
It will be shown that theI(T) and thenP(T) data belowTN1exhibit distinctly different characters depending on the high-Telectropol- ing in the PM–PE region. The existence of an electrically polariz- able magnetic cluster state in this PM–PE phase region is proposed and supported by the first-principles calculations and measured broad bump of dielectric response. It is argued that these high-T polarizable magnetic clusters lead to the unusual ferroelectric behaviors in the low-Tmultiferroic region.
II. EXPERIMENTAL DETAILS
A. Sample preparation and characterizations
The GdMn2O5 single crystals were grown using the flux method, as reported previously.11,49For the present experiments, the typical size of crystals was 1.0 mm in dimension, and the orien- tation of these crystals was determined using the Laue diffraction method. The lattice structure at room temperature is the high- symmetryPbamorthorhombic phase, as determined by the X-ray diffraction and will transfer into the Pb21mstructure at T∼TN2, thus allowing for a ferroelectric polarization along thebaxis.28,50
The samples were submitted to a set of characterizations and the obtained results are reproducible from sample to sample. The dcmagnetizationMalong the three main axes (a= [100],b= [010], c= [001]) at a measuring field of 2.0 kOe under the zero field- cooled (ZFC) mode and field-cooling (FC) mode was measured using the Quantum Design Superconducting Quantum Interference Device (SQUID). The specific heat Cp was measured using the Quantum Design Physical Property Measurement System (PPMS) that also provided the cryogenic environment for dielectric and fer- roelectric measurements.
The samples were cut and polished into 0.1 mm thick plates normal to one of the three main axes for electrical measurements, using the silver pads as bottom and top electrodes. Each platelike sample was preannealed at 500 °C for 120 min in the air ambient before the silver pads were deposited on the top and bottom surfaces.
This annealing was done to avoid possible external effect on the virgin sample and/or possible oxygen deficiency on the surface layers.
The dielectric constants along the three main axes were mea- sured, respectively, using the HP4294A Precision Impedance Analyzer with the stimulating ac signal of 50 mV, during the sample cooling from room temperature. It was found that the sharp dielectric peak around TN2 was only observed along the b FIG. 2. (a) A simplified drawing of the multiferroic phase diagram of GdMn2O5along theTaxis, where PM denotes paramagnetic, PE denotes paraelectric, ICM denotes incommensurate antiferromagnetic, CM denotes commensurate antiferromagnetic, FE denotes ferroelectric, FE1, FE2, FE3 are all ferroelectric phases,TN1is the Mn spin ICM ordering point,TN2(TC) are the Mn spin CM ordering point where the FE phase emerges defining the ferroelectric Curie pointTC,TGdis the Gd spin reordering point with no essential change of magnetic structure at this point. It should be mentioned that several features appear aroundTN2(TC), and thus no strict definition of them is made here. We crudely refer this point as the FE transition point and CM ordering point. (b) The emergence of two FE polarization componentsPMM,PGM, and total polar- izationPtotas a function ofTin a schematic manner. In the high-TPE–PM phase region, local magnetic clusters may appear generating local electric dipoles which may align randomly if the electropolingfieldEP= 0 or along the direction ofEPso that a very weak macroscopic polarizationp0may be available in the PE–PM phase region.
(c) The electropoling scenario employed in the present study, whereTendis the temperature at which the applied polingfieldEPis terminated. Subsequently, the sample is cooled down to 2 K in the short-circuited state before the pyroelectric current probing during the warming process from 2 K.
axis, consistent with earlier reports on the ferroelectric polarization direction. Subsequently, the high-T electropoling treatments and pyroelectric current measurements were done mainly along theb axis, unless stated elsewhere.
B. Electric poling and pyroelectric polarization
In our experiments, the electropoling scheme is plotted in Fig. 2(c). Each platelike sample was cooled down slowly at a rate of 1.0 K/min from room temperature to an assigned ending tempera- ture Tend under a DC electric field EP = 10 kV/cm unless stated elsewhere. After an isothermal equilibration at thisTend, the poling field was removed and the sample was electrically short-circuited for 30 min and then further cooled down to the lowest temperature (2 K) in the short-circuited mode. It implies no more electric poling of the samples belowTend, which is a scheme of specific advantage. The pyroelectric currentI(T) was measured during the sample heating from 2 K up to 50 K at a fixed warming rate vt between 1.0 K/min and 5.0 K/min, using a high-resolution Keithley 6514 electrometer. It is noted that in our experiment, the current was probed without any electric bias, and thus no any contribution from leaky current was possible. The polarizationPwas evaluated from theI(T) data.
For a consideration of integrity,Tendin our measurements was varied step by step from 200 K down to 2 K in sequence, and our focus was on the region ofTend>TN1, i.e., on the poling only in the high-T PM–PE phase region. In these cases (Tend>TN1), the sample before entering the low-TCM + FE phase region was no longer under any electric bias. Our common understanding is that a pyroelectric current is nonmeasurable unless the sample is pre- poled electrically from the PE phase region into the FE phase region. Nevertheless, non-negligible low-Tpyroelectric current was found even ifTend>TN1.
The reliability of the measured pyroelectric current data was checked carefully from various aspects by excluding those possible other sources. The most-concerned sources are from those possible charged defects. To our best knowledge, there are possibly two types of charged surface defects in our single crystals. Thefirst type includes those charged defects generated during the sample polish- ing. If these defects would be generated, the charge-induced electric field would polarize the sample during the sample cooling and then low-Tcurrent signals during the warming sequence should be observed. Our checking excluded this possibility. The second type includes those injected or trapped defects during the electropoling.
For this side effect, extensive discussion in the literature was given and we checked every particular to exclude its influence. For example, we set various warming ratesvtand compared the mea- suredI(T) curves which should be overlapped with each other if no other sources contribute. The validity of this technique and related data reliability are established and no more discussion on the details will be given here.
III. EXPERIMENTAL RESULTS
A. Magnetic and ferroelectric transitions
We first present the M(T) curves measured along the three main axes, as shown in Fig. 3(a) where the H/M vs T data are
plotted too. For each case, no separation between the data under the ZFC and FC modes can be identified at the cooling and measuring fields of 2.0 kOe. It is seen that the M(T) along the b axis and c axis increases monotonously with decreasingT with no identifiable anomaly. However, theaaxisM(T) curve does show a broad bump around ∼10 K, reflecting the 4f-spin reordering FIG. 3. Measured physical quantities of GdMn2O5as a function ofT: (a) mag- netizationMalong the three axes (a,b,c) respectively, with the measuringfield of 2.0 kOe. No difference of the data between the ZFC and FC modes is shown. TheH/Mdata measured underH//baxis mode are plotted too with a linearfitting of the high-Tdata by the Curie-Weiss law. The deviation of data from the linear dependence appears roughly atTm∼100 K. (b) (dM/dT) data along theaaxis with two clear anomalies, definingTN2handTN2lfor the Mn spin ICM–CM transition and induced Gd spin ordering. Hereafter, we no longer distinguish the delicate difference amongTN2landTN2h, and denote them by TN2 unless stated specifically. (c) Specific heat data normalized byT,CP/T, whereTm,TN1,TN2,TGdare marked, respectively. (d) Dielectric constant data along thebaxis,εb, at several frequencies.
along the a axis, as evidenced previously.43 Since the Gd3+ has much larger moment than Mn3+/Mn4+ions, the measured M is mainly from the contribution of Gd3+spins and that from Mn ions is more or less covered. The Mn antiferromagnetic ordering cannot be clearly identified only from theM(T) data.
Nevertheless, one can still find some features related to the magnetic ordering. First, a replotting of theH/MvsT data, fol- lowing the Curie-Weiss law, reveals a clear deviation from the linear dependence atT=Tm∼100 K, a roughly estimated value.
The linear extrapolation down to H/M= 0 marks a negative T-intercept, suggesting the antiferromagnetic background.51 Furthermore, a plotting of the derivative ofM(T) curve along the aaxis overT, as shown inFig. 3(b), does disclose two anomalies at T=TN2h∼33 K (weak anomaly) and T=TN2l∼26 K (strong anomaly). They are most likely generated from the ICM–CM transition for Mn spins and the induced Gd spin ordering. This feature is quite weak and cannot be clearly identified due to the much larger Gd3+moment than Mn3+/Mn4+ moments. The two transitions indicate that Mn and Gd spins order into the CM structure roughly along theaaxis, respectively, whereas no such anomalies in theCp/TvsTcurves along thebaxis andcaxis are observed. The two transitions allow the generation ofPMM and PGM, respectively. Hereafter, for simplified consideration, we no longer distinguish the delicate difference betweenTN2land TN2h, and denote them byTN2unless stated specifically, since our atten- tion is paid to the high-Tregion.43,51
The specific heat data, plotted by the Cp/T vs T curve in Fig. 3(c), also exhibit several anomalous features. First, a broad bump appearing around Tm echoes the feature in the H/M vs T curve. While the value of Tm may not have definite physical meaning and the bump is broad and weak, it suggests a broad T-range aroundTm, say from 200 K down toTN1, within which the magnetic state may no longer be an ideal PM state, while it is believed in literature that the system above TN1 is in the PM state.43,46An intermediate state consisting of small magnetic clus- ters embedded in the PM matrix likely appears inside thisT-range and thus the magnetic state is distorted from ideal PM state. This state is dynamic likely with strong spin fluctuations. Second, a sharp peak and a weak kink appear respectively atTN1andTN2. It is believed that the ICM ordering occurs atTN1and the weak kink marks the ICM–CM ordering atTN2. Third, an additional peak at
∼5 K is the consequence of the Gd spin reordering and the position of the valley is defined asTGd∼10 K.
The measured dielectric constants along the three main axes show different features. The dielectric constant data along the b axis,εb(T), at different frequencies (f) and plotted inFig. 3(d), do show a clear and large anomaly fromTN1and peaked atTN2. This anomaly does mark the FE transition at which an electric polariza- tion emerges.52Besides this main peak, a small bump around TGd
and a broad/weak bump aroundTmcan be seen but these features are minor with no convincing speculation at this stage. In addition, the dielectric constants along theaaxis andcaxis,εa(T) andεc(T), increase monotonously with increasingTover the wholeT-range, although there are indeed extremely weak bumps aroundTN2.35It should be mentioned that the broad/weak bump around Tmis a signature of the magnetic clusterfluctuations and we shall come back to this issue in Sec.IV.
B. Pyroelectric polarization
Based on the data about the magnetic and ferroelectric transi- tions, one can discuss the measured I(T) and evaluatedP(T) data measured along the baxis if not stated elsewhere. The data show high quality with negligible background noise. We present in Fig. 4(a) the data with Tend= 2 K, i.e., the sample was electrically poled over the whole T-range. Here, fourI(T) curves are plotted, and three were obtained by setting vt= 1.0, 3.0, 5.0 K/min at EP= 10 kV/cm and one by settingvt= 3.0 kV/cm atEP=−10 kV/cm, respectively. A quantitative comparison of these curves clearly excludes any dominant contribution of charge release other than the pyroelectric effect. For details, it is shown that nonzero current signals are detectable from 2 K until∼33 K above which the current signals are smaller than 0.05 pA. All theI(T) curves have two consec- utive sharp peaks around∼31 K (∼TC). For details, the starting point isTN2h∼33 K, thefirst peak is atTN2m∼31 K, and the second peak is atTN2l∼26 K. These peaks remain nonshifted for differentvtand the area under curve is proportional tovt, indicating that the current is indeed from the pyroelectric release without other contributions.
Given the dominant contribution from the pyroelectric effect, one can check the polarization reversal upon the reversed poling
FIG. 4. Measured pyroelectric currentIand evaluated polarizationPalong the baxis as a function ofT, respectively. (a) TheI(T) curves measured at various EPandvt, (b) theP(T) curves evaluated atEP= ± 10 kV/cm, respectively.
field. The evaluatedP(T) curves atEP= ± 10 kV/cm are plotted in Fig. 4(b). They are symmetric with respect to the axis P= 0. The two-steplike FE transition aroundTN2(fromTN2htoTN2l) is iden- tified and no other remarkable anomaly is observable. BelowTN2l, the polarization continues to increase with decreasing T and becomes much lessT-dependent or saturated.
C. Effect of high-T electropoling
Now, we look at the evolutions of I(T) andP(T) curves with varying Tend. The experiments were carried out following the sequence shown inFig. 2(c)step by step, starting fromT= 200 K.
As T> 200 K, the sample was leaky and a poling field of EP= 10 kV/cm can be applied when T was lower than 200 K.
Therefore, for each cycle of measurements at a fixed Tend, the sample was warmed to room temperature before cooling-down to 200 K and then the electropoling was applied. For Tend= 2 K to Tend= 140 K, some of the measured curves are presented in Figs. 5(a)–5(k), givenvt= 3 K/min.
Here, instead of describing in detail each set ofI(T) andP(T) curves, we highlight the similarity and difference among these curves. First, eachI(T) curve shows a group of sharp peaks around TN2, and some peaks are positive and the others are negative. These peaks are sharp and mark the appearance ofPMMandPGM, and in most cases they are both positive or both negative, so arePMMand PGM. They are aligned along the same direction for each case, marking the two-step FE transition aroundTN2. Second and sur- prisingly, nonzero macroscopic polarization is observed in the low-Tregion, although the sample is electrically poled only in the PE phase region. This phenomenon has never been possible in con- ventional ferroelectrics because a macroscopic polarization can be detected only if the sample under poling enters the FE phase region. For conventional ferroelectrics, this is understandable because the domains in the FE phase region are randomly oriented if the sample is not prepoled electrically. Here, a nonzero polariza- tion is still detectable even ifTend100 KTN2(TC) whileEPis only∼10 kV/cm.
Third and even more surprisingly, one sees a positive–negative reversal of theP(T) curve in response to increasingTend. In detail, we take the value ofPatT= 2 K,P(T= 2 K), as a function ofTend and plot the data in Fig. 5(l). The P(T= 2 K) is positive as Tend<∼50 K and zero as Tend> 140 K, while it is negative at 50 K <Tend< 140 K. A reversal occurs atTend∼50 K. This polariza- tion reversal strongly suggests some unknown physics in the PM– PE region, which controls the ferroelectric behaviors in the low-T FE phase. It is seen that the positive maximal P(T= 2 K) value is ∼0.27μC/cm2 at Tend= 2 K, much larger in magnitude than the negative maximal P(T= 2 K) value of ∼−0.05μC/cm2 at Tend= 85 K. This is reasonable since the sample in the FE state should not be in a fully poled state ifTend is high, and thus the macroscopic polarization is small. Instead, the polarization is much larger ifTendis inside the FE phase region.
IV. A SCENARIO OF ELECTROPOLING INDUCED POLARIZATION
The emergent phenomenon, as described above, is unusual to our conventional understanding of ferroelectricity. To understand
this behavior, thefirst issue is the mechanism for polarization com- ponents PMMandPGM, the second is why an electropoling in the PE region induces a polarization in the FE region, and the third is why the polarization is negative when the poling field in the PE region is positive. It can be a challenge to resolve all these issues in this work, considering the complexity of underlying physics. We intend to present a preliminary scenario as a reference for future investigation.
A. Two polarization components
Thefirst issue was once discussed in earlier work and a multi- ferroic model for the two polarization components was proposed.11 Since the net polarization is aligned along thebaxis, one may map the low-T lattice and magnetic structures of GdMn2O5 onto the ab-plane, as shown inFig. 6(a)so that the underlying mechanism can be illustrated more clearly.
It is accepted thatPMMis generated by the Mn3+–Mn4+–Mn3+
symmetric exchange striction associated with chainlike blocks each consisting of one Mn3+O5 pyramid unit, one Mn4+O6octahedral unit, and one Mn3+O5 pyramid connected in sequence, as sche- matically drawn inFig. 6.31In the PM–ICM transition atTN1, the Mn spins are aligned from the PM state into an antiferromagnetic order along theaaxis with small out-ofaaxis canting, and subse- quently the ICM–CM transition aroundTN2 occurs, characterized by the smaller peak of (dM/dT)aaxisatTN2h, as shown inFig. 3(b).
The Mn spin structure is drawn inFig. 6(a). Simultaneously, com- ponentPMMemerges via the mechanism inFig. 6(c)where a Mn3
+–Mn4+–Mn3+block (block A) with the↑↑↓or↓↓↑configuration is drawn. In this block, the Mn3+and Mn4+ions with roughly par- allel spin alignment tends to be away from each other, and the Mn3
+and Mn4+ions with roughly antiparallel spin alignment tends to be close with each other. If the Mn4+ion is set as thefixed point (zero point), a local polarization pointing downward, i.e., PMM, is generated.
In spite of the Gd–Mn coupling in GdMn2O5 is relatively weak, the Mn spin ordering can induce the Gd spin ordering which occurs at a lower T, marked by the larger peak of (dM/dT)a axis
at TN2l, as shown inFig. 3(b). As proposed in earlier work,31the Gd3+-Mn4+-Gd3+chainlike block, as shown inFig. 6(d), may gen- erate a local upward or downward polarization. The macroscopic component over the whole lattice would generate a polarization PGM which is parallel to PMM, making the total polarization Ptot=PMM+PGM. Here, it should be mentioned that for RMn2O5 systems with strong R-Mn coupling, PGM may not be parallel to PMMand a ferrielectric behavior was observed for DyMn2O5where PMMis antiparallel toPGM.31
B. Electronic polarizationfluctuations in the PM–PE region
The second and third issues are challenging and in fact the underlying mechanism is complicated. The high-T PM–PE phase must be an electrically polarizable state that is the source or seed for the domain alignment in the low-TFE phase region, resulting in the macroscopic polarization. Along this line, an earlier theoreti- cal investigation based on thefirst-principles calculations comes to our attention.53This work predicted that for an RMn2O5structure
FIG. 5. (a)–(k) TheI(T) andP(T) curves measured along thebaxis at differentTendas marked, whereEP= 10 kV/cm,vt= 3 K/min. (l) Evaluated polarizationP(T= 2 K) as a function ofTend, marking the polarization reversal atTend∼50 K.
where the 4f-spin’s role is not considered, the polarization (here it isPMM) contains the ionic contributionPionand electronic contri- bution Pele. Unfortunately, the two contributions are antiparallel, leading to a largely canceled polarization that is consistent with measured value. A basic character here is thatPionandPeleare on the same order of magnitude of∼μC/cm2but Pion is larger than Pelein magnitude.
Nevertheless, the ionic polarizationPioncannot exist in the PE region which is a high-symmetryPbam phase, but the electronic polarizationPelecan still exist in this high-symmetry phase with a proper magnetic structure. In the other words, if the PE phase region contains local magnetic clusters that have the ↑↑↓ or
↓↓↑-like configuration, these clusters may exhibit local polarization Pele. These are the basic ingredients of physics for understanding the emergent phenomenon in the present work. In fact, theM(T) andCp/Tdata shown inFig. 3do show a broad anomaly around Tm∼100 K, hinting the existence of magnetic clusters in the PM–PE phase region, as discussed previously. These clusters may be sufficiently small in this wide region which is macroscopically occupied by the PM and PE phase matrix with embedded magnetic clusters.
For a better interpretation of the existence ofPele, we consider a high-symmetry Pbam lattice where the Mn spins take the CM order, same as the low-TCM phase. Such an assumption is made only for the convenience of subsequent computation, and in fact we have no evidence for the CM magnetic structure of those mag- netic clusters. In the other words, we don’t believe that the spin configuration of those magnetic clusters in the high-T PM phase region follows strictly the CM configuration. Certainly, no ionic polarization Pion is allowed in such a lattice. We perform the first-principles calculations on this lattice and investigate whether a nonzeroPeleexists or not. Our calculations are based on the gener- alized gradient approximation (GGA) with the Perdew-Burke-
Ernzerhof (PBE) functional54using the projector augmented wave (PAW) method55as implemented in Vienna ab initio simulation package (vasp).56The 5p65d16s2, 3p63d54s2and 2s22p4valence elec- tron configurations for Gd, Mn and O atoms are used respectively, and the Gd-4felectrons are treated as core electrons. The cutoff energy for the plane wave basis is set at 550 eV. A Γ-centered Monkhorst-Packk-point sampling method with a 2 × 4 × 6k-mesh is used. The convergence thresholds are set at 1.0 × 10−6eV in energy and 0.005 eV/Å in force. The strong on-site Coulomb inter- action on the Mn 3dstates is treated by the DFT + U scheme57and the effective U, expressed as Ueff, is set to 5.2 eV, which have been successfully used in the manganese oxide calculations.58We has a pretesting on the cases for Ueff= 2.0 eV to 5.2 eV, and only a slight difference in polarization is found. The polarization is calculated using the Berry phase method.59Here, only the collinear magne- tism without the spin-orbit coupling is considered.
The structure used in the calculations is constructed by extending the unit cell of GdMn2O5in thePbamspace group to a 2 × 1 × 1 supercell. The lattice constants are taken from experimen- tally determined values. Wefirst optimize the supercell with ferro- magnetic (FM) configuration for Mn atoms, which has the centrally inversion symmetry. Then the atomic positions arefixed to maintain the central symmetry. Subsequently, the antiferromag- netic (AFM) configuration is used for calculating the polarization.11 The calculated results show that bothPionandPelealong thea-and c-axes are zero. While the ionic polarization along theb axis, as expected, must be zero, a remarkable electronic polarization Pele∼0.20μC/cm2along thebaxis is obtained. This confirms that nonzero electronic polarization can be available in the “PM–PE phase”ofPbamsymmetry for RMn2O5.53
For a clear illustration, we present inFigs. 7(a)and 7(b) the charge distributions in the Mn3+-O2−plane near Mn4+ions, given the FM order and collinear AFM order as reported FIG. 6. A schematic of the measured spin structure belowTN2, referring to neutron scattering data available in the literature. (a) The spin structure projected on the ab-plane with the square pyramidal Mn3+–O2− unit and octahedral Mn4+–O2− unit shown in (b). The structural block A, composed of one Mn4+–O2− octahedra con- nected by two Mn3+–O2−pyramids roughly along theb axis, is shown in (c). The structural block B, composed of one Mn4+–O2−octahedra, connected by two Gd3+roughly along thebaxis, is shown in (d). The proposed polariza- tionsPMMandPGMgenerated by the two types of blocks due to the symmetric exchange strictions, are labeled in (c) and (d), respectively.
experimentally.23 A first glance at the charge pattern shows no difference in the charge profile between Figs. 7(a)and7(b), or the difference between them is too weak to be identifiable. This is rea- sonable since the absolute charge density is so large in comparison with the charge difference associated with the possible electronic polarization (Pele∼0.20μC/cm2). In order to illustrate clearly the charge profile difference associated withPele, we extract the charge difference between the two magnetic configurations and the results are plotted inFig. 7(c). Since the FM configuration corresponds to the centrosymmetric case and the charge profile distribution is of high symmetry and can be set as a reference distribution, so that any deviation of the charge distribution representing a reduction in charge distribution symmetry can be obtained by extracting the charge profile difference between the FM and AFM lattices. This difference should be the electronic polarization. In fact, Fig. 7(c) does show an asymmetric profile in the charge density difference along thebaxis, where the yellow contours indicate the excess elec- tron density while the blue contours mark the deficient electron density. The red arrow indicates the local electric polarizationpthat is purely electronic. Here, it should be mentioned that the charge profile associated with such an electronic polarization can also be obtained by extracting the difference between the charge profile and
the spatially averaged charge density for this AFM lattice unit, and the as-obtained charge profile is similar to that shown inFig. 7(c).
It is now understandable that thePbamGdMn2O5lattice with the magnetic clusters can accommodate a nonzero electronic polar- ization (Pele) even if the ionic polarization (Pion) is zero. The exis- tence of such magnetic clusters in the high-T PM-PE phase is hinted by the data shown inFig. 3, considering the antiferromag- netic background. This allows us to propose a physical scenario drawn inFig. 8. InFig. 8(a)are drawn two small clusters as exam- ples and each cluster consists of the Mn3+–Mn4+–Mn3+blocks that have the local↑↑↓or↓↓↑-like configuration. Consequently, an elec- tric dipole is created with such a block. These clusters are randomly aligned and no macroscopic polarization is available if no poling field is applied in this PE phase. Therefore, one has Pele∼0 and Pion= 0 ifEP= 0. However, if a nonzeroEPis applied, the local elec- tric dipole of each cluster will be aligned with the direction ofEP. The poling process is illustrated in Fig. 8(b), and thus one has Pele> 0 andPion= 0. This state can be called the electrically polariz- able state, and of course, this state is dynamic upon externalfield or varying temperature. For instance, with decreasingT, these clus- ters may grow and interact with each other, and then long-range magnetic and ferroelectric orders gradual develop.
FIG. 7. The calculated charge (ρ) distributions in the Mn3+–O2−plane near Mn4+ions for the chosen structural unit, given the ferromagnetic (FM) order (a) and collinear antiferromagnetic (AFM) order (b), respectively. The lattice symmetry isfixed by thePbamgroup. The mag- netic structure in (b) is taken from the experimentally determined spin configuration, ignoring the noncollinear component. The difference in charge profile (ρAFM–ρFM) between the FM and AFM lattices is plotted in (c), where the excess negative charge in the upper region (marked withϴ) and excess positive charge in the bottom region (marked with⊕) are shown. Clearly, a local polarizationp as indicated by the red arrow is generated from the elec- tronic polarization.
C. Negative polarization at Tend> TN2
When the electropoling is ended at a Tend>TN1, i.e., the sample poling is terminated in the PE region, some of those aligned clusters will be eventually frozen into the FE region with decreasingT, generating a macroscopic electronic polarizationPele. Once the system enters the FE region that has thePb21msymme- try, ionic polarizationPion that is larger than but opposite toPele emerges. Consequently, the measured polarization is actually polar- izationPMM=Pion+Pele< 0. As discussed above, since polarization PGMis induced byPMMand parallel toPMM, the total polarization would be negative, as schematically drawn inFig. 8(c).
It should be mentioned that, as T<TN2, those well-aligned and frozen clusters only occupy a fraction of the whole sample and the other volume is occupied with randomly oriented FE domains.
Therefore, the measured polarization is small in magnitude in spite of negative in sign. For simplicity consideration, we present in
Fig. 8(d) the domain structure where only two types of domains, upward and downward domains, are sketched. In each domain are there antiparallel Pion and Pele, resulting in polarization PMM parallel toPionin this domain.
D. Positive polarization at Tend< TN2
When the electropoling applied to the sample sustains into the FE region, the situation is very different. Wefirst look at the case of T∼TN2, at which the magnetic clusters grow in size and in degree of ordering, and then eventually a long-range of mag- netic order is developed. The ionic polarization Pionis generated.
Since the sample is under the electropoled state andPionis larger than Pele in magnitude and opposite to Pele in sign, the poling field will switch these FE domains, leading to a reversal of Pion and thus Pele. Consequently, the effective polarization PMM=Pion+Pele becomes positive. This is the reason why we FIG. 8. The proposed evolution of mag- netic and polarization structures upon high-T electropoling. (a) Magnetic clus- ters randomly embedded in the PM matrix atEP= 0 and these clusters take the spin alignment similar to that in the low-T CM phase and thus have local polarizations from the electronic contribu- tion. However, in statistics,Pele= 0 and Pion= 0. (b) Under EP> 0, pointing downward, these clusters are reorga- nized so that their local polarizations are aligned along the direction ofEP. In sta- tistics, Pele> 0 but Pion= 0. (c) At T∼TN2(TN1) <Tend, the lattice symme- try changes from the nonpolar Pbam structure to the polarPb21mgroup, and the ionic polarizationPionis generated in parallel toPele. SincePion>Pelein mag- nitude, the total polarizations of these clusters point upward and the macro- scopic polarization PMM are negative.
(d) At TTN2(TN1),Tend, the FE domains are randomly aligned except those clusters frozen from the high-T poling, the macroscopic polarizationPMM
is only contributed from those clusters and is thus negative. (e) At T∼TN2
(TN1) >Tend, the lattice symmetry changes from the nonpolarPbamstruc- ture to the polarPb21mgroup, and the ionic polarization Pion is generated in parallel to Pele. Since Pion>Pele in magnitude, the total polarization of these clusters is reversed by EP and point downward and the macroscopic polarization PMM is positive. (f) At TTN2(TN1).Tend, the FE domains including those clusters frozen from the high-T poling are all aligned along the direction ofEP, and the macro- scopic polarizationPMMis thus positive.
measured a positive polarization at Tend∼TN2 and below, as shown in Fig. 8(e). When Tend falls far below TN2, the whole sample under the electropolingfield can be of single-domain, as shown in Fig. 8(f ). In this case, the measured polarization is much larger than that case shown inFig. 8(d).
The discussion in above two subsections gives a qualitatively reasonable scenario with which theP(T= 2 K) behavior as a func- tion ofTend, as shown inFig. 5(l), can be understood. It should be mentioned that the positive-to-negative reversal of P(T= 2 K) occurs atTend∼50 K. This value should not be much concerned in quantitative sense, considering the measurement uncertainties and the fact that this is only a preliminary and simplified scenario.
A quantitative comparison seems to be overcritical at this stage.
E. Discussion
To this stage, this scenario seems to explain the observed phenomena in a crude and qualitative way. Nevertheless, it can still be questioned from various aspects. First, one may question the existence of electrically polarized magnetic clusters because the magnetic state around Tm is believed to be paramagnetic.
Nevertheless, RMn2O5 manganites are typically strongly corre- lated systems and the short-range ordered clusters in the para- magnetic phase is highly possible. The second and also the most critical question is what is the evidence with the existence of such electronic polarizationPelein the high-T PE region of thePbam symmetry. A direct observation of these clusters experimentally is beyond the scope of this work, but any indirect signature of them would be appreciated.
As we assume, these magnetic clusters, if existing, are electri- cally polarizable. They may be reflected from the dielectric response owing to the local polarization relaxation. We come back to the dielectric response data along the main axes and check their behav- iors in the high-T PE region. For an illustration, the measured dielectric constant along thebaxis,εb(T), and the constant along thecaxis,εc(T), at frequencyf= 100 kHz, are plotted inFig. 9(a).
Since the ferroelectric polarization is aligned along thebaxis, it is understandable thatεb(T) exhibits a sharp peak aroundTN2whole εc(T) does not. Furthermore, one sees clearly the difference betweenεb(T) andεc(T) curves in the high-T-range, and a broad bump ofεb(T) covers the high-T-range but no such a broad bump forεc(T). This difference suggests that the broad bump of εb(T) may be somehow related to the electrically polarizable magnetic clusters in the high-T-range.
In proceeding, it is known that the dielectric response of a homogeneous dielectric media can be characterized by thermally activated relaxation time. Just for a guide of eyes, we replot the εb(T) data inFig. 9(b)where the dashed curve can be a reference if GdMn2O5would be a pure and ideal homogeneous dielectric. This dashed curve should overlap with the measured dielectric data in the high-T region where GdMn2O5 is a paraelectric. In fact, GdMn2O5is not an ideal paraelectric in the low-Tregion but a fer- roelectric where a clear dielectric peak is identified belowTN2.
When the difference curve, Δεb(T), between the εb(T) curve and this reference curve is extracted, one can see two anomalies.
This extraction is certainly crude and shows no quantitative signifi- cance. The difference shows not only the sharp peak at TN2 but
also a broad bump well above Tm, as shown in Fig. 9(c) at f= 100 kHz. This broad bump is not from release of any thermally trapped charges, since such a release would generate much stronger dielectric response. Similar data processing is applied to otherεb(T) curves at differentfand the results are summarized in Fig. 9(c)where theΔεb(T) curves at differentfare shifted upward for easy illustration.
Although the validity of the obtained Δεb(T) curves may be questioned due to the somehow arbitrary data processing forΔεb(T), it is shown that each curve does show a broad bump which shifts gradually toward the high-Tside with increasingf. This feature is a consequence of magnetic cluster formation in the high-T region.
These clusters are polarizable electrically, contributing to the dielec- tric bump. On the other hand, the bump shifting with varying fre- quency is the reasonable for polarizable cluster state.
FIG. 9. (a) Measured dielectric constants along thebaxis and caxis,εb(T) andεc(T) atf= 100 kHz. (b) Measuredεb(T) curve atf= 100 kHz replotted and the dashed curve is the assumed dielectric response contributed by the ther- mally activated dipole relaxations. The difference between the two curves, Δεb(T), exemplifies the peak aroundTN2and the broad bump in the high-T region. (c) The as-evaluatedΔεb(T) curves at different frequencies, where the curves are vertically shifted for illustration.
Nevertheless, there remain some issues need to be given more careful consideration. One issue is the convincing and direct evi- dence with the existence of such clusters. Second issue is the dis- crepancy between this model prediction and measured results regarding Fig. 5(l) where the positive-negative crossing point appears at roughlyTend∼50 K, while the model predicted crossing point should be atTN2. This discrepancy may be contributed by a series of measuring uncertainties and unknown sources. If one assumes that this proposed model is valid, the observed phenom- ena are the features of an interesting example for electrocontrol of multiferroicity. An electropoling within a properly chosenT-range can “define” the low-T magnetic structure and thus the electric polarization. The last but far not the least issues is whether this sce- nario can be extended to other member compounds of this family.
These issues and questions are open for future investigation.
V. CONCLUSION
In conclusion, we have carefully investigated the multiferroic properties of GdMn2O5single crystals by measuring the pyroelec- tric current and polarization along thebaxis, upon the high-Telec- tropoling from room temperature down to a givenTend. It has been revealed that an electropoling in the high-T PM-PE region can induce a negative electric polarization in the low-T multiferroic CM-FE region, while a positive electric polarization is obtained if the electropoling is sustained in the low-TCM-FE region. It is sug- gested that this electric polarization reversal, in response to reduced poling-ending temperature, is related to the antiparallel electronic polarization and ionic polarization. While the ionic polarization arises from the Mn–Mn symmetric exchange striction, the elec- tronic polarization can be sustained to the high-TPE phase due to the existence of high-T magnetic clusters. This high-Telectronic polarization in coexistence with the low-Tionic polarization is the reason for the electric polarization reversal induced by the high-T electropoling. A model to account for the observed emergent phe- nomenon is proposed based on the first-principles calculations.
The present work represents a substantial forward step into the emergent phenomena of multiferroicity in the RMn2O5family.
ACKNOWLEDGMENTS
This work was supported by the National Key Research Projects of China (Grant No. 2016YFA0300101) and by the National Natural Science Foundation of China (NNSFC) (Grant Nos. 51431006, 11834002, and 51721001). The work at Rutgers University was supported by the Department of Energy (DOE) under Grant No. DE-FG02-07ER46382.
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