Review

Ferrielectricity in DyMn

O

: A golden touchstone for multiferroicity of RMn

O

family

J.-M. Liu^†,§and S. Dong^‡

†Laboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures

Nanjing University, Nanjing 210093, P. R. China

‡Department of Physics, Southeast University, Nanjing 211189, P. R. China

§[email protected]

Received 17 May 2015; Accepted 2 June 2015; Published 23 June 2015

The RMn2O5manganite compounds represent one class of multiferroic family with magnetic origins, which has been receiving continuous attention in the past decade. So far, our understanding of the magnetic origins for ferroelectricity in RMn2O5 is associated with the nearly collinear antiferromagnetic structure of Mn ions, while the exchange striction induced ionic displace- ments are the consequence of the spin frustration competitions. While this scenario may be applied to almost all RMn2O5members, its limitation is either clear: the temperature-dependent behaviors of electric polarization and its responses to external stimuli are seriously materials dependent. These inconsistences raise substantial concern with the state-of-the-art physics of ferroelectricity in RMn2O5. In this mini-review, we present our recent experimental results on the roles of the 4fmoments from R ions which are intimately coupled with the 3dmoments from Mn ions. DyMn2O5is a golden figure for illustrating these roles. It is demonstrated that the spin structure accommodates two nearly collinear sublattices which generate respectively two ferroelectric (FE) sublattices, enabling DyMn2O5an emergent ferrielectric (FIE) system rarely identified in magnetically induced FEs. The evidence is presented from several aspects, including FIE-like phenomena and magnetoelectric responses, proposed structural model, and experimental check by nonmagnetic substitutions of the 3dand 4fmoments. Additional perspectives regarding possible challenges in under- standing the multiferroicity of RMn2O5as a generalized scenario are discussed.

Keywords: RMn2O5; multiferroic; ferrielectricity; 3d-4fcoupling; exchange striction.

1. Introduction

Multiferroic compounds of magnetically induced ferroelec- tricity, as promising magnetoelectric materials for immediate applications, are more or less despised currently but have been receiving continuous attention from the condensed matter physics community.^1–4On one hand, these compounds do enable a generation of ferroelectricity by magnetism-rel- evant mechanisms rather than lattice phonon-mode softening widely known in textbooks of ferroelectricity,^5–7since such phenomena had never been observed in realistic materials before. On the other hand, the strong coupling between electric polarization (P) and magnetization (M) plus their cross-controls via electric and magnetic stimuli routes have inspired continuous interest in the underlying mechan- isms.^8–11It is believed that these mechanisms for ferroelec- tricity generation and magnetoelectric cross-controls may be useful in searching for novel multiferroics with improved performances at high temperatures (T).^12,13

Up to date, extensive investigations on these emergent phenomena show off two major microscopic mechanisms for ferroelectricity generation,^8,11,14as sketched in Figs. 1(a)

and 1(b) for a guide of eyes where a charge-ordered spin chain is chosen for illustration, although other mechanisms for individuals were proposed.^15–17 Details for discovering these phenomena and relevant physics can be found in several recent review papers.^1,3Figure1(a)shows a noncollinear spin chain where a spin-pair is bridged by a ligand ion (e.g., oxygen O) and the spins are noncollinearly ordered in counterclockwise spiral (a1) or clockwise spiral (a2) align- ment.¹⁸The relativistic correction of the spin–orbit coupling to the exchange interaction, i.e., the so-called Dzyaloshinskii– Moriya interaction (DMI), drives a small shift of the ligand ions, since the exchange interaction can be enhanced at the cost of the shift-induced lattice energy.^8,9,14Given the spiral spin order along the chain direction, all the ligand ions shift along the same direction, leading to a net electric polarization perpendicular to the spin chain. This is the DMI mechanism and the generated polarizationPðPÞ e_ij ðS_iS_jÞ. The other mechanism refers to some specific collinear spin orders and one example is illustrated in Fig. 1(b) where the spin chain favors the ""## collinear order.^11,19 The symmetric exchange striction drives the two parallel nearest spins to near

*In celebration of the eightieth birthday of Prof. Xi Yao.

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 3.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.

JOURNAL OF ADVANCED DIELECTRICS Vol. 5, No. 2 (2015) 1530003 (18 pages)

© The Authors

DOI:10.1142/S2010135X15300030

Review

with each other and those antiparallel to apart from each other. Concomitantly, the ligand ions bridging the spin pairs will shift towards and away the chain, respectively, leading to net polarizationsPðPÞ ðS_iS_jÞ. It is called the exchange striction mechanism.

In spite of other mechanisms proposed, the above two have been well recognized for most multiferroics of noncol- linear and collinear spin orders, in particular for orthorhombic manganites RMnO₃ with R being rare-earth.³ Two generic characteristics associated with the spin order induced polar- ization P as functions of T and magnetic field H can be highlighted. First, both the noncollinear and collinear spin orders are the compromises of multifold exchange competi- tion which enables the spin structure highly frustrated. This leads to, in a usual way, a sequence of spin ordering starting from commensurate (C) and incommensurate (IC) antiferro- magnetic (AFM) orders with noncollinear or collinear alignment becomes possible and is often identified in multi- ferroic oxides such as manganites, ferrites, cobaltates, vana- dates, cuprates, etc.^3,12 It certainly implies that the temperatures for these spin orderings are low, and so is the FE Curie point (T_C). Obviously, driving the transitions between these spin orders does not need much additional exchange energy on cost of lattice distortion energy for ferroelectricity, implying that the as-generated electric polarization must be small either. In consequence, the measuredPðTÞcurve would exhibit anomalies at these ordering points. Second, these spin orders are not robust against intrinsic and external stimuli due to the strong spin frustration, which can be well illustrated by the giant magnetoelectric response. Even though, the two mechanisms show distinct difference in terms of the response, and the DMI induced polarization is quite sensitive toHbut the exchange striction induced one is not. Surely, details of such responses can be fascinating and materials dependent, and readers may consult recent review papers.^1,3,4,10

Apart from the two generic aspects, reality is that many more observed phenomena cannot be reasonably understood within the two respect frameworks. One issue to be covered in this mini-review is the very different FE behaviors in

compounds with coexisting 4fand 3dmoments.^20–23Without losing the generality, one may take the well-known multi- ferroic manganite DyMnO₃as an example. First, this material has two kinds of moments: 3d-Mn^3þ and 4f-Dy^3þ, which unfortunately add complexity to the two mechanisms for ferroelectricity generation and are appreciated due to in- volvement of additional physics.^21,22Second, the 3d-4fcou- pling in DyMnO₃is quite strong, which makes the Mn and Dy spin ordering sequences quite different.^20,24 It is known that the 4fmoments in rare-earth oxides free of 3dmoments may not order until extremely low temperature (T <1:0K).^25,26 One assigns this ordering temperature as T_Dy for DyMnO₃ (also DyMn₂O₅ to be discussed here).

However, this ordering in DyMnO₃occurs at a much higher temperature T_Dy10 K, which is believed to be driven by the strong Dy–Mn coupling, given that the Mn spins begin to order at40 K or higher.^22,24An immediate consequence is not only the much higherT_Dy, but more importantly the co- herent Dy spin ordering atT >>T_Dy, induced by the Dy–Mn coupling. For DyMnO3, this coherence results in the ""##

Mn–Dy–Mn–Dy spin alignment along the c-axis in the bc-plane, while the Mn spiral spin structure has its spiral wavevector along theb-axis.²²This specific Mn and Dy co- herent spin structure allows the co-existence of two FE sub- lattices generated respectively from the DMI mechanism (P_Mn sublattice) and exchange striction one (P_Dy sub- lattice).^22,27–29 Fortunately, the two components both align along thec-axis, enabling DyMnO₃to be a system with the largest polarization P¼P_MnþP_Dy ever observed in ortho- rhombic RMnO₃. The relevant physics can be illustrated in Fig.2and details can be found in an earlier paper.²⁹

DyMnO₃represents the first ever measured multiferroic compound where two FE sublattices coexist and coherently contribute to the total polarization which exhibits an unusual T-dependence, as shown in Fig. 2 (bottom).²⁹ It is usually believed that two coexisting FE sublattices most likely favor an antiparallel alignment, leading to an antiferroelectric (AFE) or ferrielectric (FIE) lattice, as often found in normal FEs.^30,31 For a reference, a FIE lattice and its T-dependent

∆P ~eijx (SixSj) (a2) CW spiral

∆P

∆P

O Sj

Si

(a1) CCW spiral

e_ij

(a)

∆P ~ (Si•Sj) (b2) Phase B

∆P

wavevector q_ij (b1) Phase A

∆P

S_i S_j

(b)

Fig. 1. (Color online) Two major microscopic mechanisms for polarization generations in single phase multiferroic compounds.¹⁸(a) The Dzyaloshinskii–Moriya interaction (DMI) mechanism associated with a noncollinear spiral spin order and the local polarizationPðPÞ e_ij ðS_iS_jÞwhere e_ij is a vector connecting one neighboring spin pair S_i andS_j bridged with oxygen as a ligand. (b) The symmetric exchange striction mechanism associated with a collinear""##(or !!) spin order and the localP(P) is proportional toSiSjwhere the spin pairS_iandS_jis bridged with oxygen as a ligand.

polarization are schematically shown in Fig.3where the two FE sublattices (blue and red) have different ordering tem- peratures, leading to a crossover from P<0 to P>0 (P¼P_þþP) upon decreasingT. This crossover is a prime characteristic for a FIE lattice.

An immediate motivation to this end is whether any FIE multiferroic is available or not. In fact, this issue was once concerned when another class of multiferroic manganites RMn₂O₅was claimed to exhibit ferroelectricity. As early as 2004, DyMn₂O₅was observed to exhibit a clear crossover of itsPðTÞbehavior (Palong theb-axis) and was argued to be a FIE system,³² while this phenomenon was not well charac- terized until recently.^33,34 Based on the knowledge of the ferroelectricity in DyMnO₃,²⁹ one has sufficient reason to expect possible AFE or FIE behavior in DyMn₂O₅. First, DyMn₂O₅also has 3dand 4fmoments: Mn and Dy ions, and strong Dy–Mn coupling is well confirmed.^35–40 More than this, here Mn has two valence states: Mn^3þ and Mn^4þ, im- plying the Dy^3þ–Mn^3þ and Dy^3þ–Mn^4þ couplings in ad- dition to the 3d and 4f exchange interactions themselves.

Such multifold coupling may bring more possibilities for two

or more FE sublattices to develop. Second, a remarkable perturbation of polarization P in response to complicated magnetic ordering sequence was identified, suggesting more than one polarization component in DyMn₂O₅.32–34,41–43

Third, recent investigations based on extensive neutron scattering and resonant X-ray scattering data disclosed the magnetic structure and its transitions, tampering a basis to find a correlation between spin structure and FE polarization.^35–43Finally, some RMn₂O₅members other than DyMn₂O₅ (R¼Ga, Tb, Ho, Er, Tm, Y, Bi, etc.) have been repeatedly revealed to be multiferroics and their polarizations show unusual behaviors too,32,33,35,37,39,43–48suggesting that ferrielectricity may be a common characteristic of some members of this family.

In the last several years, various attempts to figure out the microscopic origins for ferroelectricity in DyMn₂O₅ have been made32–34,41–43and so far available data demonstrate the ferrielectricity in DyMn₂O₅ in a self-consistent manner.

Several aspects were carefully investigated, addressing the pure, Mn-site substituted, and Dy-site substituted DyMn2O5.^49,50 The major features associated with the fer- rielectricity of pure DyMn₂O₅were sorted out. Our strategy was to start from these features and propose a phenomeno- logical framework.³⁴ The subsequent Mn-site and Dy-site substitution experiments were designed to check this frame- work.^49,50 In this mini-review, we intend to present all our data on the multiferroicity of DyMn₂O₅ in an integrated package, eventually revealing the FIE nature of DyMn₂O₅. The remaining part is organized as follows. In Sec. 2 are outlined the crystal structure, magnetism, dielectric and FE behaviors, and discussion on the underlying mechanisms for multiferroicity in literature on RMn₂O₅ and particularly DyMn₂O₅. Our improved experiments on polarizationPas a function ofTand Hand proposed FIE lattice model will be discussed in Sec.3. Subsequently, measured data on substi- tution trials at the Mn site and Dy site in order to validate this (a)

(b)

(c)

Fig. 2. (Color online) Well-recognized multiferroic scenario for DyMnO3with both 4fDy^3þspins and 4dMn^3þspins.²⁹(a) The spin structures on thebc-plane at four differentTas indicated in (c). (b) The as-generated two FE sublattices P_Mn and P_Dy at the fourT, respectively. ThePMn sublattice is generated via the DMI mecha- nism (PMn ½SiSjMn) and thePDysublattice is generated via the exchange striction (P_Dy ½S_DyS_Mn), as respectively shown in Fig.1. (c) The proposedPMn,PDy, andP¼PMnþPDyas a function ofT, respectively.

Fig. 3. (Color online) The polarizationPin a FIE upon decreasingT down to the negative–positive crossover pointT_P¼0. The FIE lattice consisting of two FE sublatticesP_þ andP at four differentTare inserted for guide of eyes.

model will be described in Secs.4and5. The conclusion and perspectives will be presented in Sec.6.

2. State-of-the-Art on Multiferroicity in DyMn₂O₅ 2.1. Crystal structure

All known RMn₂O₅ members have the same orthorhombic crystal structure of the Pbam space group at low T (<43 K),^35,39,46 while details of the lattice distortion depend on the R ionic size. The structural complexity is re- markably simplified by the well-demonstrated built-in or- dered ionic occupation and thus the charge order. The lattice consists of two types of alternatively stacked structural units.

One is the square pyramid where five oxygen ions occupy the corners and Mn^3þoccupies the center (not exactly at the center but shifted towards the square base). The other is the octahedral unit in which Mn^4þ takes the center position. On the ab-plane, the two structural units are corner-sharing via either the base or apex of the pyramids, while two neigh- boring pyramids contact via the base. Along the c-axis, the octahedral units align via the edge sharing and constitute the c-oriented Mn^4þ–Mn^4þ chains where the Mn^4þ coordinate along thec-axis isz₁0:25 (orz₁0:75). Thec-axis co- ordinate of Mn^3þ in pyramid units is z₂ 0:50.³⁹ This implies that the lattice consists of alternatively stacked Mn^4þO₆octahedral planes atz₁0:25, Mn^3þO₅pyramidal planes atz₂0:50, and Mn^4þO₆octahedral planes atz₁ 0:75 along thec-axis. The R ions occupy the empty space of the MnO₆octahedral and MnO₅pyramidal network, coordi- nating roughly atz₁0:0 andz₂1:0 along thec-axis, i.e., roughly on the MnO₆octahedral planes. Therefore, the onion stacking sequence along the c-axis is Dy^3þ–Mn^4þ–Mn^3þ– Dy^3þ–Mn^4þ–Mn^3þ– .

If such a lattice geometry applies to DyMn2O5, the as- generated lattice structure can be schematically drawn in Fig. 4(a) for a guide of eyes.^35–42 The ab-plane projected pattern is shown in Fig.4(b) where the Dy and Mn spins are labeled as color arrows and the oxygen ions on corners are ignored. It is seen that the two sets of pyramids and octahedra (gray and light-gray groups) constitute the plane network and the Dy^3þions occupy the empty space (white). There is ac/4 shift (cis the c-axis lattice constant) between the light-gray and gray sets of pyramids and octahedra, and for each set, the pyramids also have ac/4 shift with respect to the octahedra.

In spite of the structure complexity, the projected ab-plane block configuration shown in Fig. 4(b) can be the basis for discussion on magnetism and ferroelectricity of DyMn₂O₅.

2.2. Magnetic ordering and spin structure

The magnetic structures of RMn₂O₅, in particular that of DyMn₂O₅, have been extensively investigated mainly using neutron diffraction and resonant X-ray scattering techni- ques.^36,38–42 As expected, a series of IC-AFM and C-AFM

ordering events of Mn spins is discovered upon decreasingT from T_N043 K, above which the magnetic structure is paramagnetic (PM) with no ferroelectricity. If R is magnetic, the spin ordering can be more complicated. For DyMn₂O₅ where the Dy^3þ moment is 10B, the Mn^3þ/Mn^4þ PM phase transits into an IC-AFM phase belowT_N0, entering a C-AFM phase below T_N140 K which was found to be FE. Subsequently, two phase transitions at T_N228 K and T_N320 K were identified, accompanied with the gradual C-AFM to IC-AFM transitions until T_N3 below which the C-AFM phase disappears. The two phases are both FE but the dielectric permeability and electric polarization at these points show strong anomalies.^36,41 To the end, again a magnetic transition at T_Dy9 K was observed, which is believed to arise from the additional Dy spin ordering into a C-AFM phase plus the sustained Mn IC-AFM phase. This additional ordering is driven by the 4f-4f (Dy–Dy) interac- tions, as well recognized in many rare-earth oxides.^25,26

Up to date, it remains unclear whether the magnetic transitions atT_N2andT_N3are related to the Dy spin ordering or not. Most likely they are driven by the Dy^3þ–Mn^4þ and Dy^3þ–Mn^3þ couplings, given that the Dy^3þ–Mn^4þ separa- tion shorter than the Dy^3þ–Mn^3þ distance may favor a stronger Dy–Mn coupling. The consecutive magnetic transi- tions can be qualitatively explained by the competing inter- actions. The three major Mn–Mn exchange terms are denoted

(a)

(b)

Fig. 4. (Color online) The lattice structure of DyMn2O5(a), andab- plane projected lattice with Dy^3þ, Mn^3þ, and Mn^4þ spins denoted by color arrows (b). The Mn^4þO6octahedra and Mn^3þO5pyramids are drawn only for guide of eyes.

asJ₃,J₄, andJ₅in Fig.4(a),³⁹while the minor Mn^4þ–Mn^4þ, Dy^3þ–Mn^4þ, and Dy^3þ–Mn^3þ exchanges cannot be neglected either. These exchange interactions together with the relevant frustrations and anisotropies were discussed in detail but only qualitatively.^35–42

Nevertheless, it is interesting to find that almost all RMn₂O₅members with strong ferroelectricity exhibit nearly identical spin structure if the R moments are not consid- ered.³⁹ Otherwise, the structure can be slightly different, particularly in the low-Trange where the Dy spin ordering appears, as shown in Fig.4(b) for DyMn₂O₅.^35–42First, all the Mn spins have the major components lying on the ab-plane, implying that the in-plane anisotropy is dominant and the out-of-plane one is relatively weak. Second, the in- plane Mn spins are roughly collinear although the noncol- linear components cannot be negligible.⁵¹ It seems that the collinear components align along the b-axis for DyMn2O5

but along thea-axis for other RMn₂O₅members. The minor noncollinear alignment was claimed to be attributed to the competition between the exchanges and the DMI. Consider- ing the DMI mechanism for ferroelectricity, this noncollinear issue was discussed but no sufficient evidence echoing the major role of the DMI has been settled down.⁵¹ Third, the Dy spins also favor the collinear alignment with the Mn spins below T_N2 and T_N3, as shown in Fig. 4(b) too. The major collinear Dy spin structure developed above T_Dy makes the Dy spin re-ordering at T_Dy less essential in terms of ferroelectricity. It is thus suggested that this Dy re- ordering may even benefit to the ferroelectricity, different from the case of DyMnO3.

2.3. Ferroelectricity and magnetoelectric responses The ferroelectricity in RMn₂O₅and its magnetic origin have been highly concerned since the discovery of ferroelectricity in HoMn₂O₅, DyMn₂O₅, and TbMn₂O₅.^51–64 Phenomeno- logical theories on electric polarization has been developed, whose predictions seem to be qualitatively consistent with experimental results.⁶⁵⁶⁷ If only the Mn^3þand Mn^4þ spins are considered, the polarization is believed to be generated via the second mechanism shown in Fig.1(b). The exchange striction effect arises from the three-spin blocks, as sche- matically drawn in Fig.5where the open dots represent the Mn^3þions without exchange interactions. Despite the nearly collinear Mn spin ordering may take different configurations with two examples shown in Figs. 5(a) and 5(b), the ex- change striction induced Mn^3þ ionic displacements with re- spect to Mn^4þ are majorly along the b-axis, leading to polarizationP_Mnroughly aligned along theb-axis too. Based on this mechanism, a consensus on the ferroelectricity has been reached regarding the following several issues, while some issues remain unclear.^51–64

(1) No matter magnetic or nonmagnetic R, all the multi- ferroic RMn₂O₅members have their polarization along

the b-axis without exception. A connection of this property with the spin structures allows an argument that the polarization is essentially generated by the collinear Mn moments while the noncollinear moments play only minor roles if any.

(2) For all the cases, polarization P enters right below T_N1 and exhibits anomalous variations at those magnetic or- dering temperatures (e.g., at T_N2 or T_N3 for DyMn₂O₅), reflecting the intimate correlation between the spin structure and ionic displacement. This effect is particu- larly remarkable as R is magnetic, suggesting the sub- stantial roles of the 4felectrons.

(3) Regarding the responses ofPand dielectric permeability

(") to H, it has nearly no exception that remarkable

PðHÞ and "ðHÞ responses can be observed only in the

low-T range, typically below 20 K (below T_N2 for DyMn₂O₅), at least for the cases under weak magnetic stimulation. Interestingly, one can find that the low-T response, if any, is strong in those members with strongly magnetic R. It implies once more the essential roles of the R moments in determining the multiferroicity of RMn₂O₅, which is an issue less concerned so far but will be addressed in this mini-review.

Nevertheless, more than the reached consensus issues are those inconsistent and unclear issues. We highlight here several major but yet confusing points. For illustration con- venience, one focuses on the PðTÞ data, whose qualitative features are presented in Fig.6for a guide of eyes. It is noted that these data were measured by means of two different techniques, i.e., the Pyro method and Poling method,^32,41 which will be discussed later. We highlight those unclear issues first.

(1) Very different PðTÞ dependences were identified for different RMn₂O₅ members, leaving puzzling on the complicated physics associated with ferroelectricity.

These puzzles are more or less related to the techniques

(a) (b)

Fig. 5. (Color online) The exchange striction induced local polari- zationPMnin RMn2O5where the R spin if any is ignored. (a) The three ion blocks with roughly ! ð!! Þspin chains and (b) the three ion blocks with toughly""# ð##"Þspin chains. The solid (open) dots represent the ionic sites considering (ignoring) the ex- change striction effect, with the Mn^4þ ion as reference position in each block.

used for probing thePðTÞdependences. These distinct differences are shown in Fig.6(a) for R¼Ho, Dy, and Tb, where the three curves are taken from the data in Ref.32 obtained using the Pyro method and thoseT_N1,T_N2,T_N3, andT_Dyare referred to DyMn₂O₅. This was the first time to report the FIE-like behavior for DyMn₂O₅, while the PðTÞdependences for HoMn2O5and TbMn2O5are un- usual too.

(2) Given the Poling method used for measurements,⁴¹ the PðTÞdependences of different members also show dis- tinct differences, as shown in Figs.6(b)–6(f ). DyMn₂O₅ does show several clear anomalies atT_N1,T_N2,T_N3, and T_Dy.⁴¹ The polarization of HoMn₂O₅ becomes nearly disappeared below20 K,⁶⁸while GdMn₂O₅does not.⁴⁸ The most surprising is the positive-to-negative crossover of Pat T 20 K for YMn₂O₅,⁶⁴ noting that Y is non- magnetic.

(3) While magnetoelectric response of RMn₂O₅in terms of response ofPtoHis known to be weak, which is true in the high-T range, very remarkable responses are identi- fied in the low-Trange. A sufficiently highHcan trigger off large low-T polarization for HoMn2O5but suppress the low-Tpolarization for ErMn₂O₅.⁶⁸

(4) Continuous debate on the reason for nearly zero polari- zation in DyMn2O5below T_Dy remains, so does it for HoMn₂O₅ below 20 K.^34,41 The \non-FE" phase belowT_Dyfor DyMn₂O₅is called the X-phase. While Dy moment is big and believed to couple strongly with Mn moment, leading to destruction of the Mn spin exchange striction effect, no such phenomenon is observed in GdMn₂O₅where the Gd–Mn coupling is also strong.⁴⁸ In short, a general scenario for ferroelectricity in RMn₂O₅ family seems unavailable at this stage, and a case-by-case checking on each member is needed.³⁹In addition, the con- fusing issue of polarization measurement should be con- cerned since the two methods do prepare very different data.

Finally, it should be mentioned that ferroelectricity in mul- tiferroic oxides with strong electron correlations has both the electronic and ionic contributions.³¹In some cases, one may be negligible with respect to the other, while the two con- tributions are comparable and even cancelled in other cases.

The latter was predicted in HoMn₂O₅ by first principles calculations recently.⁶⁹In the present study, this issue will not be addressed, but it can be a critical ingredient for the physics of ferroelectricity in multiferroics.

2.4. Comments on polarization measurements

As mentioned above, so far available data on polarizationP as a function ofTandHwere measured mainly by means of two techniques. The first is the conventional pyroelectric current (Pyro) method, which has been extensively used in measuringPðT;HÞfor multiferroics with smallP(as small as 1.0C/m²) and low transition temperature. A schematic illustration of the Pyro method is given in Fig. 7(a). The sample covered with the top and bottom electrodes (e.g., Au) is submitted to electric poling under a fieldE_pole during the cooling run until T¼T_end, and then electrically short- circuited for sufficient time atT_end. TheT_endshould be as low as possible and for typical case T_end¼2 K. The released currentI_pyro from the sample under zero electric bias is pro- bed during the subsequent warming run fromT_end up to an assigned temperatureT₀. The I_pyroðTÞ is integrated from T₀ down to T_end, generating polarizationP as a function of T.

The Pyro method is applicable only ifPatT_end is nonzero, otherwise the electric poling down toT_end is almost ineffec- tive even ifPis nonzero at anyTother thanT_end.

The second is the Poling method, as drawn in Fig. 7(b).

Instead of the separated poling and probing steps, here the poling and probing are carried out simultaneously. The sample under a poling fieldE_poleis gradually cooled down to T_end from a highTduring which the total currentI_tot across the sample is probed. This field is supposed to be small sufficiently so that the field induced leaky current I_leaky is much smaller than I_pyro over the whole T-range. A proper fitting procedure may allow an exclusion of I_leaky, leaving I_pyroðTÞand thusPðTÞto be evaluated. An immediate ques- tion is the validity of assumptionI_leaky <<I_pyro, which may Y (f)

Gd (e) Er (d) Ho (c) Dy (b) H=0 (a)

Fig. 6. (Color online) Schematic traces of measured polarization PðTÞ data along theb-axis for RMn2O5: (a) R¼Dy, Tb, and Ho;

(b) R¼Dy; (c) R¼Ho; (d) R¼Er; (e) R¼Gd; (f ) R¼Y; res- pectively.32,41,48,64

The methods (Pyro method and Poling method) for measuring the polarizations are marked aside. The magnetic field applied for the measurement in each case is labeled.

not be always true for RMn₂O₅, since a smallE_poleimplies an incomplete poling of the sample and thus the evaluatedPmay not be the saturated one. Furthermore, a separation ofI_pyro fromI_totis anyway a matter if the dependencesI_leakyðTÞand I_pyroðTÞare unknown. In fact, Higashiyamaet al.discussed these issues in their work.⁴¹The problem here for RMn₂O₅is that this method may not identify correctly the FIE state.

Given the above discussion, we again come back to the Pyro method and have applied it for careful measurements of the releasedI_pyroðTÞdata, noting that our Pyro technique is of precision as high as 0.05 pA. The details of experiments covered in this mini-review can be found in earlier literature, including samples synthesis, microstructural characteriza- tions, and measurements on thermodynamic, magnetic, and electric properties, which will not be described here any more.

3. Results on DyMn₂O₅

Our data reported here are on well-prepared polycrystalline DyMn₂O₅ samples,³⁴ while data reported in literature on single crystals are taken for comparison. Since special emphasis will be oriented onto the Mn- and Dy-sites

substitutions, a preparation of whole set of single-crystal samples is challenging, and polycrystalline samples are much easier to access.

3.1. Magnetic and electric characterizations

The magnetic ordering sequence can be sensitively probed by specific heat data (C_P), while magnetization data are insen- sitive to the Mn spin ordering due to that the magnetic signals are mainly from the Dy moments much stronger than Mn moments. TheT-normalized specific heat (C_P/TÞandMas a function ofTare plotted in Figs.8(a) and8(b), respectively.

Earlier determined magnetic ordering points T_N1, T_N2, T_N3, and T_Dy are labeled and the assigned paraelectric (PE), fer- roelectric (FE1, FE2, FE3), and X phase regions are marked too for reference, where differences of the three FE phases (FE1, FE2, FE3) remain unclear and the X phase was claimed to be non-FE.⁴¹It is seen that theC_P/TðTÞcurve shows clear anomalies at these points, while theMðTÞcurve exhibits no anomaly except the broad peak atT_Dy, reflecting gradual Dy spin ordering proceeding over the broad T-range in the low-Trange (belowT_N2 orT_N3).

(a)

(b)

Fig. 7. (Color online) Schematic drawing of the (a) Pyro method and (b) Poling method for probing polarizationP. In the Pyro method, the electrode-coated sample is pre-poled electrically from a sufficiently highTdown to a givenT_endat which the electric fieldE_poleis removed, followed by a sufficiently long time electric short-circuiting of the sample. Then the sample is slowly warmed up fromTendduring which the pyroelectric currentI_pyro released from the two electrodes is collected. In the Poling method, a low electric fieldE_pole is applied to the electrode-coated sample from a sufficiently highT, followed by a slow cooling of the sample during which the current passing across the sample is collected. Then an author-dependent procedure is taken to separate the leaky current and polarized current, so that polarizationPcan be obtained from the polarized current data.

The magnetic ordering can also find sensitive response in dielectric permeability ("), as shown in Fig.8(c). The stron- gest anomaly atT_N1 and broad peak atT_N3 suggest the FE transitions. The transition at T_N1 can be tentatively assigned as the consequence of the collinear Mn spin order- ing and that atT_N3 marks the induced Dy spin ordering in coherence with the Mn order. The anomalies at T_N2 and T_Dy are relatively weak, indicating the minor variations of polarizationPat these points. In particular, the small bump at T_Dy reflects the variation ofPdue to the Dy spin ordering driven by the Dy–Dy exchange interaction which is no longer negligible at lowT.

TheI_pyroðTÞis also sensitive to these spin orderings, and the data are plotted in Fig. 8(d). The one-to-one correspon- dence among the I_pyroðTÞ peaks, the "ðTÞ peaks, and the C_P=TðTÞanomalies is clearly identified, suggesting that the I_pyro signals are indeed from the variation ofPon one hand and the pyroelectric current may be one of the most sensitive parameters to magnetic ordering in multiferroics on the other hand. Here, more significant are the negative peak at T_N1

and the positive peaks at T_N3 and T_Dy, immediately allowing an argument that DyMn2O5 may be a FIE rather than a FE.

In addition, thePðTÞdata in earlier reports from various groups are reproduced for comparison purpose, as shown in Figs. 8(e)–8(h). The data in Fig. 8(e) are from Ref. 32 obtained using the Pyro method, showing the negative–pos- itive crossover of P roughly at T_N3, consistent with our results. It is noted that the assigned X phase has nonzeroP, suggesting that it is FE. ThePðTÞdata in Figs.8(f)–8(h) were obtained using the modifiedP–Eloop method from Ref.41, the Poling method from Ref.41, and the so-called positive-up and negative-down (PUND) method⁶⁰ in our group on polycrystalline sample, respectively. For these cases, the measuredP must be positive since the measurements were performed under an electric bias. Even though, one sees various features of thesePðTÞcurves aroundT_N1,T_N2,T_N3, andT_Dy. These methods basically cannot identify the ferrie- lectricity if any, but thePin the low-Trange is indeed small.

In fact, no clear explanations for these features have been available so far. In short summary, there appears substantial difference between the results obtained using different methods, appealing for more careful handle of these issues.

This is the reason for us to come back to the Pyro method which can more reliably and precisely probe the pyroelectric current without the electric bias induced leaky current and other activations.

Subsequently, the measuredI_pyroðTÞdata at three different warming rates (2, 4, 6 K/min) are plotted in Figs.9(a)–9(c), given E_pole¼10 kV/cm. The three I_pyroðTÞ curves almost overlap onto a master curve, demonstrating that the current is indeed from the pyroelectric effect. Furthermore, theI_pyroðTÞ data givenE_pole¼ 10 kV/cm are plotted in Fig.9(d) and a completePreversal is demonstrated by the sign-opposite but magnitude-identical two curves, as further concurred by the as-evaluated PðTÞin Fig. 9(e), revealing the FIE character- istics. The negative–positive crossover occurs roughly at TT_P¼0T_Dy, while thisT_P¼0may vary upon the different measuring conditions. More detailed analysis on the data can be found in earlier report.³⁴

3.2. Model for ferrielectricity

Given the FIE characteristics, one is concerned with the un- derlying mechanism. Starting from the structural model shown in Fig.4(b) for DyMn₂O₅, it is noted that the Dy spins are disordered untilT_N2 (orT_N3), below which the Dy spin ordering proceeds. Therefore, the spin configuration in Fig. 4(b) represents the state below T_N2 (or T_N3). Without losing generality, we discuss the structural model in Fig.4(b).

Consulting to the exchange striction scenario shown in Fig.5 for RMn₂O₅with nonmagnetic R ion, one can easily propose a similar scenario for DyMn₂O₅, taking the Mn^4þ ions as reference points. The spin lattice projected on theab- plane is presented in Fig.10(a), while the three-spin blocks to

0.0 0.3 0.6 0.9

0.0 0.1 0.2

21 22 23 24

0 10 20 30 40 50 -20

0 20

-0.6 -0.3 0.0 0.3 0.6

0 1 2

0 1 2

0 10 20 30 40 500.0 0.1 0.2 0.3

X phase FE3 phase FE2 phase FE1 phase PE phase

X phase FE3 phase FE2 phase FE1 phase PE phase

Ipyro (pA)εM (emu/g)CP/T (J/mol K2 ) (a)

T_N1 T_N2 T_N3 T_Dy

(b) _ZFC

FC

(c)

Pyro method

T (K) T (K)

(d)

2K/min, T_end=2K

E_pole=10kV/cm 2 PPPP⇐ (mC/m) PUNDpoleP-Epyro (e) data taken from Ref.[32]

Pyro method

single crystal along the b-axis

(f) data taken from Ref.[41]

single crystal along the b-axis

P-E loop

single crystal along the b-axis (g) data taken from Ref.[41]

Poling method

T_N3

(h) data by PUND method

T_N1 T_N2 T_Dy

Fig. 8. (Color online) Measured T-normalized specific heat CP/T (a), dc magnetization M under zero-field cooled (ZFC) and field cooling (FC) modes with measuring field of 1000 Oe (b), di- electric permeability"at 10 kHz underacsignal of 50 mV (c), and pyroelectric current Ipyro (d) for polycrystalline DyMn2O5, as a function ofT, respectively. The measured polarizations as a function ofTrespectively taken from Ref.32using the Pyro method (e), from Ref. 41 using the P–E loop method (f), from Ref. 41 using the Poling method (g), and measured using the PUND method (h), re- spectively, are presented for comparison. The data in (e)–(g) were obtained for DyMn₂O₅single crystal samples.

be considered are plotted in Figs. 10(b) and 10(c), respec- tively. In spite of the non-negligible noncollinear compo- nents, the three spins in each block are roughly parallel or antiparallel along the b-axis. For the Mn^3þ–Mn^4þ–Mn^3þ blocks, the two Mn^3þions shift upward along theb-axis with respect to the central Mn^4þion due to the exchange striction, leading to a local polarization P_MM. Contrary to this effect, the two Dy^3þ ions in the Dy^3þ–Mn^4þ–Dy^3þ blocks shift downward along the b-axis, leading to a local polarization P_DM. These blocks organize themselves by alternative stacking and occupy the wholeab-plane, constituting two FE sublatticesP_MM andP_DM, to be discussed in detail below.

What should be reminded here is that various RMn₂O₅ members may have different spin structures. For GdMn₂O₅ and most members other than DyMn₂O₅, the Mn spins align majorly along thea-axis instead of theb-axis.⁴⁸However, the exchange striction model remains similar and the P_MM still aligns along theb-axis. In addition, for DyMn₂O₅here, the

P_DM sublattice is not generated untilT <T_N2 (orT_N3), im- plying that only theP_MM sublattice is available aboveT_N2(or T_N3), which disappears atT_N1.

We discuss the details of this ferroelectricity. Upon de- creasingTfromT_N0, the negativePappears atT_N1 and its magnitude increases rapidly, as shown in Fig.11, curve (a), implying that the P_MM sublattice aligns in opposite to the poling field (E_pole). TheP_DMsublattice, opposite to theP_MM sublattice, enters atTT_N2(orT_N3) and theP_DMmagnitude increases gradually untilT_P¼0 below whichP_DM jP_MMj, enabling the crossover from theP<0 to theP>0 (Fig.11, curve (a)).

In addition, for those RMn₂O₅with nonmagnetic R, the magnetic ordering is far from complicated as that in DyMn₂O₅, implying that the latter is more or less related to the Dy–Mn coupling.^43–48As the zero-order approximation, one may assume that theP_MMsublattice is irrelevant with the Dy–Mn coupling which is actually not true to some extent, and thus P_MM as a function of T reaches smoothly the

(a)

(b)

(c)

(d)

(e)

Fig. 9. (Color online) Measured pyroelectric currentI_pyroðTÞcurves at warming rate of 2 K/min (a), 4 K/min (b), 6 K/min (c), respec- tively, using the Pyro method withEpole¼10 kV/cm. TheIpyroðTÞ curves at 2 K/min withE_pole¼ 10 kV/cm and the corresponding polarizationPðTÞcurves are presented in (d) and (e), respectively.

(a)

(b)

(c)

Fig. 10. (Color online) (a) Spin structure of DyMn2O5belowTN2

(T_N3) projected in theabplane, where the solid (open) dots represent the ionic sites considering (ignoring) the exchange striction effect, with the Mn^4þ ions as the reference positions. The four types of three-ion blocks are plotted in (b) and (c) with the exchange striction induced local electric polarizationsPMM andPDM. The ionic sizes are shown only for guide of eyes.

saturated value. This P_MMðTÞ dependence is shown in Fig. 11, curve (b) (dashed blue line). Consequently, the as- extractedP_DMðTÞcurve is plotted in Fig.11, curve (c). The minor features at T_N2, T_N3, and T_Dy, are all due to the Dy–Mn coupling induced magnetic orderings. To this stage, the P_MM andP_DM as a function ofT respectively are inten- tionally separated based on the several assumptions.

In correspondence to theP_MMðTÞandP_DMðTÞcurves, the two FE sublattices below T_Dy and T_N1 are schematically shown in Figs. 11(b), 11(c) and 11(d), 11(e), respectively, with the FIE lattice shown in Fig. 11(a). The observed PðTÞ dependence is reasonably explained by the proposed FIE model at least qualitatively, although it may be over- simplified and many details associated with the magnetic ordering are ignored, which is questionable but the FIE scenario remains unaffected.

3.3. Magnetoelectric effect

As mentioned in Sec.2, the 4fspin order in oxides is usually fragile against stimuli and the magnetic field driven re- orientation of 4fspins can be realized at a field far lower than 1.0 T. In DyMn₂O₅, the Mn spin order is sufficiently high against magnetic field above 10 T.^35–42 In this case, one has reason to expect that the Dy spin order stability can be enhanced significantly by the Dy–Mn coupling, up to several Tesla. Therefore, the Dy spin re-orientation can be illustrated in Fig. 12(a), where an H//a-axis drives the Dy spins along the b-axis to re-orient and thus disables the exchange

striction induced Dy ions' shift along theb-axis, i.e., melts away the P_DM sublattice, resulting in significant magneto- electric effect.

Our experiments did confirm this prediction. The sample was first electrically poled down toT 6 K, and the poling was removed, followed by applying a given H. After the sample was sufficiently short-circuited, the pyroelectric current under the givenHwas collected during the warming process. The measuredPðTÞcurves under a series ofHare plotted in Fig.12(b). The magnetic field does suppress the positive P in the low T-range, leading to the negative P over the whole T-range at H>3:0 T. This effect is quali- tatively drawn in Fig. 12(c) where the vertical solid olive arrows indicate theH-induced suppression ofP_DM and then P, while P_MM remains little suppressed. The responses of the two sublattices to H are schematically drawn in Figs. 12(d)–12(f).

(a) (b) (c)

(d) (e)

Fig. 11. (Color online) The proposed FIE lattice model for DyMn2O5. The measured PðTÞ curve as well as the speculative PMMðTÞandPDMðTÞcurves are plotted together. The proposed FIE lattice,PDMsublattices andPMMsublattices atT<TDyandT<TN1

are plotted in (a)–(e), respectively, only for guide of eyes.

(b)

(c)

(e) (f)

(e) (f)

(d) (a)

Fig. 12. (Color online) The proposed three-ion spin blocks under H¼0 andH>0 (e.g., 10 T) are plotted in (a). The measuredPðTÞ curves under various Hare presented in (b). As an example, the PMMðTÞ and PDMðTÞ curves together with thePðTÞ curves under H¼0 andH>0 (e.g., 10 T) are plotted in (c), whereP_MMðTÞis assumed to be robust againstH. The FIE lattice is given in (d), and the corresponding two sublattices under H¼0 and H>0 are shown in (e) and (f ) for illustrating the consequence of applying magnetic field.

3.4. Discussion

The proposed FIE model seems to reasonably explain all the observed phenomena associated with the unusualPðTÞ and PðHÞdependences in DyMn₂O₅, although those features at T_N2,T_N3, and T_Dy remains unclear yet. Nevertheless, addi- tional more convincing evidence concurring with this model is required, since a connection of the polarization crossover at T_P¼0 with the FIE model is far from sufficient.

The magnetoelectric effect reported above suggests an alternative strategy. While the suppression of the collinear Dy spin order contributing to the P_DM can be realized by ap- plying a magnetic field, it would be done too by nonmagnetic substitution of Dy, which can definitely inactivate the ex- change striction in the Dy(R)^3þ–Mn^4þ–Dy(R)^3þblocks and thus remove gradually the P_DM sublattice with increasing substitution level. Stimulated by this approach, one can consider a nonmagnetic substitution of Mn^3þtoo, which can surely remove gradually theP_MM sublattice. Given a proper

design of the substitution experiments, one may reach a status in which one sublattice is gradually removed while the other remains less affected so that an FIE–FE transition is expected at certain substitution level. In addition, for the latter case, a critical issue is that the Mn-site substitution has to exclude the replacement of Mn^4þions since the two sublattices would be removed simultaneously of the Mn^4þ site is occupied with nonmagnetic ion.

The above discussion can be highlighted in Fig.13, where the double-line arrows denote theP_MMandP_DM, respectively and their coarseness scales the magnitude. The exchange striction modes forP_MM andP_DMin DyMn₂O₅are shown in Fig. 13(a), while the consequences of nonmagnetic sub- stitutions at Mn^4þ-site, Mn^3þ-site, and Dy^3þ-site, respec- tively, are shown in Figs. 13(c)–13(e). The substitution at either Mn^3þ site or Dy^3þ site is clearly illustrated. For comparison, the consequence of imposing a magnetic field is re-given in Fig.13(b). A realization of these roadmaps relies on several pre-requisites, while a reliable check of the FIE model will be questioned otherwise. First, the substitution should distort the lattice as weakly as possible so that the exchange interactions remain less perturbed. Second, the valence state should be maintained to avoid any charge doping. Third, the correct site occupation is critical since DyMn₂O₅is an occupation-ordered compound.

4. The Al Substitution of Mn: Proof Test I 4.1. Structural distortion, chemical valence states,

and magnetism

As the one side of the evidence coin for the FIE model, the Mn^3þ-site substitution by Al^3þ is considered.⁴⁹ It is noted that Al^3þ is only slightly smaller than Mn^3þ/Mn^4þ and the electronegativity values of Mn and Al are similar too. While details of the polycrystalline DyMn_2xAl_xO₅sintering were described previously, we present in Fig. 14(a) the room temperature 2X-ray diffraction patterns for a series of samples. All the reflections can be indexed by the standard database of DyMn₂O₅, and peak shifting towards the high- angle side is observed as seen in the insert of Fig. 14(b).

Substitution up to x0:20 does not change the lattice symmetry and induce any minor impurity phase. As an ex- ample, the Rietveld refining of the data for samplex0:04 is as shown in Fig.14(b), with the refining reliability as high as R_wp4:48%.

The evaluated lattice unit volume Vas a function of x plotted in Fig.14(c) shows a linearly decreasing dependence consistent with the Vegard's law, implying the favored sub- stitution of Mn^3þ ions by Al^3þ ions. Additional careful checking of the valence states of Mn using the XPS deter- mination upon the substitution is performed, revealing no trace of intensity from Mn^5þ or Mn^2þ within the appa- ratus resolution. Since the binding energies for the Mn^3þ2p₁₌₂/Mn^4þ2p₁₌₂and Mn^3þ2p₃₌₂/Mn^4þ2p₃₌₂are close Fig. 13. (Color online) The proposed substitution strategy for

DyMn2O5, as illustrated by the three-ion spin blocks. The solid (open) dots represent the ionic sites considering (ignoring) the ex- change striction effect, with the Mn^4þ ions as the reference posi- tions. The spin structures in these blocks for (a)x¼0 andH¼0, (b)x¼0 andH>0 (e.g., 5–10 T), (c) Al substitution of Mn^4þand H¼0, (d) Al substitution of Mn^3þ and H¼0, and (e) Y substi- tution of Dy^3þ and H¼0, are schematically drawn, respectively.

The blue+ and red*arrows denote the PMM and PDM for these cases, with the coarseness representing the Magnitudes.