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J Materiomics Vol 2, 2016 Graphical Abstracts

REVIEW ARTICLES

J Materiomics 2016, 2,213e224 DyMnO₃: A model system of type-II multiferroics

Chengliang Lu^a,*, Jun-Ming Liu^b,**

aSchool of Physics&Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China

bLaboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

In this short review, some recent experimental results on tailoring the multiferroicity and magnetoelectric coupling in DyMnO3were represented. The multiferroicity and magnetoelectric coupling of DyMnO3were described based on various approaches including chemical substitution and strain/domain engineering. These results may indicate some alternative strategies in designing superior multiferroicity and unconventional magnetoelectric controls for multiferroic applications.

J Materiomics 2016, 2,225e236 Recent development of n-type perovskite

thermoelectrics

Hongchao Wang*, Wenbin Su, Jian Liu, Chunlei Wang**

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, China

SrTiO3and CaMnO3-based bulk thermoelectric perovskite oxides have been systematically reviewed. The element doping as traditional modification is generally used for improving the figure of merit of oxide. Nanostructuring, nanocomposite and defect chemistry engineering are beginning to significantly enhance the thermoelectric performance, especially for SrTiO3based oxide and more state-of-the-art values of figure of merit have been achieved. So nanostructuring, nanocomposite and combining doping and defect chemistry engineering can be developed to further optimize the thermoelectric performance of oxides as the effective methods. And then more significant breakthrough on high-temperature thermoelectric oxides will be achieved in future.

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DyMnO

₃

: A model system of type-II multiferroics

Chengliang Lu

^a,

* , Jun-Ming Liu

^b,

**

aSchool of Physics&Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China

bLaboratory of Solid State Microstructures and Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

Received 14 January 2016; revised 14 March 2016; accepted 7 April 2016 Available online 3 May 2016

Abstract

One of the main motivations for multiferroic researches is to explore distinctive magnetoelectric controls for conceptually novel electronic devices and information storage technologies. DyMnO3possesses two major microscopic mechanisms for ferroelectricity generation, i.e., the inverse DzyaloshinskiieMoriya interaction between Mn spin pairs and the exchange striction between DyeMn spin pairs, making it an aggressive model to address various opportunities for magnetoelectric controls. In this short review, some recent experimental results on tailoring the multiferroicity and magnetoelectric coupling in DyMnO3were represented. By means of various approaches including chemical substitution and strain/domain engineering, we have demonstrated the multiferroicity and magnetoelectric coupling of DyMnO₃, which can be manipulated over a broad scale. These results may bring alternative strategies in designing superior multiferroicity and unconventional magnetoelectric controls for multiferroic applications.

Keywords:Multiferroic; Ferroelectricity; Exchange striction; Thin film; Domain

Contents

1. Introduction . . . 213

2. Dual nature of multiferroicity in DyMnO₃. . . 214

3. Ferroelectricity by tuning the Dy³^þeMn³^þspin coupling . . . 216

4. “Copy”bulk multiferroicity to DyMnO₃thin films . . . 217

5. Continuous ME control . . . 220

6. Conclusion . . . 223

Acknowledgments . . . 223

References . . . 223

1. Introduction

The terminology“multiferroics”refers to those materials in which two or more ferroic orders such as ferroelectricity and

(anti-)ferromagnetism coexist [1,2]. Among all the available multiferroic materials, type-II multiferroics of magnetic origin stand out due to the unique one-to-one correspondence between ferroelectric (FE) and magnetic orders [3e6]. The intimate coupling between the two orders gives rises to giant magnetoelectric (ME) effect, such as polarization (P) switching in multiferroics hosting a spiral spin order (SSO) [7]. So far, dozens of type-II multiferroic materials have been explored, and our understanding of the ferroelectricity and magnetism coexistence which otherwise would have been

*Corresponding author.

**Corresponding author.

E-mail addresses: [email protected] (C. Lu), [email protected] (J.-M. Liu).

Peer review under responsibility of The Chinese Ceramic Society.

Available online atwww.sciencedirect.com

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impossible within the framework of ferroelectricity- magnetism exclusion[8].

In general, these type-II multiferroics with magnetic origin for ferroelectricity can be further classified according to the details of microscopic mechanism. The first group includes those having a noncollinear spiral spin order, making a broken space inversion symmetry and thus a spontaneous FE polarization via the well-known inverse Dzya- loshinskiieMoriya interaction (DMI). The as-generated polarization is formulated asP~eij(SiSj), whereeijis the vector connecting two neighboring spins Si and Sj [9]. A unique property of these multiferroics in this group is the magnetic field (H) driven polarization switching, leading to a giant ME effect which has been repeatedly revealed in TbMnO₃ (TMO) and DyMnO₃ (DMO) [10]. The second group has a specific collinear spin configuration, and consequently an improper ferroelectricity may be driven by the so- called exchange striction mechanism. The polarization can be expressed asP ~ Si,Sj, as demonstrated in Ca₃Co_1xMn_xO₆ and orthorhombic HoMnO₃etc[11e15]. The FE polarization generated via this exchange striction mechanism is usually much larger than that from the DMI mechanism, and actually among the largest for all the type-II multiferroics. In addition to these two mechanisms, there is still one more worthy mentioning, namely the spin dependentp-dhybridization, and the polarization is written asP~ (Si,eil)²,eilwhereeilis the vector connecting Siand the neighbor ligand ions [16]. One symbolic material featured with this p-d hybridization is Ba2CoGe2O7, in which the polarization can be rotated in harmonization with the spin Si rotation driven by magnetic field [16]. However, the as-generated polarization Pin such multiferroics is usually small (<100 mC/m²) despite this manipulation is impressive.

Indeed, a bunch of novel ME control functionalities have been demonstrated in these type-II multiferroics. Importantly, it is found that the magnetic manipulation of P can be fundamentally distinct in different multiferroics because of different microscopic origins. For instance, the magnetic field control of polarization Pin the first group of multiferroics is relatively easy but the polarization magnitude is insufficiently large. The opposite situation is often observed for the second group of multiferroics where the polarization is large but its controllability using magnetic field is far from expectation [10,12].

Besides, the physics of multiferroics is evidenced with much more fascinating phenomena, and one of them is the more than one mechanism has been found to be involved in some multiferroics, coined as the duality or triplicity of multiferroicity. This property provides an avenue for unconventional ME functionalities. As a typical example, one considers DyMnO₃(DMO) as one member of the RMnO₃family where R is the rare-earth element, which was classified into the first group and the ferroelectricity was thought to originate the noncollinear spiral spin order until recent experiments [17].

Now it is well accepted that the total polarizationP_calong the c-axis in DMO includes two components, one from the symmetric exchange striction between the R³^þeMn³^þspin pairs

(R is the rare earth element), i.e.,P_R¼P_Dy~SDy$SMnand the other from the inverse DMI mechanism between the MneMn spin pairs, i.e., P_Mn ~ (Si Sj)_Mn. The total polarization reaches up to P_c ~ 2800 mC/m². Furthermore, a colossal magneto-capacitance up to ~500% was reported, owing to the subsequent response of the two components to magnetic field.

In this sense, DMO can be viewed as a model system to investigate a series of unusual issues like multiferroic duality and multi-fold ME manipulation, not only benefiting to our understanding of unconventional phenomena in type-II multiferroics but also allowing more opportunities for functionality realization and optimization. We shall present a breakthrough point at which one sees how DMO opens up these aspects. For example, a specific domain structure in DMO thin films properly deposited on some substrates has been found, which as an additional degree of freedom adds more functionality[18e20]. Some research aspects regarding cation substitution, strain and domain engineering, and magnetoelectric control in both bulk and thin film DMO were represented.

2. Dual nature of multiferroicity in DyMnO₃

We start from the duality of DMO, which is the basis for the present work. A seminal work among a huge number of earlier investigations on multiferroics was the discovery of multiferroicity in TbMnO₃(TMO) in 2003 and the ferroelectricity appears as a consequence of spiral spin ordering[21].

Subsequently, several more materials in this category were found[10,22], while DMO has been receiving more attention than TMO because of its intriguingly large FE polarization and colossal magento-capacitance [23,24]. However, these superior properties were not well understood until 2009 when the details of magnetic structure were unveiled.

In fact, DMO has an orthorhombic perovskite structure with lattice parameters a ¼ 5.8337(1), b ¼ 7.3778(1), and c ¼ 5.2785(1) Å at room temperature [25]. A significant structural characteristic, owing to the small ionic size of Dy^3þ, is the GdFeO₃-type distortion which drives the MnO₆ octahedra tilting in theab-plane and rotation with respect to thec- axis. Such a distortion reconstructs the multifold exchange interactions among Mn³^þ, and thus stabilizes the Mn³^þspiral spin order if the Jahn-Teller effect is taken into account[26].

As revealed by neutron diffraction, the Dy³^þ spins do align coherently with the Mn³^þspins below a certain temperature due to the strong Dy^3þeMn^3þcoupling[27], making the Dy^3þ spins to align noncollinearly and incommensurately in coherence with the Mn^3þspiral spin order.

Indeed, the spin configurations of DMO are illustrated in Fig. 1. In the cooling sequence, DMO experiences the Mn^3þ spin ordering to a sinusoidal antiferromagnetic (AFM) structure at temperatureT ¼ T_N ~ 39 K, and then to an incom- mensurate (ICM) spiral structure at T ¼ T_C ~ 19 K. An emergent FE polarization along thec-axis (P_Mn) is induced via the inverse DMI mechanism. Further cooling causes a remarkable enhancement of total polarizationP_c, which can be twice that of TMO in whichP_Mnis the dominant contribution

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toP_c[10,27]. When the Dy^3þspins evolve coherently with the Mn^3þ spins below T_C, as shown in the upper of Fig. 1, a specific magnetic structure is developed, in which the Mn³^þ spins on each Mn-chain align parallel to the Dy³^þspins on one of the nearest neighboring Dy chain but antiparallel to those on the other nearest neighboring Dy-chain. This configuration, called the synchronization between the Dy³^þ spin sublattice and Mn^3þ spin sublattice, fits well the requirement for the exchange striction mechanism, giving rise to an additional net componentP_R¼P_Dyand thus one hasP_c¼P_MnþP_R [17].

AtT¼T_R~ 7 K, the Dy^3þeDy^3þinteraction goes beyond the Dy^3þeMn^3þ coupling, and an independent commensurate (CM) ordering of Dy^3þ spins appears. This ICM-CM transition of Dy^3þspins eliminates the polarization componentP_R, leaving the polarization componentP_Mnalone and thus leading to a rapid drop of P_c below T_R ~ 7 K. As revealed by neutron diffraction, this ICM-CM transition exhibits an evident thermal hysteresis, well illustrating the bifurcation of P_c(T) curves obtained through different cooling procedures [23,27]. The Pc(T) dependence in bulk DMO is shown in Fig. 1(a). On the contrary, this ICM-CM transition can be suppressed by a magnetic fieldH, resulting in a reentrancy of componentP_R, and thus a remarkable enhancement of P_c, as shown inFig. 1(b) [24].

Interestingly, Schierle et al. observed the sizableb-axis and c-axis components of Dy^3þ spins using the soft X-ray diffraction at the Dy-M5 resonance on DMO[28]. This sug- gests a cycloidal Dy^3þspin order atT_R<T<T_C, which may also contribute to the ferroelectricity further via the inverse DMI mechanism between Dy^3þspin pairs. This issue remains to be addressed in future. Even though, such a possible cycloidal Dy^3þspin order is still coherent with the Mn^3þspin

structure, allowing the Dy^3þeMn^3þ exchange striction mechanism active.

To this stage, the above results do allow one to claim that DMO could not be better to act as a platform for illustrating the rich physics of multiferroicity. In fact, the strong R³^þeMn³^þcoupling is not an unusual phenomenon for multiferroic RMnO₃. TMO is another system in which the Tb spins develop an order with the same propagation vector (t^R) as that (t^Mn) of the Mn spin order, i.e., t1Tb ¼t^Mn¼0.274, right belowT_C¼27 K[29]. AtT¼T_R~ 7 K, vectort1Tbshifts to a higher value of 0.286, and simultaneously a second wave vectort2Tb¼0.4285 for the Tb^3þsublattice appears, leading to an evident kink in the P_c(T) curve. The orthorhombic HoMnO₃ with an E-type AFM order was theoretically predicted to show a remarkable FE polarization along thea-axis via the exchange striction of Mn^3þ spins [11]. However, experimentally only a FE phase withP_c~ 1500mC/m²which continuously increases with decreasing Tdown to ~2 K, was identified[12]. Neutron diffraction on HoMnO₃revealed that the Ho spins also evolve coherently with the E-type AFM order of Mn³^þspins, responsible for the emergentPcviathe Ho³^þeMn³^þ exchange striction. As compared with DMO, a surprising feature for HoMnO₃ is that the HoeMn coupling contributes to the FE phase significantly till a very low Tfar below T ¼ T_R, suggesting no independent ordering of the Ho^3þ spins [12,30]. The situation in GdMnO₃is a bit more complicated since this material doesn't show apparent ferroelectricity [10], unless a magnetic field is applied, which rigidly tracks the field-induced modification of Gd^3þ spin sublattice. While the underlying mechanism for the ferroelectricity in GdMnO₃ has still not been well understood because of the absence of sufficient magnetic data, the Mn^3þ

Fig. 1. (a) TheT-dependence of out-of-plane FE polarizationPcfor DyMnO3(red and purple lines) and TbMnO3(dashed line). Three regions can be identified belowTC, and the corresponding spin structures projected onto thebc-plane are shown in the top of figure. Reprinted by permission from Ref.[27]. (b) TheT- dependence of polarizationPcunder various magnetic field for DyMnO3, in which the enhancement ofPcis due to the CM-ICM transition of Dy^3þspins.

Reprinted by permission from Ref.[23].

215 C. Lu, J.-M. Liu / J Materiomics 2 (2016) 213e224

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cycloidal spin order modulated by the Gd^3þAFM phase at low Twas proposed[31,32].

While the above discussed R^3þeMn^3þ coupling contributes to the multiferroicity, Mochizuki et al. discussed the nature of multiferroicity in RMnO₃which is of multifold even if R^3þ is nonmagnetic. In this case, both the symmetric (P ~ (SiSj)_Mn) and antisymmetric (P ~ (Si Sj)_Mn) components from the Mn spiral spin order are possible [33]. This explains why the spontaneous FE polarization associated with theab-plane spiral spin structure is larger than that associated with thebc-plane spiral spin structure for RMnO₃. Neverthe- less, such multifold multiferroicity solely from the Mn³^þ spiral spin order remains to be identified experimentally.

3. Ferroelectricity by tuning the Dy³^þeMn³^þspin coupling

As discussed, the duality of multiferroicity in DMO provides an ideal platform to integrate the multiferroicity from various mechanisms, i.e., the giant ME effect associated with magnetic field driven polarization switching. Keeping in mind this motivation, Zhang et al. carried out systematical experiments on tuning of the duality of multiferroicity, which in turn demonstrates the significant role of the Dy^3þeMn^3þexchange striction[17,34,35].

In details, the Dy³^þ spin order undergoes the ICM-CM transition at T_R, which destabilizes the coherence of Dy³^þ spins with Mn³^þspins. Consequently, polarization component PR is no longer available, making the total polarizationPcto fall down drastically from ~2800 mC/m²to 600mC/m²[23].

An alternative to save this component P_R is to stabilize the Dy^3þICM order against the ICM-CM transition atT_R, which can be accessed by applying a magnetic field, as demonstrated already. Apart from this way, cation substitution is shown to be another approach to manipulate P_R. Similar to DMO, HoMnO₃ also accommodates the strong Ho^3þeMn^3þ coupling to preserve the coherence between the Ho^3þ spins and Mn^3þ spins down to the lowest T [30], while no such ICM-CM transition occurs. In this case, the polarization component (P_R) arising from the Ho^3þeMn^3þ exchange striction can be saved.

In proceeding, a set of experiments on substitution of Dy³^þ in DMO by Ho³^þwere performed. Two effects upon the Ho³^þ substitution can be expected. First, the substitution is expected to preserve the R³^þeMn³^þ coupling, essential for ferroelectricity generation via the exchange striction. Second, the substitution would dilute the Dy^3þsublattice, which certainly hinders the independent Dy^3þ spin ordering below T_R since the 4fe4felectron coupling is relatively weak. Nevertheless, such a substitution does not affect much the coherency of the Dy^3þspins with the neighboring Mn^3þspins, noting that most likely the substituting Ho^3þ spins may also align coherently with the neighboring Mn^3þspins. In this sense, the substitution does not qualitatively change the ICM R^3þ alignment induced by the Mn^3þspin orderviathe R^3þeMn^3þcoupling.

In short, one is expected to observe a remarkable enhancement of the total polarization P_c in the extremely low-T end

(T < T_R), crediting with the reentrancy of component P_R. Fig. 2 presents the P_c(T) curves of Dy₁_xHo_xMnO₃ (0x0.3)[34]. Indeed, a drastic enhancement ofP_cin the low-Trange is observed, suggesting a successful preservation of the synchronization of the Ho^3þspins with the Mn^3þspins in the spiral alignment.

Regarding the Ho^3þsubstitution in DMO, the second effect is a natural consequence of chemical substitution, but the first effect can still be different if a nonmagnetic/weak magnetic R^3þor other trivalent species. Along this line, Y^3þcould be an ideal candidate since it is nonmagnetic and has nearly the same ionic radius as Ho³^þ. In this case, the diluted Dy³^þspin sublattice on one hand would prevent the onset of the independent Dy³^þspin ordering, and consequently prevent the drop in the P_c(T) curve belowT_R. On the other hand, the damaged Dy³^þ spin network will certainly suppress the overall Dy³^þeMn³^þ coupling, leading to a suppression ofP_c(T) withinT_R<T<T_C. As shown inFig. 3, one sees that the polarizationP_cfalls down over the wholeT-range first upon increasing Y^3þup tox~ 0.1, owing to the global breakage of the Dy^3þeMn^3þ coupling.

Fig. 2.T-dependence of FE polarization in Dy_1xHoxMnO3(0x0.3). The inset shows the polarization atT¼2 K as a function of Ho^3þsubstitution level x. Reprinted by permission from Ref.[34].

Fig. 3.T-dependence of FE polarization in Dy1xYxMnO3 (0 x 0.2).

Reprinted by permission from Ref.[35].

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Further increasing ofx makes the dilution of the Dy³^þsub- lattice strong enough so that the independent Dy³^þCM order is replaced, leading to a reversal of the low-T P(T) curve[35].

This is a good example showing the tunable duality of multiferroicity in DMO. A detailed discussion on this duality and its modification by chemical substitution in DMO can be found in a previous mini-review paper[17].

4.“Copy” bulk multiferroicity to DyMnO₃thin films

While enthusiastic endeavors have been motivated by the fascinating physics of type-II multiferroics, the inherent AFM nature does not give rise to any macroscopic magnetization, which seriously hampers the potential applications of multiferroics. Given this unfortunate situation, several approaches to enhance the ferromagnetism and to achieve the sizable spontaneous magnetization have been reported. The favorable strategy includes the strain and domain engineering in thin films and nanostructures [19,20,36e40]. In fact, multiferroic thin films belong to an inter-discipline bridging the novel cross-control of multiple ferroic orders and multifunctional devices.

The TMO thin films deposited on SrTiO₃ single crystal substrates have been intensively investigated during the past few years, and interesting emergent ferromagnetism has been

evidenced. Two possible origins for ferromagnetism were proposed. One is the release of the MnO6octahedron distortion induced by the substrate transferred strain[36]. The other one is the difference of electronic structure at domain walls, which may give rise to apparent ferromagnetism [18]. In particular, a twin-like domain structure was observed in these thin films [19,20], which may lead to unconventional ME

Fig. 4. Microstructural characterizations on the (001) DyMnO3thin film on (001) NbeSrTiO3substrates. (a) X-rayqe2qscan of the film. The inset shows a sketch of the epitaxial growth of the film. (b) The rocking curve around the (002) reflection of the film. The reciprocal space mapping data around the (103)cand (113)c

reflections of the substrate are shown in (c) and (d), respectively. (e) The atomic force microscopy of the film.

Fig. 5. The plane-view transmission electron microscopy image of the film, in which the twin-like domain structure can be identified.

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controls to be discussed below. Although exciting weak ferromagnetism in TMO thin films has been reported, the magnetically induced ferroelectricity known in the bulk counterpart seems to be suppressed simultaneously, raising a challenge. According to the phase diagram of RMnO₃, the novel spiral spin structure is rather sensitive to the structure distortion and can only exist within a very narrow region[23].

It is physically reasonable to expect a destabilization of the spiral spin structure in strained TMO thin films, since the magnetism of bulk TMO locates quite close to the phase boundary between the A-type AFM and spiral spin order in the phase diagram. However, a clear signature of the ferroelectricity in RMnO₃thin films, which is associated with the spiral spin structure, can be found. For instance, a recent ultrafast

Fig. 6. (a) Measured out-of-plane dielectric constantεcas a function ofT, in which the multiple phase transitions are indicated by dashed lines. (b) MeasuredPc(T) data upon different cooling sequences. (c) Measured FE hysteresis loop and the corresponding switching current. In the upper of (c), a sketch of spiral spin orders with the opposite chirality (Q_aandQa) are presented.

Fig. 7. MeasuredPc(T) data under various magnetic fields applied (a) along thec-axis, and (b) in theab-plane.

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optical spectroscopy study on TMO thin films revealed an anomaly aroundT~ 30 K, which is very close to the FE Curie temperatureT_C¼27 K in TMO bulk crystals. A coexistence of Mn^3þspiral spin order and ferroelectricity in the thin films was thus argued[41]. The bulk orthorhombic YMnO₃has an E-type AFM ground state, and the observed FE state was associated with the exchange striction mechanism. However, for YMO thin films grown on SrTiO₃ (001) substrates, a possible spiral spin structure and switchable FE polarization were identified [42,43]. These phenomena encourage us to explore more emergent phenomena of multiferroicity in RMnO₃thin films, in particular the DMO thin films.

We then prepared DMO thin films on STO (001) single crystal substrates and a set of characterizations on various aspects of microstructures and multiferroic functionalities have been performed [44]. Two motivations drive us to investigate the DMO thin films. The first is the superior multiferroicity of DMO, and the second one is the location of DMO in the multiferroic phase diagram of RMnO₃, where DMO seems to be more proper than TMO in terms of the multiferroic manipulation[23], and the two issues allow more flexibility in DMO thin films. For example, a relatively small

compressive strain in the DMO thin films was evidenced by structural characterizations (Fig. 4), although the lattice misfit between STO and DMO can be huge. Such a huge misfit may bring into some more variants such as twin-like domain structure, which could release the strain energy largely. A number of techniques have been employed to characterize the twin-like structure, including the X-ray reciprocal space mapping and the plane-view image from transmission electron microscopy (TEM) which presents clear evidences, as shown inFig. 5.

We look at the experimental results. First, the dielectric and polarization data of the as-prepared DMO thin films shown in Fig. 6evidence clearly the ferroelectricity and its relevance with the spiral spin ordering of Mn^3þspins. The dielectric constant as a function ofT,εc(T), marks the multiple phase transitions at

Fig. 8. Measured magnetization (M) as a function of magnetic fieldHapplied (a) in theab-plane and (b) along thec-axis at various temperatures.

Fig. 9. A sketch of spin spiral plane flopping from thebc-plane to theab-plane driven by magnetic field along theb-axis ora-axis, giving rise to different critical fieldsHc1orHc2, respectively. HereQdenotes the chirality of Mn^3þ spiral spin order.

Fig. 10. Top:4is defined as the angle between the applied magnetic field and [100] of the SrTiO3substrate. Bottom: Sketch of the twin-like domain structure comprisinga- andb-domains, in which arrows indicate the local domain [010] directions of the film.

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T_N~ 40 K,T_C~ 21 K, andT_R~ 10 K, demonstrating the one-to- one correspondence between the bulk crystals and thin films.

Secondly, such magnetically induced ferroelectricity can be further demonstrated by the non-zero polarization P_c below T_C~ 21 K, as shown inFig. 6(b). The measuredP_c(T) hysteresis is believed to be associated with the ICM↔CM transition of Dy^3þspins and coupled Mn^3þspinsvia the Dy^3þeMn^3þex- change striction. Third, the positive-up-negative-down (PUND) method was used to attest the FE polarization, as shown in Fig. 6(c). A well-defined polarization-electric field (P_c ~ E_c) hysteresis is obtained too. According to the scenario of DM interaction associated with the spiral spin order of Mn³^þ, the FE polarization is determined by the chirality of the spiral spin order. A reversal of polarizationPcmarks an electric control of this chirality, one aspect of the ME coupling. On the other hand, tuning polarizationP_cby magnetic field is also attractive. As shown inFig. 7, a variation ofP_cupon a magnetic field in thea-b plane can be as high as ~800%.

The multiferroicity of DMO thin films highly resembles that of the DMO bulk counterpart. First, the polarization of the DMO thin films is about ten times smaller than that of the bulk. This difference is reasonable considering the modified microstructure (twin-domains) in the films. The magnetic properties of the as-prepared thin films, noting that the ferroelectricity originates from the specific magnetic structure, are shown in Fig. 8 where the measured magnetization M(H) curves with H//ab plane show quick enhancement around H ~ 1.5 T, owing to the reorientation of Dy³^þ spins. This behavior is similar to the observation of DMO bulk crystals.

However, a close checking of theM(H) curves shows a big in- plane to out-of-plane magnetization ratio (M_ab/M_c) of ~10, which is much bigger than the ratio of bulk DMO. This discrepancy evidences the spin order modulation in thin films by strain and microstructure [44].

In addition, we have investigated the ferroelectricity and ME coupling in TMO and GdMnO₃ thin films deposited on STO (001) substrates. For TMO films [45], the spiral spin ordering induced ferroelectricity was identified too, highly resembling the observation in bulk TMO. However, it was identified that the ME effect in TMO thin films finds sub- stantial contribution from the Tb³^þspin ordering far aboveT_R, which is different from the bulk counterpart. This contribution should be associated with the strain modified microstructure.

For GdMnO₃thin films[46], the FE phase with giant polarization (~5000 mC/m²) and relatively high T_C (~75 K) was identified although the bulk GdMnO₃ doesn't show such ferroelectricity induced magnetically. This was discussed based on the twin-like domain structure and the Gd^3þeMn^3þ exchange striction.

5. Continuous ME control

A unique feature of the ferroelectricity associated with the Mn^3þ spiral spin ordering is the polarization switching from the c-axis to thea-axis (i.e. P_c/ P_aswitching) as a consequence of the Mn^3þspiral plane flop from thebc-plane to the ab-plane. This spiral plane flop can be triggered by magnetic

field or other stimuli, i.e., done by a magnetic field above a critical valueH_c1along the b-axis. This is also the origin for the giant ME effect. Interestingly, for bulk DMO, the polarization switching can also be triggered when magnetic field is applied along the a-axis but with a higher critical field H_c2>H_c1, as shown inFig. 9. The difference (H_c2H_c1) can be as big as ~6.0 T atT¼5 K in bulk DMO [10].

For the DMO thin films, a twin-like domain structure is evidenced by a series of structural characterizations, which allows sufficient space to explore additional strategies towards the magnetic control of polarization. For instance, one can intentionally make use of the distinct polarization switching driven by magnetic field H along certain direction. One representative example is shown in Fig. 10, where the microstructures are denoted as a- and b-domains in which the arrows represent the [010] direction of the DMO orthorhombic lattice, and the angle between the in-planeHorientation and the<110>direction of DMO thin film is denoted as4. Based

Fig. 11. A sketch of concurrent and distinct polarization switching events asH is applied at (a)4 ¼ 45 and (b)4 ¼0 in the DyMnO3 thin films. The macroscopic polarization, includingPc,Pa1associated with the polarization switching ofa-domains, andPa2associated with the polarization switching of b-domains, are also illustrated.

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on such a twin-like domain structure, two characteristic pathways can be expected for the polarization switching sequence[47]. For4 ¼0, magnetic field Haligns along the diagonal direction of both thea- andb-domains, and hence the polarization P within the two types of domains can be switched concurrently asH>√2H_c1. However, for4¼45, magnetic fieldHis parallel to theb-axis of thea-domains but perpendicular to that of theb-domains, and then two separated polarization switching events can be anticipated, i.e., the polarization switching in thea-domains first occurs asH>H_c1 and then in theb-domains asH>H_c2, which are schematically shown inFig. 11.

To identify the above arguments, various measurements on the ME effect in the DMO thin films have been carried out. In Fig. 12, the measured out-of-plane dielectric constant εc and polarizationP_care plotted as a function ofH. We first look at theεc(H) curves for both4¼0 and4¼45 by sweepingH up and down in a continuous manner, noting that dielectric constant in comparison with polarization P_c(H) seems to be more sensitive in detecting the phase transitions. It is revealed that three peaked anomalies in theεc(H) curve for4¼45at

H~ 1.5 T, ~2.6 T, and ~6.0 T, can be seen. However, only two anomalies in theεc(H) curve for4¼0 appear atH~ 1.5 T and

~4.0 T. Obviously, the first anomaly for the two cases is associated with the Dy^3þspin CM↔ICM transition driven by magnetic fieldH, since the critical field coincides with that of the metamagnetic transition as identified in the M(H) curves (seeFig. 8). For the case of4¼45, the second peak around H ¼ H_c1~ 2.6 T features the P_c ↔ P_aswitching of the a- domains, leading to a gradual decrease ofP_c. The third peak aroundH¼H_c1~ 6.0 T reflects theP_c↔P_aswitching of the b-domains. As expected, the polarization switching would happen in thea- andb-domains concurrently for4¼0, and the critical field should be H ¼ √2Hc1. This is well represented in the experiments shown in Fig. 12(b), in which the critical field of the second anomaly is about 4.0 T, close to

√2H_c1(i.e.,¼3.7 T).

To obtain a comprehensive understanding of the ME coupling in DMO thin films, a series of εc(H) curves were measured at variousT. The data obtained atT¼4 Ke18 K for 4 ¼45 are shown in Fig. 12(c), in which the critical fields H_R, H_c1, and H_c2 are marked as olive, red, and blue bars,

Fig. 12. TheHdependences ofPcandεcmeasured at (a)4¼45and (b)4¼0 atT¼5 K. (c) Measuredεc(H) curves at variousTlabeled at the right side of figure. The short bars indicate the fieldsHDy,Hc1, andHc2. (d) TheHc1as a function ofTevaluated from the measured dielectric data. The predicted difference term (PMn2

ePDy2

) is also plotted for a comparison.

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respectively, where H_R is the field for suppressing the independent Dy^3þ spin ordering. As usual, H_R shifts gradually towards the low-H side upon increasing T until T_R ~9 K, beyond which no more Dy^3þ CM spin order can be perse- vered. The critical field H_c1(T) first shifts towards the low-T side but starts to turn to the high-Tside asT~T_R. The critical fieldH_c2(T) dependence is trivial by a gradual increasing of H_c2over the entireT-range.

To explain the dependences H_c1(T) and H_c2(T), one may discuss the stability of thebc-plane spiral spin state againstH.

An increasing of Hbeyond H_R(T) drives the CM-ICM transition of Dy³^þ spins via the Dy³^þeMn³^þ coupling. This transition is compensated by the stability penalty of the Mn³^þ spiral spin state. The ME energy terms for thebc-plane Mn³^þ spiral spin state and Dy³^þ ICM state, and the H-induced magneto-static energy can be described respectively by:

D X

MnSSO

¼ X

<i;j>

D_Mn$

S_Mn_;_iS_Mn_;_j

¼ 1 2pεMn

P²_Mn

D X

DyICM

¼ X

<i;k>

aMnDy$

S_Mn;iS_Dy;k

¼ 1 2pεDy

P²_Dy X

static

¼ H$X

<i>

S_Mn¼ H$S_eff

ð1Þ

whereDSMn-SSOis the variation of the ME energy associated with the DM mechanism forPMn, which can be expressed by the corresponding electric static energy, D_Mn is the DM factor, and εMn is the dielectric permittivity of Mn “ferroelectric sublattice” corresponding to P_Mn. DSDy-ICM is the variation of the ME energy associated with the Mn^3þeDy^3þ exchange striction mechanism for P_R ¼ P_Dy, which can be replaced by the corresponding electric static energy,aMn-Dyis the exchange striction factor and εDy is the dielectric permittivity of Dy“ferroelectric sublattice”corresponding to P_Dy. Sstatic is the magneto-static energy and S_eff is the effective moment accounting for the Mn^3þ spins S_Mn. In a zero-order approximation, the instability of the bc-plane Mn³^þ spiral spin state and the P_c / P_a will occur at the point defined by:

X

static

¼D X

MnSSO

þD X

DyICM

; ð2Þ

which yields

Hc1¼ 1 2pS_eff

1 εMn

P²_Mn 1 εDy

P²_Dy

; ð3Þ

Equation (3) explains H_c1(T) and H_c2(T) in a qualitative sense, clarifying the physics of magnetic control of polarization. The evaluatedH_c1values from the data inFig. 12(c) as a function of T are plotted in Fig. 12(d) where the predicted difference term (P_Mn² e P_Dy² ) is plotted too, revealing the qualitative consistency between Hc1 and (PMn2 e PDy2

) as a function ofT. A detailed discussion about the evaluation of the P_Mn(T) andP_Dy(T) can be found in a previous paper[17].

A phase diagram for the DMO thin films is summarized in Fig. 13, based on the above discussion. It is seen that the phase diagram of the DMO thin films shows almost identical features to an integration of the two phase diagrams for bulk DMO, givenH//a-axis and H//b-axis respectively[10]. The diagram is divided into five regions. The region atT>T_c1is occupied by the paraelectric phase. In 10 K<T<20 K, there appear in order the FE phase with P//c-axis (P_c), the FE phase with mixed componentsP//c-axis andP//a-axis (P_cþP_a), and the FE phase with P//a-axis (P_a), with increasing H. Below T¼10 K, the increasingHdrives the transitions from the FE phase with P//c-axis (P_Mn), to the FE phase with P//c-axis (Pc¼PMnþPDy), then to the FE phase with mixed compo- nentsP//c-axis andP//a-axis (PcþPa), and eventually to the FE phase withP//a-axis (P_a).

The above described experiments have demonstrated that the polarization switching in the thin films can be one step or separated events, corresponding to 4 ¼ 0 and 4 ¼ 45, respectively. A natural question is what would happen ifHis applied along a direction in-between4¼0 and4¼45? In the framework of Landau theory on ferroelectricity, the free energyF(P_c,H) can be schematically drawn inFig. 14(a) for a guide of eyes. The polarizationP_c¼0 state corresponds to the ab-plane spiral spin state where the polarizationP_areaches the maximum. Intentionally, one expects that a highly sensitive modulation of polarization by magnetic field H should be reachable aroundH~H_c1to√2H_c1, at which there are three comparable free energy minimal states with relatively low barriers between them, so that the inter-state transitions are kinetically easy. In the experiments, the in-planeH(i.e.,¼3.0 T), which is higher thanH_c1and lower than√2H_c1, is rotated, triggering the P_c ↔ P_a switching of the a-domains and b-

Fig. 13. The multiferroic phase diagram of the DyMnO3thin films withHat 4¼45. The values ofTcwere obtained from theεc(T) data. Open and closed symbols denote the data obtained with increasing H and decreasing H, respectively. For a comparison, the critical fields of anomalous transitions with H applied at 4 ¼ 0 are also shown as circles (increasing H) and dots (decreasingH) in the phase diagram. The olive crosses denote the effective fieldH,cos45along thea-orb-axis.

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domains, alternatively, so that the measured P_c(4) oscillates with the two-fold rotation symmetry. One set ofP_c(4) data are plotted inFig. 14(b). It is seen that the minimal and maximal are ~125 mC/m²and ~250mC/m², consistent with the model prediction inFig. 11. More interesting is the continuous and periodic modulation of macroscopic P_c. This modulation is highly robust and can be well reproduced upon an electric field at different swamping frequencies. So far, no such a continuous modulation of polarization has been reported in either bulk DMO or other multiferroics of spiral spin structure[7].

One is for Eu_0.55Y_0.45MnO₃where the rotation of a developed conical spin structure from an ab-plane spiral phase was observed, driven by a magnetic field perpendicular to the spin propagation vector[48]. The present continuous response of polarizationP_cto the in-plane rotatingHis essentially determined by the in-plane twin-like domain structure of the DMO thin films, while the generation of polarization P_Dyin DMO also makes contributions.

6. Conclusion

In this mini-review, we have thoroughly discussed the multiferroicity and magnetoelectric coupling tailored by chemical substitution and strain/domain engineering in DyMnO₃(bulk and thin film states), which can be a model system for type-II multiferroic materials. The experiments demonstrated the duality of multiferroicity in DyMnO₃, i.e., the ferroelectricity is generated from the symmetric Dy³^þeMn³^þexchange striction and antisymmetric interaction (DM interaction) among Mn³^þ spins. The multiferroicity could be modulated intentionally by means of various stimuli routes. In particular, designable magnetoelectric controls have been identified in DyMnO₃thin films grown on SrTiO₃substrates, owing to the cooperation between the twin-like nano- domain structure and the duality of multiferroicity. The experimental results outlined in this review would open additional possibilities for exploring additional multiferroic

materials with superior properties and distinctive magnetoelectric control roadmaps.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11374112, 51332006, 11374147) and the National Basic Research Program of China (973 Program) (Grant No. 2015CB654602).

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Dr. Chengliang Lu is an associate professor of material science of School of Physics, Huazhong University of Science and Technology, Wuhan, China. He received Ph.D. in 2009 from the Nanjing University. He worked in Nanyang Technological University as a postdoc from 2009 to 2010, and in Max-Planck Institute of Microstructure Physics as a Humboldt Research Fellow from 2013 to 2015. His recent research focuses on multiferroic materials and 5diridates. Email:[email protected]

Dr. Jun-Ming Liu is a Professor of Physics with Department of Physics and Laboratory of Solid State Microstructures, Nanjing University. He obtained his Pd.D degree from Northwestern Polytechnical Uni- versity in 1989 before joining the Department of Physics, Nanjing University. He specializes in correlated quantum materials and computational materials sciences. He has co-authored more than 600 technical papers in international referred journals. More information can be found athttp://pld.

nju.edu.cn. Email:[email protected].