Introduction

Multiferroics of magnetic origins have become a fertile ground of understanding the coupling between magnetic and ferroelectric (FE) order parameters, which provide the possibilities of mutual controlling of electric polarization P (magnetization M) by magnetic field H (electric field E)1,2,3,4,5,6,7. In general, the correlation between the two ferroic orders can be built up via three mechanisms. The first one is the inverse Dzyaloshinskii-Moriya interaction (DMI) mechanism generating a polarization P ~ eij × (Si × Sj), where eij denotes the unit vector connecting the neighboring spins Si and Sj, as long as the two spins are noncollinear8. The second one refers to the symmetric exchange striction which leads to a polarization P ~ Si · Sj9,10,11,12. The spin-dependent p-d hybridization which accommodates a polarization P ~ (Si  · eil)2 · eil, where eil is the vector connecting the transition metal and neighboring ligands13, is the third one. Naturally, the magnetically induced polarization can be effectively modulated by magnetic field H in these materials, giving rise to large magnetoelectric (ME) coupling, as first discovered in TbMnO3 (TMO)14. However, the magnetic control of polarization can be fundamentally distinct in different multiferroics because of the different microscopic origins and microstructural details. In some cases, the polarization generation can be of dual or triple magnetic origin, while in some other cases the specific domain structures may bring in additional variants to the control roadmaps.

Not only for practical applications, magnetic control of polarization is also a central topic in condensed matter physics and has been studied intensively in recent years. In particular, for multiferroics with spiral spin order (SSO), such as orthorhombic manganites RMnO3 (R is the rare earth element), polarization P generated via the inverse DMI mechanism can be completely switched via the H-driven 90° flop of the spiral spin plane. This event is commonly accompanied with a gigantic ME coupling15,16,17,18,19. The well-known demonstration of the second mechanism (P ~ Si · Sj) was given in orthoferrite DyFeO3 where P can be tuned by H-realignment of the spins20,21. So far only a few multiferroics were found to follow the third mechanism and the generated P is usually small but can be smoothly rotated due to the H-driven rotation of Si, as evidenced in Ba2CoGe2O713. Other than this, quite a few of multiferroics have been demonstrated to accommodate more than one mechanism, i.e. dual or triple magnetic origin of polarization generation. In this case, magnetic control of polarization becomes an issue with implication of additional ingredient since every mechanism does offer its specific behaviors, making the underlying physics affluent. Actually, this issue would be of high interest and practical significance, since the dual or triple magnetic origin, if properly utilized, may open additional possibilities for distinctive ME control roadmaps.

One of the best objects for settling this issue is orthorhombic DyMnO3 (DMO) in which the polarization is of dual magnetic nature22,23,24, as illustrated in Fig. 1(a) for the lattice and spin structures in a certain temperature (T) range. A polarization P along the c-axis (PMn) is generated via the first mechanism associated with the bc-plane Mn SSO state25. In addition, the strong Dy-Mn coupling can drive the Dy spins to align coherently with the Mn SSO state, thus contributing a polarization along the c-axis too (PDy), via the second mechanism, i.e. the symmetric exchange striction between the Dy and Mn spins (PDy ~ SDy · SMn)22,23,24. A detailed description of this consequence can be found in the Supplementary materials, Figure S1. It is seen that the bc-plane Dy spins align in parallel or antiparallel to the neighboring Mn spins and the total polarization of dual magnetic origin becomes Pc = PMn + PDy, allowing large polarization and gigantic ME control. This effect has been revealed in bulk DMO and confirmed in DMO thin films deposited on (001) SrTiO3 substrates26. Besides, the Dy-Mn coupling was revealed to modify the multiferroic phase diagram of DMO drastically27.

Figure 1
figure 1

Dual multiferroicity and polarization switching in DMO.

(a) Sketch of the coherence of magnetic configuration for Dy and Mn moments. In this picture, there are two components of the magnetically driven ferroelectric state. One comes from the spiral-spin-ordered phase of Mn moments and the other one originates from the exchange striction between Mn and Dy spins due to their coherent configurations. (b) Ferroelectric polarization switching process due to the magnetic field induced 90° rotation of the spin spiral-plane. Here Q = Si × Sj is the spin chirality.

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While the dual magnetic origin motivated us to explore an emergent manipulation of P in DMO, possible undiscovered ME control stemming from domain engineering would further inspire such a motivation28,29,30. For bulk DMO, the polarization P can be switched from the c-axis to the a-axis (Pc → Pa) by field H along the b-axis or a-axis (Fig. 1(b)), as the consequence of the Mn spin spiral flop from the bc-plane to the ab-plane25. The critical fields for the two flops are denoted as Hc1 and Hc2. The Pc → Pa switching can be triggered more easily by the H//b-axis than that along the a-axis and the difference (Hc2 − Hc1) can be as big as ~6.0 T at T = 5 K25. Apart from the above physics, a major issue goes to DMO thin films epitaxially grown on proper substrates. Indeed, several recent studies on RMnO3 thin films on (001) SrTiO3 (STO) revealed general twin-like domain structures26,29,31,32,33,34. As revealed26, some of the well-known multiferroic properties of bulk DMO have been identified in epitaxial DMO films. The twin-like domain structure allows sufficient space to explore additional strategies towards the magnetic control of polarization. For example, one can subtly make use of the distinct P-switch sequences upon H applied along the b-axis or a-axis, respectively. The two types of domains in the twin-like domain structure, i.e. α-domains and β-domains, can have concurrent or distinctly different P-switching events, i.e. emergent phenomena absent in bulk DMO.

In the present work, we will explore these phenomena in high quality DMO thin films by measuring the response of dielectric permittivity ε and polarization P to H in different spatial geometries. The two distinct P-switching sequences enabled by the twin-like domain structure will be demonstrated. In particular, we have observed an interesting smooth and periodic modulation of macroscopic P by in-plane rotating H, ascribed to the twin-like domain structure and the dual magnetic origin of polarization.

Results

Twin-like domain structure in DMO films

The cross-section transmission electron microscopy (TEM) image in Fig. 2(a) shows the column structure of one sample, which represents the typical characteristic of multiferroic RMnO3 thin films on (001) STO, arising from the twin-like structure due to its most efficient release of the in-plane strain, consistent with our previous reciprocal-space-mapping data and twin-like diffraction spots26. The corresponding diffraction pattern in Fig. 2(a) plus the clear lattice planes revealed by the high resolution TEM image (Fig. 2(c)) indicate the single crystal nature and high quality of the film. Additional plane view TEM provides more evidence of the twin-like domain structure, shown in the Supplementary materials, Figure S2. The twin-like structure consisting of alternatively stacked in-plane α- and β-domains is drawn in Fig. 2(b) where φ is the angle between in-plane H and STO [100]/DMO <110> direction and the rectangles show the domains with arrows indicating the [010] directions (i.e. the b-axis) of the local domains. At φ = 0, field H aligns along the diagonal directions of both the α- and β-domains and the bc-spiral planes of the two types of domains are expected to flop simultaneously onto the ab-plane under sufficient H (H > √2Hc1). At φ = 45°, field H is in parallel to the b-axis of the α-domains but perpendicular to that of the β-domains, possibly leading to the flop of the bc-spiral spin plane of the α-domains at H > Hc1 and then to the flop of the bc-spiral spin plane of the β-domains at H > Hc2.

Figure 2
figure 2

TEM observations of microstructure in a DMO thin film.

(a) Top: cross-section transmission electron microscopy of the film of ~270 nm in thickness. Bottom: corresponding electron diffraction pattern along [010]S. The subscript ‘S’ and ‘F’ denote substrate and film, respectively. (b) Top: definition of angle φ, which is the angle between the applied magnetic field and [100] of the SrTiO3 substrate. Bottom: Sketch of the twin-like domain structure composed of α- and β-domains, in which arrows indicate the local domain [010] directions of the film. (c) High resolution transmission electron microscopy image of the film.

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Based on the twin-like domain structure, one can propose the pathway by which the two types of domains are switched. The two cases at φ = 45° and φ = 0 as examples are sketched in Fig. 3(a,b) at low T, where the values of Hc1 and Hc2 are taken from our measurements at T = 5 K. Given the initial state that all the domains have their P along the c-axis (Pc), we look at the P-switching of the two cases. At φ = 45°, the P-switching of the α-domains occurs at H > Hc1 but the β-domains remains non-flopped until H > Hc2 ≫ Hc1. This implies that the remnant Pc in Hc1 < H < Hc2 would be roughly a half of that at the initial state. Similar analysis can be done for φ = 0 but the consequence is different. Both the α- and β-domains have the Pc → Pa switching only at H > √2Hc1 when the H-components along the b-axis of both α- and β-domains are higher than Hc1.

Figure 3
figure 3

Sketch of concurrent and distinct polarization switching events as H is applied at (a) φ = 45° and (b) φ = 0 in DMO thin films. Macroscopic polarization, including Pc, Pa1 (due to P-switching of α-domains) and Pa2 (due to P-switching of β-domains), of each polarization switching event are also illustrated.

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Magnetic control of polarization

Given the proposed scheme in Fig. 3, one can now investigate in details the P-switching induced by H. It is noted that the Mn SSO state and thus the induced Dy incommensurate (ICM) order are robust against magnetic fields beyond a threshold of ~10.0 T, although the spiral spin plane will flop at a field far below this threshold25. We first look at the εc(H) and Pc(H) at φ = 45° and T = 5 K below the Dy’s spin ordering temperature TDy ~ 9 K, as shown in Fig. 4(a), while the T-dependences of εc and Pc can be found in the Supplementary materials, Figure S3. The εc-H curves in the H-increasing and decreasing cycle show some difference but their qualitative features are similar. The first dielectric peak around H = HDy ~ 1.0 to 1.5 T is due to the variation of PDy associated with the commensurate (CM) ↔ ICM transition of Dy spins. The second peak around H = Hc1 ~ 2.6 T features the Pc ↔ Pa switching of the α-domains. The third peak at H = Hc2 ~ 6.0 T reflects the Pc ↔ Pa switching of the β-domains. The Pc(H) curve obtained by the positive-up-negative-down (PUND) shows corresponding fast increase around HDy and then decreases gradually with further increasing H. Since the Pc(H) was measured using PUND at a series of selected magnetic fields, it is indeed not as sensitive as the dielectric response εc(H) obtained by sweeping the magnetic field in a continuous manner in detecting P-switching events.

Figure 4
figure 4

Magnetoelectric coupling in DyMnO3 thin film.

Measured Pc and εc as a function of H applied at (a) φ = 45° and (b) φ = 0 at T = 5 K. (c) Magneto-dielectric data measured at various T with a step of 1 K from 4 K to 15 K. The short bars indicate the fields HDy, Hc1 and Hc2.

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For φ = 0, the measured εc(H) and Pc(H) data at T = 5 K are shown in Fig. 4(b). Distinctly different from the case at φ = 45°, here we only observe two peaks. The first peak at HDy ~ 1.5 T is similar to the above case. The second peak appears at H ~ 4.0 T instead of Hc1 ~ 2.6 T. The reason can be easily understood from the model in Fig. 3. For φ = 0, the b-axes of all the domains are ~45° inclined from the H direction. The Mn/Dy spiral spin planes can’t be flopped onto the ab-plane until H ~ 4.0 T ≥ √2Hc1. In this case, the anomaly at √2Hc2 is no longer available. Similarly, the measured Pc(H) reaches a maximum at H ~ 1.8 T. In addition, it is easily understood that the measured Pc(H) at H > Hc1 for φ = 45° is much smaller than that for φ = 0. Owing to the high sensitivity of dielectric permittivity, we measure a series of εc(H) curves at various T in the H-increasing sequence to evaluate the HDy, Hc1 and Hc2 (if any). For φ = 45°, the data at T = 4 K to 18 K are plotted in Fig. 4(c), where the numbers on the right border are temperatures and the HDy, Hc1 and Hc2 are marked. As expected, the HDy shifts gradually towards the low-H side with increasing T until TDy ~ 9 K, beyond which no more Dy CM order is sustained. The Hc1(T) first shifts towards the low-H side but turns to the high-H side as T ~ TDy, an unusual behavior. The Hc2(T) dependence is trivial by gradual increasing of Hc2 over the whole T-range here.

To explain the dependences Hc1(T) and Hc2(T), one may discuss the stability of the bc-plane Mn SSO state against H. An increasing of H beyond HDy(T) drives the CM-ICM transition of Dy spin order via the Dy-Mn coupling. This transition is compensated by the stability penalty of the Mn SSO state. As shown in Figure S3(b), PDy reaches the maximum at TDy, which would impact the bc-plane Mn-SSO most seriously, leading to the smallest critical field Hc1 around TDy. At high field region, PDy has already been fully recovered and will not be enhanced by H anymore, giving rise to a monotonous variation of Hc2(T).

Ferroelectric phase diagram

Based on the above discussion, we can construct the FE phase diagram in the (H, T) plane for the DMO thin films. The phase diagram for φ = 45° is presented in Fig. 5, where the different sets of dots are from the dielectric data in the cooling and warming sequences, respectively. The phase diagram for φ = 0 is qualitatively similar while the phase borders may be quantitatively different. The diagram is divided into five regions. The region at T > Tc1 is occupied by the paraelectric phase. At 10 K < T < 20 K there appear in order the FE phase with P//c-axis (Pc), the FE phase with mixed components P//c-axis and P//a-axis (Pc + Pa) and the FE phase with P//a-axis (Pa), with increasing H. Below T = 10 K, the increasing H drives the transitions from the FE phase with P//c-axis (Pc = PMn), to the FE phase with P//c-axis (Pc = PMn + PDy), then to the FE phase with mixed components P//c-axis and P//a-axis (Pc + Pa) and eventually to the FE phase with P//a-axis (Pa).

Figure 5
figure 5

Multiferroic phase diagram of the DMO thin films with H at φ = 45°.

The values of Tc were obtained from the εc(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 φ = 0 are also shown as circles (increasing H) and dots (decreasing H) in the phase diagram. The olive crosses denote the effective field H · cos45° along the a- or b-axis.

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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, given H//a-axis and H//b-axis respectively25. However, the H-driven Pc ↔ Pa transition is not as sharp as that in bulk DMO. Instead, a broad region with coexisting Pa and Pc domains is identified in the phase diagram, primarily due to the in-plane twin-like domain structure of the DMO thin films.

Continuous control of macroscopic polarization

While the central issue of multiferroic applications is the electric and magnetic controls of P and M, it is more significant to investigate the FE hysteresis under modulation of magnetic field. In the framework of Landau theory on ferroelectricity, the free energy F(Pc, H) can be schematically drawn in Fig. 6(a) for a guide of eyes. The Pc = 0 state corresponds to the ab-plane SSO state where the Pa reaches the maximum. Intentionally, one expects that a highly sensitive modulation of P by H should be reachable around H ~ Hc1 to √2Hc1, 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 our experiments, we choose H ≥ 2.0 T and T ~ 5–10 K, noting that Hc1 ~ 2.0 T in this T-range. A series of Pc-E loops at various T in the cooling sequence for both φ = 45° and φ = 0, using the PUND method, have been cautiously measured. The saturated Pc(T) and coercive field Ec(T) are evaluated from these loops and summarized in Fig. 6(b–d), respectively.

Figure 6
figure 6

(a) Energy diagram on ferroelectric switching under various magnetic fields. Measured Pc(T) and Ec(T) data with H = 0 (b), H = 2.0 T at φ = 45° (c) and H = 2.0 T at φ = 0 (d). (e) Angular dependence of Pc measured under H = 3 T at T = 5 K.

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In general sense, the data in Fig. 6 are consistent with the model predictions given in Fig. 3. For H = 0, the measured Pc increases rapidly with decreasing T down to TDy and then falls down due to the disappearance of PDy. The measured Ec increases with decreasing T too, noting that no reliable Ec values can be extracted for the loops of very small Pc. The situation for H ~ 2.0 T at φ = 45° is different, as shown in Fig. 6(c). The measured Pc does increase too with decreasing T down to TDy, below which Pc remains roughly unchanged because of the recovery of PDy. The measured Ec(T) curve roughly coincides with that for H = 0. Here, the Pc at T > TDy are smaller than that for H = 0, due to the H ~ 2.0 T driven Pc → Pa switching of the α-domains. For the case of H ~ 2.0 T at φ = 0, as shown in Fig. 6(d), noting H ~ 2.0 T < √2Hc1, insufficient for driving Pc → Pa switching in any domain, confirmed by the overlapping Pc(T) curves in Fig. 6(b,d) at T > TDy. The further enhancement of the Pc below TDy is ascribed to the recovery of PDy.

To this final stage, we are in a position to track the continuous H-control of macroscopic Pc enabled by the domain engineering for the present thin films. The in-plane H ~ 3.0 T, which is higher than Hc1 and lower than √2Hc1, is rotated, triggering the Pc ↔ Pa switching of the α-domains and β-domains alternatively, so that the measured Pc(φ) oscillates with the two-fold rotation symmetry. One set of Pc(φ) data are plotted in Fig. 6(e). It is seen that the minimal and maximal are ~125 μC/m2 and ~250 μC/m2, consistent with the model prediction in Fig. 3. More interesting is the continuous and periodic modulation of macroscopic Pc. This modulation is highly robust and can be well reproduced upon different swamping frequencies of the electric field. So far no such continuous modulation of polarization has been reported in either bulk DMO or other SSO multiferroics3,25. One exception, to our best knowledge, is for Eu0.55Y0.45MnO3 where the rotation of a newly developed conical spin structure from an ab-plane spiral phase was observed16, driven by the H perpendicular to the spin propagation vector. In the present work, the continuous response of the Pc to in-plane rotating H is essentially determined by the in-plane twin-like domain structure of the DMO thin films, while the PDy generation in DMO also makes contributions.

Remarks

The central feature of the DMO thin films is the in-plane twin-like domain structure which determines the emergent behaviors observed here. These behaviors may allow additional functionalities, such as the continuous modulation of macroscopic polarization. Such a twin-like structure can be easily realized in many strain-sensitive materials, stimulating us to add some remarks on possible phenomena beyond those observed here. The twin-like structure may add another spatial scale/symmetry besides the lattice level scale/symmetry and macroscopic level scale/domain pattern. For the DMO thin films, the polarization generation mechanisms are on the lattice scale and the twin-like structure adds the nano-scale α- and β-domains which show the two-fold symmetry in terms of the P response to in-plane H. Because DMO has a number of companions like other RMnO3 multiferroics of the SSO state, the present work suggests similar consequences in these systems, deserving for explorations.

Beyond these in multiferroics, the impact of such an additional scale has been demonstrated to be substantial in other materials on other properties. For examples, in metals where dislocations are responsible for deformation, the nano-scale twin-like structure may bring super-plasticity and ductility, as shown in copper35. The twin-like structure may even enable the micro-hardness of some materials higher than diamond36. These are two cases where the twin-like structure exhibits super and unexpected functionalities.

Methods

The DMO thin films were epitaxially grown on conductive Nb-doped (001) STO substrates using pulsed laser deposition method and details of the microstructural and electrical characterizations were reported earlier26. The epitaxial relationships are DMO (001)//STO (001) and DMO [100]/[010]//STO [110], seen in Fig. 3(b). We performed additional cross-section and plane view transmission electron microscopy and electron diffraction studies using the Philips CM20T microscope at 200 kV and high resolution TEM using the JEOL JEM-4010 microscope, in order to check the structural details of the epitaxial films.

Based on the standard capacitor structure with Au as the top electrode, the FE hysteresis loops were measured using the PUND pulse train technique (TF Analyzer 2000 from AixACCT Co) with a mode frequency of 100 Hz at various T during the cooling and warming processes. As the complimentary, the pyroelectric current method was also used for probing the remnant polarization under zero electric field24. Here, the measured polarization is the Pc in response to the out-of-plane electric field E. The out-of-plane dielectric permittivity εc (real part) was measured as a function of both T and H using the LCR meter. For the angular dependent ME coupling, H was aligned within the ab-plane. The cryogenic and magnetic field environment was provided by a Physical Properties Measurement System (PPMS, Quantum Design Inc.).

Additional Information

How to cite this article: Lu, C. et al. Continuous Magnetoelectric Control in Multiferroic DyMnO3 Films with Twin-like Domains. Sci. Rep. 6, 20175; doi: 10.1038/srep20175 (2016).