1. Introduction
The coupling between ferroelectricity and magnetism is one of the core issues of high concern in recent intensive researches on multiferroic materials [1, 2]. While a number of potential applications have been promised, so far not many realistic devices associated with these functionalities have been reported, even at the laboratory level. The major con- cern is, on the one hand, the relatively low ferroelectric (FE) Curie point (<100 K) and small FE polarization in magneti- cally induced ferroelectrics (type-II multiferroics), although the magnetoelectric (ME) coupling is strong. On the other hand, for those magnetic ferroelectrics whose magnetic struc- tures are only weakly coupled with the primer ferroelectricity, the ME coupling is however quite weak. Along these lines, substantial efforts on type-II multiferroics, which neverthe- less have strong ME coupling primarily important for multi- ferroic applications, have been made [3, 4]. Indeed, in these multiferroics, magnetic field control of FE polarization has been well demonstrated [5–11]. However and unfortunately, electric field control of magnetism as the mirror effect of
magnetic field control of ferroelectricity has been much less reported. The main reason lies in the fact that the electrostatic energy term P·E, where P and E are the FE polarization and electric field, is too small to counteract the exchange interac- tions. Here, polarization P is generated by an asymmetric or symmetric exchange striction mechanism, depending on the noncollinear or collinear spin order. This physics determines that polarization P is a second-order effect of the exchange interactions, and thus small.
Nevertheless, it should be noted that a number of type-II multiferroics have the highly frustrated spin structures [12, 13]
no matter how the spin alignments are – noncollinear or col- linear. The involved exchange interactions may be strong, but their competition generates a set of nearly degenerate mag- netic states, including noncollinear and/or collinear spin states which are ferroelectric. The transitions between these states may be easily induced due to the low energy barriers between them. If these barriers are sufficiently low and comparable with the electrostatic energy P·E, an electric field control of magnetic structure via electric field driven evolution of the FE domain structure may be enabled.
Journal of Physics: Condensed Matter
Electric field control of ferroelectric domain structures in MnWO 4
H W Yu1,2, X Li1, M F Liu1, L Lin1, Z B Yan1, X H Zhou1 and J M Liu1
1 Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China
2 School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, People’s Republic of China
E-mail: [email protected]
Received 18 March 2014, revised 15 May 2014 Accepted for publication 10 June 2014 Published 10 July 2014
Abstract
Competing interactions make the magnetic structure of MnWO4 highly frustrated, and only the AF2 phase of the three magnetically ordered phases (AF1, AF2, AF3) is ferroelectric.
The high frustration may thus allow a possibility to tune the magnetic structure by means of an electric field via magnetoelectric coupling. By using the pyroelectric current method, we measure the remnant ferroelectric polarization in MnWO4 upon application of a poling electric field via two different roadmaps. It is demonstrated that an electric field as low as 10 kV cm−1 is sufficient to enhance the stability of a ferroelectric AF2 phase at the expense of a non-ferroelectric AF1 phase. This work suggests that electric field induced electrostatic energy, although small due to weak magnetically induced electric polarization, may effectively tune ferroelectric domain structures, and thus the magnetic structure of highly frustrated multiferroic materials.
Keywords: multiferroics, ferroelectricity, electric field control of multiferroic phase.
(Some figures may appear in colour only in the online journal)
H W Yu et al
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doi:10.1088/0953-8984/26/30/305901 J. Phys.: Condens. Matter 26 (2014) 305901 (7pp)
The above argument seems applicable to MnWO4 (MWO), a representative member of type-II multiferroics [14, 15]. The mineral hübnerite MWO has monoclinic symmetry with point group P2/c and has been studied extensively not only for its multiferroicity. Regarding the magnetic structure, it first tran- sits from a paramagnetic state to a sinusoidal and incommen- surate (ICM) antiferromagnetic (AFM) structure (AF3 phase) with wave vector q3 = (0.214, 0.5, − 0.457) at temperature T = TAF3 ~ 13.5 K, then to the ICM noncollinear helical spin structure (AF2 phase) at TAF2 ~ 12.6 K with wave vector q2 = q3. This AF2 phase is ferroelectric. At TAF1 ~ 7.8 K, the AF2 phase is replaced by a commensurate (CM) AFM state (non-ferroe- lectric AF1 phase) which shows a ↑↑↓↓ spin pattern with wave vector q1 = (−0.25, 0.5, 0.5). Therefore, MWO interestingly exhibits three magnetic phase transitions in a narrow T-range of only 13.5 K, very unusual even in terms of spin frustration.
It is established that the transitions between the three mag- netic phases are the consequence of competing interactions;
some of these interactions are believed to extend up to the 11th neighboring spin pairs, indicating a high spin frustration tendency [16]. In addition, careful density functional theory (DFT) study predicts that the AF2 phase is slightly more stable than the AF1 phase in terms of the exchange interac- tions alone [17]. The AF1 phase as a re-entrant non-FE phase below TAF1 is attributed to the presence of weak magnetic anisotropy at each Mn2+ site. This suggests that these phases may be nearly degenerate and the transitions between them are highly possible in response to intrinsic or external weak perturbations. Earlier experiments did confirm this predic- tion. It was reported that low hydrostatic pressure (as low as 2.7 kbar) can shift the three phase transitions to higher tem- perature, while the AF1 phase is stabilized and the AF2 phase is slightly suppressed [18]. Experiments on chemical substitu- tions revealed that a replacement of Mn by 3d species (e.g.
Co and Zn) at a substitution level as low as 0.5% can sub- stantially suppress the AF1 phase in replacement by the AF2 phase. However, the Fe substitution of Mn destabilizes the AF2 phase slightly [19–22]. A tiny substitution of Mn by 4d Ru is also effective in destabilizing the AF1 phase, most likely resulting in the coexistence of the AF1 and AF2 phases in the original AF1 phase region [23]. It should be noted that in all the chemical substitution cases, the AF2-AF1 transition can be seriously influenced, but the AF3-AF2 transition is much less affected. In particular, the AF2-AF1 transition seems to be weakly first-ordered and the transition point TAF1 is hard to define accurately.
The above discussion and relevant experimental evi- dences allow the possibilities that an external electric field can tune the stability of the FE AF2 phase over the non-FE AF1 phase and thus influence the AF2-AF1 transition. The physics is simple and direct, and can be schematically shown in figure 1, where the free energy functional F for various spin states is plotted in several T-ranges, respectively, where the free energy curves are drawn only for a guide of eyes.
Thermodynamically, because the AF2 phase is ferroelectric, an external electric field will possibly lower the free energy minimal of the AF2 phase by a term P·E. As long as this term is bigger in magnitude than the energy minimal difference
between the AF1 phase and AF2 phase, the AF1 phase will become destabilized against the AF2 phase, as indicated by the difference between the dark cyan curve and magenta curve. Dynamically, electric field modulation of magnetism is realized by the evolution of FE domain structure driven by an electric field, such as polarization flip and domain nucleation/
growth. Again, because only the AF2 phase is ferroelectric, this evolution represents a scenario of electric field control of the magnetic structure to be addressed in this work. In fact, a very recent seminal work [24] addressed the dynamics of FE domains by measuring the broadband dielectric spectroscopy of MWO single crystals. Quite unusual dielectric relaxation behaviors associated with FE domain dynamics different from normal ferroelectrics were revealed.
We intend to investigate this scenario by adopting specifi- cally designed roadmaps for measuring the polarization using the highly sensitive pyroelectric current method. Our major intention is to establish the correlation between the polari- zation and the path for electric poling of the samples, and thus to demonstrate the above proposed scenario. Our earlier experiments revealed that for polycrystalline MWO samples, the AF2 phase as a minor phase can survive below TAF1 even though the AF1 phase is the major one [23, 25]. This feature is much weaker in single crystal MWO [20, 26], suggesting that a polycrystalline sample may provide more pinning sites for stabilizing the AF2 phase. We choose polycrystalline MWO as the object of the present experiment. Our results show that an electric field, here referring to the poling field Epole, can indeed control the magnetic structure of MWO by stabilizing the FE AF2 phase against the non-FE AF1 phase below TAF1.
The remaining parts of this article are organized as fol- lows. In section II we describe the sample preparation and characterization procedures. In particular, two specially designed methods for imposing the Epole and pyroelectric cur- rent probing are introduced. The main results on the magnetic and FE behaviors are presented in section III, together with our interpretation of the data and relevant discussion. A short summary is then given in section IV.
Figure 1. A schematic illustration of the free energy (F) landscape in the spin state space. In each T-range, the free energy shows three minimal corresponding to the AF1, AF2, and AF3 phases respectively.
Because the AF2 phase is ferroelectric, an electric field is expected to deepen the free energy minimal of the AF2 (at T < TAF1, E = 0 and E > 0). The F = 0 line is drawn for a guide of eyes.
2. Experimental details
2.1. Sample preparation and characterizations
The MWO sample was prepared by conventional solid- state reactions. Stoichiometric amountx of high-purity WO3 and MnO were chosen as reagents and thoroughly mixed for 24 h. Then the dried mixture was ground for 1.0 h and then annealed in air for 12 h at 600 °C. The output mixture was ground again and compressed into pellets with diam- eter of 20 mm, and then annealed at 950 °C for 20 h in air.
Subsequently, the synthesized samples were submitted to structural and property characterizations. The crystal- linity was checked using x-ray diffraction (XRD) (Bruker Corporation) equipped with Cu Kα radiation at room tem- perature and the stoichiometry was checked using x-ray pho- toelectron spectrometry (XPS). The sintered samples have well-defined crystallinity and highly density, as confirmed by the high quality XRD θ-2θ data. The relevant structural refining and lattice parameters extracted from these data have been reported earlier [20, 22, 23, 27].
The dc magnetization M was measured in the zero-field cooled (ZFC) mode and field-cooling (FC) mode respectively by a Quantum Design superconducting quantum interference device (SQUID) and the cooling and measuring magnetic fields are both 1.0 kOe. The magnetization M as a function of magnetic field H was measured too. The specific heat CP was measured using the Quantum Design physical properties measurement system (PPMS) in the standard procedure. The dielectric constant ε was probed using an HP 4294 A imped- ance analyzer connected with the PPMS apparatus.
2.2. Electric poling and pyroelectric current measurement Particular attention was paid to the FE measurement. Due to the fact that all the three magnetic phases (AF1, AF2, AF3) are antiferromagnetically ordered, identification of these phases using magnetization probing is challenging. Considering the high precision of the electric current probing, pyroelectric current (Ip) is a highly sensitive quantity to sign the magnetic transitions in type-II multiferroics, and the sensitivity can be much higher than common magnetic measurement tech- niques. In addition, since the Ip signals are probed without any electric bias, the proposed electric field control of magnetic structure must be performed via imposing electric poling of the sample prior to the Ip signal collection.
The Ip(T) data were collected using a Keithley 6514 elec- trometer connected to the PPMS. It should be mentioned that well-sintered polycrystalline MWO samples are highly insu- lating and the leakage current under a field of ~10 kV cm−1 is below 10 nA at T < 100 K for a sample of 10.0 mm in diam- eter. The background of our apparatus below 100 K can be as low as 0.05 pA, insuring the data reliability and high sensi- tivity. Each sample was polished into a thin disk of 0.1 mm in thickness and 5.0 mm in diameter, and then coated with Au electrodes on the two surfaces. We developed two different methods for the Ip measurement, as plotted in figure 2, for clarification. Method 1 uses the commonly used procedure for
pyroelectric current. Typically, the sample was cooled under an electric poling field Ep = 10 kV cm−1 from T = 100 K > >
TAF3 down to Tend < TAF2 at a cooling rate of 2 K min−1, and then the poling field was removed, followed by a long-time short-circuiting (>30 min) of the sample at Tend. Afterwards, the electric current released from the sample was recorded during the slow warming process from Tend and the warming rate was 1 K min−1. This sequence and a typical Ip(T) curve are shown in figure 2, top part. We repeated this measurement sequence by choosing a series of Tend < TAF2.
Method 2 takes an alternative sequence, as shown in figure 2, bottom part. Again for the typical procedure, the sample was cooled under Ep = 10 kV cm−1 from T = 100 K > > TAF3
down to the lowest T = 2 K at a cooling rate of 2 K min−1 and warmed back to Tend at a warming rate of 1 K min−1. Then the poling field was removed and the sample was short-circuited at Tend for a long-time (>30 min). Afterwards, the electric cur- rent released from the sample was recorded during the slow warming process from Tend while the warming rate was 1 K min−1. A typical Ip(T) curve is shown in figure 2. We repeated this measurement sequence by choosing a series of Tend < TAF2.
The difference between the two methods lies in that the sample in the Method 2 sequence was electrically poled during the continuous cooling-down to the lowest T and warming-up to Tend. The motivation for Method 2 comes from a rough esti- mation of the electrostatic energy, which includes two parts.
One is the electric field induced part, which is ~P·E~0.01 meV per unit cell (Ep ~ 10 kV cm−1) for the MWO AF2 phase. If the FE interaction between the electric dipoles is also taken into account, one can believe that the total electrostatic energy is about 0.05~0.1 meV, which is comparable with the thermal energy of several Kelvin (~0.1 meV). This implies that poling field induced AF1 → AF2 transitions below TAF1 cannot be maintained unless the processing temperature is sufficiently low e.g. 2 K in our experiment. This consideration seems to be critical for revealing the electric field control of the AF1 → AF2 transitions, as seen below.
2.3. Time-dependent relaxation characterizations
A major issue, as suggested by a recent work [24], is the slow dielectric relaxation behaviors of the FE AF2 phase below TAF2. This slowing-down effect may have potential influence on the results of pyroelectric current measurements using the two methods introduced above. Fortunately, this effect becomes negligible below TAF1 and under a dc electric poling field. In order to exclude any potential influence of this slowing-down effect, we performed pre-testing experiments. The electric poling field was constant (10 kV cm−1) and the sample was cooled from 100 to 15 K at a cooling rate of 5 K min−1. Then the following three different procedures were taken: (a) Sample cooling from 15 K to Tend (= 2 and 6 K) at a rate of 2 and 0.2 K min−1, respectively, followed by a short-circuiting for 120 min at Tend and subsequent probing of the Ip-T curve at a warming rate of 1 K min−1. (b) Sample cooling from 15 K to Tend at a rate of 2 K min−1 and then short-circuiting for 120 and 60 min at Tend, respectively, followed by probing of the Ip-T curve at a warming rate of 1 K min−1. (c) Sample cooling from 15 K to
Tend at a rate of 2 K min−1 and then short-circuiting for 120 min at Tend, followed by probing of the Ip-T curve at warming rates of 1.0, 3.0, and 5.0 K min−1, respectively.
All these measurements gave almost identical Ip-T curves within the measuring uncertainties as long as Tend is the same.
It implies that for the typical parameters chosen in the present experiments, the time-dependent relaxation of the FE domain structure is not a major issue.
3. Results and discussion
3.1. Magnetic phase transitions
For the phase transitions at low T, we perform magnetic and specific heat measurements. The measured M-T data under ZFC and FC modes are plotted in figure 3(a). As expected, due to the AFM nature of the three magnetic phases, no clear anomalies at TAF1, TAF2, and TAF3 can be identified, although small kinks may be observable. The separation between the two modes is quite common in frustrated spin systems and may also be associated with the polycrystalline nature of the samples. The specific heat CP-T data, however, show remark- able anomalies at TAF3 and TAF2, while only a weak kink at TAF1 can be seen, probably due to the sample’s polycrystal- line nature either. Such a weak feature around TAF1 may also reflect that the AF1 and AF2 phases are nearly degenerate in the present samples, and a sharp and complete transition between them may not be possible. Most likely the AF2 as a minor phase can survive below TAF1. These data are consistent with earlier reported ones [28, 29].
3.2. Path dependence of magnetization
We measure magnetization M to probe the possible path dependence of the magnetic structure. If this path-dependence
is proven to be negligible, the electric poling induced variation of the magnetic structure appears to be the only origin for the difference in the FE domain structure and then pyroelectric current. We then follow the same sequences as in Method 1 and Method 2, but imposing no electric poling, to pre-treat the sample. Immediately after the temperature reaches Tend, the M-H loops upon the H = 0 → ~1.9 kOe → 0 cycling are measured respectively. The measured loops obtained by the two methods are slightly different at Tend < 6 K, indicating the weak path-dependence of the magnetization. This is reason- able since a thermal freezing effect at very low T is inevitable.
Here the freezing effect may arise from the highly frustrated spin structures and the polycrystalline nature of the sample, and thus a finite hysteresis upon the magnetic field cycling at very low T is commonly observed. However, this path- dependence is nearly negligible and the data for three Tend
values are plotted in figure 4, considering that the difference in M between the AF2 phase and AF1 phase is as big as ~0.2 emu g−1. At this stage, it is safe to conclude that the difference in the pyroelectric current data between the two methods is mainly from the electric poling induced variation of the FE domain structure and thus the magnetic structure.
3.3. Pyroelectric and ferroelectric behaviors
Now one turns to the electric measurements. We obtained a huge package of data on the dielectric, pyroelectric, and ferro- electric behaviors as a function of T, respectively, using the two methods. For a clear illustration, we plot in figure 5 the P(T) data respectively from the two methods. In figures 5(a)–(d), the P(T) curves measured by the two methods at several Tend are
Figure 3. (a) The dc magnetization M as a function of T under the ZFC and FC modes, respectively. The magnetic field is 1000 Oe.
(b) The low-T specific heat CP(T) data, indicating the sharp peaks at TAF3 and TAF2, while only a nearly indispensible anomaly around TAF1 ~ 7.8 K is seen. PM refers to paramagnetic state.
Figure 2. Schematic drawing of the two methods for measuring the pyroelectric current Ip and M-H loops. TL = 2 K and EP is the electric poling bias. See text for details.
plotted together, respectively. Before turning to the details of the data, we look at the data obtained by Method 1 at Tend = 4 K as an example. Upon a decreasing of T, a FE transition appears at TAF2 and a re-entrant non-FE transition appears around TAF1. Furthermore, it is found that the evaluated P below TAF1 is non- zero, indicating the presence of the FE AF2 phase although the AF1 phase is dominant. The AF2 phase volume fraction at T = 4 K is estimated to be 1/7 ~ 13% by comparing the polarization magnitude in the AF2 region and the AF1 one.
Subsequently, we look at the data obtained by Method 1 given different Tend. The primer feature is that these P(T) curves overlap perfectly with each other with the measuring uncertain- ties. This implies that the electric field poling has no influence on the T-dependent magnetic/FE domain structures. However, the results obtained by Method 2 are very different, noting again that the sample is electrically poled during the 100 K → 2 K → Tend sequence before the short-circuiting. First, when Tend (<TAF2) is higher, larger polarization of the AF2 phase is observed. Second and more importantly, when Tend (<TAF2) is higher, more AF2 phase survives in the AF1 phase region below TAF1. It means that the electric field can tune the AF2 phase in coexistence with the AF1 phase in the original AF1 phase region.
While no difference between the two sets of curves at Tend ≤ 4 K is observed, remarkable differences are identified for Tend > 4 K. The larger the P, the higher the Tend is seen.
In figures 5(e), (f), several P(T) curves from each of the two methods are plotted together respectively. For Method 1, all the curves overlap into a master one, while the curves from Method 2 are well separated, illustrating more clearly the electric field poling enhanced AF2 phase stability. If one takes the case of Tend = 6 K as an example, a schematic drawing of the proposed magnetic structures upon the two different poling sequences is shown in figure 5(g). For Method 1, the magnetic structure is mainly occupied by the collinear AF1 phase, while the noncollinear AF2 phase appears as low den- sity small clusters embedded in the AF1 matrix. For Method 2, more AF2 phase clusters survive in consistence with the AF1 phase, contributing to the larger P at T > Tend.
3.4. Electric field control of FE domain structure
Referring to the proposed free energy scenario shown in figure 1, the mechanism for the electric field (poling) control
of the FE domain structure, and thus magnetic structure, can be reasonably understood. Due to the one-to-one correspon- dence between the ferroelectricity and the AF2 phase, one may start from the nucleation and growth of FE domains in connection with the AF2 phase, and see how the electric field controls the magnetic structure. This interpretation is simple and direct.
Without losing the generality, we take the case of Tend = 6 K as an example, and the model explanation is shown in figures 6(a), (b) for Method 1 and Method 2, respectively.
For the sequence with Method 1, the cooling under the elec- tric field poling enters the AF2 region below TAF2 and drives the FE domains to align well along the EP and occupy the whole sample. Upon cooling into the AF1 region below TAF1
and terminating at Tend, due to the removal of the poling and surface screening charge release, some FE domains may reverse to other directions and some domains may be replaced by the favored AF1 phase. It should be mentioned that the thermal energy at Tend is bigger than the electrostatic energy and the energy barrier between the AF1 phase and AF2 one, triggering the AF2 → AF1 transitions. In this case, the sur- vived FE domain density is low, as shown in figure 6(a).
In the subsequent warming sequence, these small domains as seeds trigger the AF1 → AF2 transitions by seed growth and random nucleation of new FE domains. Eventually, the sample is occupied with the bigger domains (red areas) along the EP and randomly oriented smaller domains (white areas).
The superimposition of these domains’ polarizations consti- tutes the remnant polarization measured experimentally in the AF2 region below TAF2.
Surely, one may question the cases when Tend is in the AF2 region (TAF1 < Tend < TAF2). Once the poling field is removed, disordering of the well-aligned FE domains is expected to some extent, and the measured polarization is always smaller than the saturated polarization under high electric field.
For the sequence with Method 2, the cooling under elec- tric bias down to the lowest T (2 K in the present experi- ments) allows the electrostatic energy comparably against the thermal energy. In this case, the surviving AF2 phase occupies a relatively high volume fraction. They are big in size and thus robust against the thermal fluctuations in the subsequent warming up to Tend, noting that the electric bias is not removed during this sequence. Upon the poling field removal and short-circuiting at Tend, the surviving AF2 domains are greater in number and bigger in size than the domains in Method 1, acting as seeds for the subsequent domain growth of the AF2 phase, as shown in figure 6(b).
This is the consequence of the electric field enhanced sta- bility of the AF2 phase over the AF1 phase. Eventually, the domains aligned along the EP direction are more in number and bigger in size than the case in Method 1, generating a larger polarization.
3.5. Remarks
Although the above discussion focuses on the FE domains, the microscopic origin for these domains is related to the AF2 phase, reflecting the nature of electric field control of the FE
Figure 4. The M-H loops measured at three temperatures (Tend
= 6, 8, and 10 K) using Method 1 (100 K → Tend) and Method 2 (100 K → 2 K → Tend), but without the electric poling bias (EP = 0).
(a) (b) (c)
domain structure and thus the magnetic structure. We unveil that this control is possible for MWO whose magnetic struc- ture is highly frustrated, even though the electric polarization is so small. For those multiferroic manganites which have much larger polarization, this effect would be more remark- able. In fact, it was demonstrated that in TbMnO3, the electric field poling along two opposite directions reverses the spiral spin structure [30]. The present experiment on MWO shows similar physics.
What is interesting in this work lies in the fact MWO allows a specific platform on which the electric polarization can be used as a prober to detect the electric control of mag- netic structure. For quite a number of type-II multiferroics, the FE phase is usually the low-T phase [2–4]. In this case, the electric field manipulation of magnetism is barely detected by measuring the electric polarization. MWO accommodates a non-FE AF1 phase below the FE AF2 phase, and their com- petition serves as the basis for detecting the electric control of magnetism. Surely, the magnetic structure and its response to an electric field can be detected by advanced techniques such as neutron scattering. One point of this work is to provide an additional prober to detect the variation of magnetic structure besides other evidences for the electric field control of the magnetic structure.
It is also necessary to mention that the above discussion is qualitative and oversimplified. For instance, we ignore the complexity associated with the polycrystalline nature. It is noted that the electric field control of magnetism in type-II
Figure 6. Proposed evolutions of the FE domains associated with the AF2↔AF1 transitions during the cooling under EP > 0 and the warming with EP = 0 for the two different methods. Here the case of Tend = 6 K is taken as an example.
Figure 5. The evaluated P(T) curves using Method 1 and Method 2 plotted together given a Tend: (a) Tend = 4 K, (b) Tend = 6 K, (c) Tend = 8 K, and (d ) Tend = 10 K. These P(T ) curves plotted together for different Tend using Method 1 (e), and Method 2 ( f ). The proposed coexistences of the AF2 clusters with the AF1 phase matrix at Tend = 6 K for the two methods are schematically shown in (g) for a guide of eyes.
multiferroics is basically possible as long as the electrostatic energy is comparable with the thermal energy, although MWO may not be a candidate for reaching practical applications of such control mechanism.
4. Conclusion
In conclusion, we have investigated the stability of mag- netic phases in MnWO4 in response to an electric field using the highly sensitive pyroelectric current method in order to explore electric field tuning of the multiferroic structure in highly frustrated magnets. In spite of the weak electric polarization and thus small electrostatic energy of the mul- tiferroic AF2 phase, we have unveiled that a low electric bias is sufficient to destabilize the low-T re-entrant non-FE AF1 phase and stabilize the FE AF2 phase. It is suggested that the electric bias induced surviving of the FE AF2 phase seeds favors the growth of the AF2 phase in the AF1 phase region, assisting the alignment of the FE domains and thus enhancing the electric polarization of MnWO4. The present work shows a possibility of tuning the magnetically induced FE domains in highly frustrated multiferroics and may shed some light on the electric field control of magnetism as a highly concerned issue.
Acknowledgments
This work was supported by the National 973 Projects of China (2011CB922101), the Natural Science Foundation of China (11374147, 11234005, 51332006), and the Priority Academic Program Development of Jiangsu Higher Educa- tion Institutions, China.
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