Congbin Liu(劉從斌), Jinbing Cheng(程晉炳), Junbao He(何俊寶), Yongsheng Zhu(朱永勝),Wan Chang(常婉), Xiaoyu Lu(路曉宇), Junfeng Wang(王俊峰), Meiyan Cui(崔美艷),Jinshu Huang(黃金書(shū)), Dawei Zhou(周大偉), Rui Chen(陳瑞), Hao Jiang(江浩),Chuangchuang Ma(馬創(chuàng)創(chuàng)), Chao Dong(董超),?, and Yongsong Luo(羅永松),,?

1Henan International Joint Laboratory of MXene Materials Microstructure,College of Physics and Electronic Engineering,Nanyang Normal University,Nanyang 473061,China

2Wuhan National High Magnetic Field Center and School of Physics,Huazhong University of Science and Technology,Wuhan 430074,China

3State Key Laboratory of Structural Chemistry,Fujian Institute of Research on the Structure of Matter,Chinese Academy of Sciences,Fuzhou 350002,China

4Key Laboratory of Microelectronics and Energy of Henan Province,Henan Joint International Research Laboratory of New Energy Storage Technology,Xinyang Normal University,Xinyang 464000,China

Keywords: polarization reversal,periodical modulation,high magnetic field

1.Introduction

Multiferroic materials in which ferroelectric(FE)and ferromagnetic orders are coupled have attracted extensive research interest because of their application potential in tunable magnetoelectric (ME) devices.[1-3]Of particular interest is a new class of type II multiferroic materials, in which noncollinear magnetic order induces FE polarization and often shows gigantic ME effects.[4]In these materials, the application of a magnetic field can control the FE polarization,and vice versa,i.e.,the ME coupling effect.The spin current model or inverse Dzyaloshinskii-Moriya interaction model,Pi j∝～ei j×(Si×Sj), is proposed to be the microscopic mechanism for induction of ferroelectricity by magnetic order.A number of multiferroic materials,such as Ni3V2O8,[5]LiCuVO4[6]and TbMnO3,[7]have been investigated extensively.In frustrated magnets,many ME phenomena have been observed in multiferroic materials due to the complicated spin structures, such as FE transition, polarization flop and polarization reversal.Indeed, the polarization reversal caused by a magnetic field or chemical doping is still a hot issue[8,9]in most cases of magnetically induced electric polarization.In this paper, we present magnetoelectricity in a frustrated spin system,antiferromagnet MnWO4,with a combination of electric and magnetic fields.We demonstrate that the FE of MnWO4can be individually reversed by electric and magnetic fields,as well as magnetic field orientation.These results suggest that there exists an exotic ME response in MnWO4,which offers a promising avenue for exploring the ME effect in multiferroics.

MnWO4is a frustrated spiral magnet, which crystallizes in a monoclinic structure with space groupP2/c.All Mn2+(S= 5/2,L= 0) ions form a zigzag chain running along thecaxis (see Fig.1).With decreasing temperature,the spins of Mn2+develop into three antiferromagnetic ordering states, AF3 (TN2

2.Experiments

Single crystals of MnWO4were grown by the flux method and determined by x-ray single-crystal diffraction as described in previous work.[14]A typical single crystal is shown in the inset of Fig.1(c).The applied magnetic field up to 52 T with a pulse width of 11 ms was generated by a nondestructive pulsed magnet in the Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology.The bias electric field was fixed along thebaxis unless otherwise stated,while the magnetic fields were rotated within theacplane.The direction of the magnetic field is presented as parameterθ,whereθdenotes the angle between the magnetic field and thecaxis.For the measurement of electric polarization,the sample was cut into a thin plate.We measured the electric polarization with a DC bias electric field of 200 kV·m-1provided by a voltage source.Platinum electrodes were sputtered onto the samples and then the platinum wires were attached to the opposite faces of the thin plate.Electric polarization was obtained by integrating the pyroelectric current stimulated by the magnetic field.

3.Results and discussion

Figure 1(c) shows the temperature-dependent magnetic susceptibilityχa,χbandχcof MnWO4single crystal for three crystalline axes.ForH=0.1 T, three kinks representing antiferromagnetic ordering with transition temperaturesTN3=13.7 K,TN2=12.8 K andTN1=6.8 K are observed when the magnetic field is along thea,bandcaxis, respectively.In accordance with the early results, these antiferromagnetic phases were defined as AF3,AF2 and AF1,respectively.In particular,phase AF2 is demonstrated to have an incommensurate magnetic structure,yielding a spontaneous FE state.In addition, the susceptibilitiesχaandχcshow a drop andχbexhibits a rise belowTN1, suggesting that the spins of Mn2+are arranged in theacplane at AF1.[15]This motivates us to explore the evolution of polarization with the application of a magnetic field within theacplane.

Figure 1(d)shows the evolution of thebaxis electric polarization tuned by the electric and magnetic fields forH ‖a(θ=90?),the value of polarization is calculated from ?Pb ≡P(H)-P(H=0).Before each measurement,the sample was cooled down from room temperature to 4.2 K (nonpolarized state) under a poling electric fieldE=±200 kV·m-1(labelled as±E) without a magnetic field.At 4.2 K, a robust change of ?Pb(～20 μC·m-2) is observed in the vicinity ofH=2 T with the bias field +E, suggesting a transition from a nonpolarized state to the FE AF2 phase.A large hysteresis is observed, which reveals a first-order phase transition.The polarization does not decay in a field of approximately 14 T,coinciding with the observations in early work.[16]Moreover,the magnetic field can render an alternative way to recover the initial polarized state ?Pbwith the removal of the bias field(E=0).As the primitive polar direction is converted to become negative, the opposite direction ?Pbreproduced by the magnetic field is observed.Those results imply that magnetic field can individually reproduce the FE information from the nonpolarized state,which is known as the ME memory effect.The field-driven polarization is similar to the case of Ni3V2O8,in which the FE phase can be reversed by the magnetic field instead of the electric field.[5]Therefore, MnWO4is a specific material whose polarization reversal by magnetic field deserves to be further studied.

Fig.2.Polarization ?Pb measured at different temperatures in a magnetic field applied along the(a)a and(b)c axes,respectively.The bias electric field is equal to E=+200 kV·m-1.The red arrows in(b)indicate the transition of polarization.

Figure 2 displays the field dependence of ?Pbin selected magnetic fields applied along theaandcaxes at various temperatures.ForHalong theaaxis,the increase in polarization is extended around 20 T and gradually reduced with increasing field to 52 T at low temperatures.For temperaturesT>TN1(～6 K),the anomalous jump of polarization disappears.This disappearance is ascribed to the suppression of the nonpolarized state AF1 by the temperature.As the temperature is increased, the boundary of the FE AF2 phase to the high-field paraelectric state V appears in the high-field region and shifts toward a low field,and the magnitude of polarization decays.AboveTN3(>12 K), all the polarizations responding to the magnetic field disappear,indicating that polarization is related to the magnetic order.The effect of magnetic field applied along thecaxis (θ=0?) is distinctly different from that ofH‖a.Except for the nonpolarized state of FE AF2,it is found that the FE AF2 phase is strongly suppressed by the magnetic field, as seen in Fig.2(b).Similar to observations forH ‖a,the phase transition from the FE AF2 phase to the paraelectric state V is shifted to the low field as temperature increases.

Fig.3.Field dependence of polarization with different bias electric fields: (a),(b)H ‖a,(c)H ‖c.The inset in(b)shows the temperature raised to 15 K and maintained for several minutes then subsequently lowered to 4.2 K,leading to the polarization between rising and falling fields being irreversible.In addition,the±E indicate the magnitude and direction of the bias electric field, and the labels (1)-(3) represent the order of the applied electric field.

Domain switching in MnWO4has a pronounced character because the polarization can be individually reversed by the magnetic and electric field.ForH ‖a,a peak of polarization is observed at around 20 T and rapidly approximates to zero at 52 T(black curve,+E(1)),as shown in Fig.3.Unexpectedly, the sign and magnitude of polarization ?Pbremain unchanged (red curve,-E(2)) when the electric field is reversed.This behavior was ascribed to the ME memory effect,which is exceptional compared with that in traditional ferroelectricity, such as in BaTiO3[17]and PbZrO3.[18]However,once the temperature is lifted to 15 K(>TN3)for several minutes and returned to 4.2 K after+E(2)measurement,two opposite electric fields-E(2)and-E(3)can completely reverse the polarization ?Pb,as shown in Fig.3(b).Amazingly,an irreversible intermediate state between rising and falling field curves emerges.This result suggests that the high temperature destroyed the history of spins responding to the magnetic field, giving rise to elimination of the ME memory effect.In this case,high temperature is exploited to remove the history process in the multiferroic.ForH ‖c, the effect of an external magnetic field on the FE polarization is shown in Fig.3(c).Firstly,the FE polarization develops a peak at 2.5 T and rapidly reduces to zero (black curve) with electric field+E(1).UnlikeH‖a,polarization along thecaxis rapidly decays when magnetic field exceeds 2 T,which reveals the strong anisotropy of polarization in MnWO4.In parallel withH ‖a,almost no change in polarization is observed if the electric field is reversed only once (red curve,-E(2)), and polarization reversal can be directly realized upon reversing the electric field for the second time(blue curve,-E(3)).In this case,realization of polarization reversal by the bias electric field requires two steps.Note that the ferroelectricity in MnWO4is ascribed to spin chirality,and the direction of polarization depends on the chiral vector.[16]These results show the reentrant FE AF2 phase driven by-E(2)is different from that observed in+E(1),which means that the chirality of spin is changed by the electric field.

Fig.4.Electric field modulates the polarization reversal in different magnetic fields: (a) 13 T, (b) 48 T.The red curves represent the polarization process with rising field, while the black curves indicate the falling field.The θ =55?shown in the inset is the tilted angle from the magnetic easy axis to the c axis. ±E(1)to±E(5)denote the direction and order of the applied bias electric field.

In order to further explore the polarization reversal, we apply a magnetic field along the magnetic easy axisu, stated asθ=55?.Figure 4 shows the polarization reversal controlled by combining the magnetic and electric fields forθ= 55?;the selected temperature is 4.2 K.Before each measurement,the sample is subjected to an electric field.At low magnetic fields (H<5 T), the FE AF2 phase robustly emerges at 2T and shows a maximum value of～60 μC·m-2.For magnetic fields above 13 T, the polarization of this FE phaseis quickly suppressed because of the alignment of spins driven by the magnetic field,[19]as shown in Fig.4(a).These experimental data are basically consistent with the corresponding results in previous works.[13,14]However,the electric field is reversed several times, and we found that the polarization?Pbremains unchanged for all the measurements.By contrast,when a magnetic field is swept up to 48 T,the paraelectric phase HF and FE phase IV emerge at 14 T and 38 T, respectively.Meanwhile, a second first-order phase transition from HF to IV is observed.Most remarkably, the FE phases IV and AF2 maintain opposite directions in each field circle.In this case, the application of two consecutive opposite bias electric fields,-E(2)and-E(3),related to the first measurement can trigger the spontaneous change in the direction of polarization.After that,the polarized state of MnWO4can be recovered by using a positive electric field two times,marked as +E(4) and +E(5).Therefore, reversal of polarized states with just an electric field is demonstrated.

Fig.5.The electric polarization and the corresponding pyroelectric current reversed by the different bias electric fields: (a) electric polarization,(b)pyroelectric current.Here,the pyroelectric current is as a function of pulse time,and the rising and falling field currents are separated by the vertical broken line.In addition,AF1 is a nonpolarized state and AF2 and IV are ferroelectric states, while HF (high-field paraelectric state)and V are paraelectric phases.

In order to further explore the occurrence of polarization reversal,a relatively high magnetic field is applied to the sample.Figure 5 shows the electric polarization and corresponding pyroelectric current induced by the magnetic field up to 52 T.Prior to the electrical measurements,a bias electric field is applied to the sample.When the magnetic field exceeds 52 T, another paraelectric state, V, is observed at 48 T, as shown in Fig.5(a).Interestingly, the polarizations in rising(red curve)and falling(black curve)fields are reversed.Thus,the trace of polarization forms a transformed ‘∞’ loop in a magnetic field cycle.Under a negative electric field-E(2),it is seen that the polarization in a falling field is completely reversed,whereas that in a rising field is not affected by the field.Repeating this process by using-E(3),the signs of polarization and the corresponding pyroelectric current are changed with respect to a falling field.This can be evidenced by the change in the peak for pyroelectric current, which is a function of time as shown in Fig.5(b).In Fig.5(b),it is seen that the currents in rising and falling fields are separated and individually reversed by the electric field.Hence,the electric field completely reverses the polarization curve in comparison with the initial state.Similar behavior is observed when the electric field is switched to a positive direction: the polarization recovers to the initial state in two steps.The symmetry of current changing with time reflects the polarization modulated by the reversed electric field,as shown in Fig.5(b).These results show that polarization reversal in combination with electric and magnetic fields is a unique characteristic of MnWO4in high fields.This behavior appears to be observed in similar systems such as Ni3V2O8,where the FE state can be manipulated by reversing the electric field.In Ni3V2O8,the high-field FE phase is directly reversed by the negative electric field,and the reversal of the low-field phase is realized in the second time field.However,the two FE phases in MnWO4can be simultaneously reversed without an intermediate state.The evolution of polarization measured at different temperatures inH‖uhas been described in the literature in detail.[14]

Our data also show that polarization responds to magnetic field in a special direction.Figure 6 shows polarization controlled by the electric field with a tilted angle ofθ=70?at 4.2 K.At low fields (H<48 T), it is obvious that a new high-field FE phase,+IV,is observed in+E(1)as well as the FE AF2 and PE HF phases.In this case, the FE phases AF2 and IV become parallel to each other rather than antiparallel.Note that the change of sign of FE phase IV originates from the magnetic field rather than the electric field, implying that magnetic anisotropy is an alternative way to manipulate the polarized state in MnWO4.Associated with the ME memory, no change of polarization is observed for the first opposite electric field-E(2).For the second negative electric field-E(3) the polarization curves in rising and falling fields are completely reversed.The above process can be returned to the initial state by applying positive electric fields twice (+E(4), +E(5)).Thus, the polarized state can return to the original configuration with periodically reversed electric fields +E(1),-E(2),-E(3), +E(4), +E(5).The highfield paraelectric state V emerges at a high field (～52 T), as shown in Fig.6(b).Compared with that inH ‖u,the process of polarization becomes reversible with a large hysteresis in a relatively high field.The discrepancy betweenθ=70?andθ=55?indicates that the polarization information in the two directions is different.On the other hand,the direction of polarization can be reversed and recovered by the negative and positive fields, respectively.Therefore, the rising and falling field curves can be individually tuned by the electric field in both directions.These experimental phenomena were first observed in MnWO4with a high magnetic field.No similar cases have been found in other compounds,such as magneticinduced FE TbMnO3[20]and CuCr2O4.[21]

Fig.6.The magnetic field dependence of polarization with a circularly changing bias electric field: (a)38 T,(b)52 T.

According to the above results, it is found that the fieldinduced FE polarization in MnWO4is strongly sensitive to the orientation of the magnetic field.Two FE phases AF2 and IV merge into a single phase in a certain magnetic field direction; detailed evolution of the polarization is described in the literature.[14]Here, we suppose that the value of polarization is approximately equal to the sum of two parts,P1(H<14 T)andP2(H>14 T),whereP1is considered a result of the FE AF2 phase[22]andP2relates to the FE IV phase, as shown in Figs.7(a) and 7(b).Hence, the strength of polarization?Pbcan be phenomenologically expressed by ?Pb ≡P1+P2below the transition temperature.The total polarization forH ‖acan be written as the sum ofP1andP2.In contrast toH ‖a, the polarization forH ‖cis shown as ?Pb ≡P1-P2due to the direction of change ofP2.In this case the emergence of the paraelectric HF in theacplane could be explained as the result of competition betweenP1andP2.In addition,the sign of FE phase IV is susceptible when the angleθexceeds 55?,as depicted in the early literature.[14]Regarding the polarization reversal, it can be realized by magnetic field,[23]electric field[24]or chemical doping, such as Co2+doping in MnWO4.[22]These results imply that the unusual ME effect in MnWO4is attributed to the spin arrangements driven by magnetic field, as has been discussed in previous work.[14]Therefore, if we suppose that the critical fields of FE transition triggered by magnetic field are marked byHc1,Hc2,Hc3andHc4,as shown in Figs.7(a)and 7(b),in the field range ofHc1-Hc2it is seen that the FE phase AF2 remains unchanged when the angleθis varied from 55?to 70?.However,the contrasting result for FE IV phase reversal by magnetic field is observed in fieldsHc3-Hc4.This result implies that the spin chirality in FE phase IV is distinguished from that in FE phase AF2.Indeed, the spiral spin structure of phase IV analogous to AF2 has been demonstrated by time-resolved neutron Laue diffraction.[19]Combined with the results for theaandcaxes,we construct a schematic diagram in which the spin chirality is determined by the magnetic field and angleθ,as displayed in Fig.7(c).In this figure,the FE phases AF2 and IV exhibit different polarization directions, and the chirality of IV is altered in certain areas.Thus,we observe that the polarization of MnWO4is strongly dependent on the magnetic field,the electric field and the magnetic field orientation.Utilizing the polarized states periodically tuned by electric field and FE phase IV modulated by anisotropy in MnWO4may help us to design a device controlled by those factors.In addition, the mechanism of the polarized states periodically tuned by electric field and FE phase IV spontaneously reversed by magnetic field is exotic.These experimental phenomena first observed in multiferroic MnWO4have not been found elsewhere.This novel behavior supplies a promising avenue in the search for fieldmodulated polarization reversal in other multiferroic crystals.

Fig.7.Schematic diagram of spin chirality of the polarization direction determined by the strength and direction of magnetic field.(a),(b)The measured polarization in a rising field for the angles θ =55?and 70?at 4.2 K, respectively. Hc1-Hc4 show the critical fields of polarization transition.(c)The change of spin chirality by rotating a magnetic field within the ac plane.The green curved arrows indicate the spin chirality.Due to the sign of polarization,two different ferroelectric phases,-IV and+IV,are defined.

4.Conclusions

In summary, the ME effect in MnWO4has been studied with the magnetic field rotated in theacplane.The fieldinduced electric polarization shows strong anisotropy in dependence on field angle.Polarization reversal can be directly realized by the electric field in two steps without intermediate states when the magnetic field is applied along theaandcaxes, and high temperature can remove the ME memory.For anglesθ=55?or 70?,the polarization is reversed or recovered by a two-step inversed electric field,accompanied with reversal of rising or falling curves.Moreover,the sign of phase IV forθ=70?is distinct from that observed atθ=55?,indicating that they are two different states.The discrepancy can be exploited to save information by changing the direction of the magnetic field.These experimental results show that polarization in MnWO4can be modulated by temperature,anisotropy,magnetic and electric fields.Finally,the reversed behaviors of MnWO4provide us with a concept for designing a ME device to save or extract information,in combination with variations in anisotropy,electric field and magnetic field.

Acknowledgements

Project supported by the National Natural Science Foundation of China (Grant Nos.12074135, 12104388, and 52272219), Nanyang Normal University, the Natural Science Foundation of Henan Province (Grant Nos.222300420255 and 232300421220), and the Key Scientific and Technological Projiect of Technology Depeartment of Henan Province of China(Grant Nos.222102230105 and 212102210448).Congbin Liu acknowledges Wanxin Liu at the WHMFC for help with the data measured in pulsed fields.