Possible coexistence of Cycloidal Phases, Magnetic Field Reversal of Polarization and Memory Effect in Multiferroic \emph{R} 0.5 Dy 0.5 MnO 3 (\emph{R}=Eu and Gd)
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Possible coexistence of Cycloidal Phases, Magnetic Field Reversal of Polarization andMemory Effect in Multiferroic R . Dy . MnO ( R =Eu and Gd) Chandan De and A. Sundaresan ∗ Chemistry and Physics of Materials Unit and International Center for Materials Science,Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064 India (Dated: October 8, 2018)We report the occurrence of both ab and bc cycloidal ordering of Mn-spins at different tem-peratures and their possible coexistence at low temperatures in the polycrystalline mixed rare-earth compounds, R . Dy . MnO ( R = Eu and Gd), which exhibit extraordinary magnetoelectricproperties. While the polarization of Gd . Dy . MnO is comparable to TbMnO , the compoundEu . Dy . MnO shows high value of polarization. However, both of them show giant magnetic tun-ability and exhibit large magnetocapacitance whose sign changes across the two cycloidal orderingtemperatures. Intriguingly, the electric polarization can be reversed upon ramping up or rampingdown the magnetic field, which has not been observed for any of the R MnO system. Most strik-ingly, these compounds show non-volatile ferroelectric memory effect even in the paraelectric andparamagnetic region (T C ≤ T ≤
80 K). We attribute these remarkable properties to the coexistenceof ab and bc cycloidal ordered phases. Among the spin driven multiferroic materials, the or-thorhombic ( o -) perovskite manganites o - R MnO ( R =Gd, Tb, and Dy) have been studied extensively [1–6].In GdMnO , the cycloidal spins that break the inver-sion symmetry, are in the ab plane and the polarizationpoints along the a direction of the orthorhombic ( Pbnm )structure [7]. In the manganites with R = Tb and Dy,the cycloidal spins are in the bc plane and the polariza-tion points along the c direction [1, 7, 8]. In the case of o - R Mn O with smaller rare-earths ( R = Ho, Er, Tm),a collinear magnetic ordering (E-type) gives polarizationalong c -direction which is substantially higher than thatof the bc cycloidal phase [9–12]. The existence of differentmechanisms of polarization in the o - R MnO with differ-ent R -ions indicate that the radius of R -ion determinesthe ferroelectric properties by controlling the competingnearest neighbor ferromagnetic and next-nearest neigh-bour antiferromagnetic interactions [8].Several studies have been carried out on mixed rare-earth manganites R − x R ′ x MnO with R = Sm, Eu, Tband R ′ = Y and Gd, where multiferroic phases of cy-cloidal and E-type collinear magnetic structure are foundas a function of average radius of rare-earth ions [13–15]. Based on magnetic field effects on polarization inSm . Y . MnO , coexistence of polarization in two dif-ferent directions has been suggested [16]. In the case ofDy − x Ho x MnO , a transition from bc cycloidal to E -typeantiferromagnetic phase occurs and coexistence of thesetwo phases is found in a wide compositional range[17].Application of external pressure in TbMnO leads tochange of bc cycloidal ordering to E -type ordering with alarge polarization ( ≈ µ C/cm ) [18].Here, we report direct evidences for the occurrenceof the two cycloidal phases ( ab and bc ) in two mixedrare-earth manganites, Eu . Dy . MnO (EDMO) and ∗ [email protected] Gd . Dy . MnO (GDMO) and their extraordinary mag-netoelectric properties. Contrary to TbMnO (TMO),the mixed rare-earth compounds show a large magneto-capacitance accompanied by a change of sign from neg-ative to positive, as a function of temperature. Further,they exhibit large enhancement of electric polarizationunder applied magnetic field. Surprisingly, they showswitching of polarization while ramping up the magneticfield from 0 to 80 kOe. We also demonstrate that theferroelectric domain state is memorized not only belowincommensurate magnetic ordering but also in the para-electric and paramagnetic region as well.Details of sample preparation and physical measure-ments are given in supplemental material [19]. Fig. 1(a, b and c) shows specific heat divided by temperature(C/T) (left-axis) and magnetization (M) data, measuredunder field cooled warming (100 Oe) condition (right-axis), with temperature for EDMO, GDMO and TMO,respectively. Since these samples are polycrystalline andthe rare-earth moments are higher than the Mn mo-ment, we do not observe magnetization anomalies asso-ciated with the ordering of Mn ions. On the otherhand, the (C/T) data clearly show the incommensuratesinusoidal antiferromagnetic ordering (T N ), commensu-rate cycloidal ordering (T C ) and R ordering [1], exceptthat the rare-earth moments in EDMO do not order downto 2 K [20]. The center panels (d, e and f) show dielectricconstant (left-axis) and loss data (right-axis) measured at50 kHz with different external magnetic fields (0, 40 and80 kOe). For EDMO and GDMO, the zero field dielectricand loss data show a broad doublet peak which becomesa single peak with a slight positive shift of temperatureunder applied magnetic field. On the other hand, onlya single peak in dielectric and loss data is observed forTMO which becomes broad in presence of magnetic field.Pyrocurrent data of the samples recorded at 4 K/min,as reported earlier [21], from 10 to 30 K at 0, and 80kOe fields, after poling the samples with an electric field(E P = 8 kV/cm, E P ⊥ H P ) from 35 to 10 K, are dis-
16 200.400.42 (c)(e)(d) (b)(a) C / T x - ( J / m o l e - K ) TMOGDMO (f) M x - ( e m u / g ) J ( A / m ) T a n () x - r EDMO 36912 bccycloidal T (K) bccycloidal (i)(h)(g) T (K) abcycloidal bccycloidalabcycloidal T (K) 0 10 20 30 40 5012 FIG. 1. First, second and third column represents the dataof Eu . Dy . MnO , Gd . Dy . MnO and TbMnO , respec-tively where (Top row) left-axis in a, b and c shows heat ca-pacity divided by temperature and the right axis shows mag-netization vs. temperature data, (Middle row) the left-axis ind, e and f shows dielectric constant and the right-axis showsloss vs. temperature data and (bottom row) g, h and i showspyroelectric current vs. temperature data. played in bottom panels (g, h and i). The warming ratedependent of pyrocurrent confirms the intrinsic ferroelec-tric nature of the sample [19]. From these data, we inferthat the ferroelectric transition temperatures ( T C ) forEDMO, GDMO and TMO are 26, 18 and 27 K, respec-tively. This is in agreement with the heat capacity anddielectric anomaly. It is interesting to note that the zerofield pyrocurrent data for both EDMO and GDMO showtwo peak feature but a single peak for TMO, similar tothat observed in dielectric and loss data. From the fol-lowing discussion, we suggest that the two peak featurein dielectric and pyrocurrent data indicates the presenceof ab and bc -cycloidal phases. It is possible that thesetwo cycloidal phases can coexist or there could be a tem-perature dependent reorientation of cycloidal spins. Con-sidering the average radius of rare earth ions in EDMOand GDMO and phase diagram of temperature versusradius of R-ions, we infer that these two compounds areat the phase boundary between the ab and bc cycloidalphases [22]. In agreement with the earlier report [23],thermal hysteresis observed around the dielectric anoma-lies confirms that the phase transition between these twocycloidal phases is first order which indicates possible co-existence of these phases [19]. However, it requires a sin-gle crystal study to confirm the phase coexistence. Basedon the theoretically obtained magnetoelectric phase dia-gram of temperature versus J (Next nearest neighbourexchange interaction), we attribute the low temperature(LT) peak to ab and high temperature (HT) peak to bc cycloidal ordering [24]. Under an applied magnetic field(80 kOe), the two peak feature disappears and becomes a single peak with enhanced pyrocurrent and significantincrease of T C . The disappearance of LT peak indicatesconversion of ab cycloidal into bc cyclodial phase whichis consistent with the enhanced pyroelectric current. Incontrast, the magnitude of the single peak observed forTMO is decreased with magnetic field without any sig-nificant change in T C [Fig.1 (i)]. The broad nature ofthe current at 80 kOe may indicate the partial conver-sion of bc cycloidal phase into ab cycloidal. It shouldbe noted that the polarization in GdMnO is suppressedstrongly with applied magnetic field through weakeningof the commensurate cycloidal ordering [19, 25].Fig. 2 (a, b and c) shows magnetocapacitance (MC)data measured at 50 kHz while sweeping the magneticfield from -70 kOe to +70 kOe at the rate of 100 Oe/secat different temperatures for all the three samples. Thedata measured at 500 Hz and 2 MHz are shown in sup-plemental material [19]. It is intriguing to note that thebehavior of MC in EDMO and GDMO is quite differentfrom TMO. Above T C , all the three samples exhibit pos-itive MC and it reaches a maximum around T C . BelowT C , the MC in TMO remains positive and at 10 K itlevels off above 40 kOe as shown in Fig. 2c. In contrast,the mixed rare earth samples show a crossover from apositive to negative MC on decreasing the temperaturefrom paraelectric to ferroelectric state through an inter-mediate temperature range (between the two pyrocurrentpeaks) where the positive MC shows a broad maximum,corresponding to a critical field, which shifts to lower fieldwith decreasing temperature. The existence of such crit-ical field indicates the change in direction of polarization -80 -60 -40 -20 0 20 40 60 800.00.20.40.6-12-8-4048-12-8-404812 H (kOe)
30 K 40 K 50 K 10 K 20 K 25 K
TMO50 kHz (c)(b)
25 K 30 K 40 K 50 K 10 K 15 K 20 K 22 K [( H - ) / ] x EDMO (a)
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FIG. 2. Magnetocapacitance data of (a) Eu . Dy . MnO ,(b) Gd . Dy . MnO and (c) TbMnO measured at 50 kHzat various temperatures. [8]. Below certain temperature, MC becomes completelynegative. This behaviour is consistent with the fact thatMC is positive below the cycloidal ordering temperaturein TbMnO and negative in GdMnO [19]. It is also im-portant to note the large MC (12%) observed in widetemperature range for the mixed rare-earth compoundscompared to that in TMO (0.6%).Fig. 3(a, b and c) shows temperature dependent po-larization data, at different magnetic fields, obtained byintegrating the pyrocurrent (inset), recorded after pol-ing the samples with E P = 8 kV/cm ⊥ H P . In TMO,it is known that the polarization changes its directionfrom c - to a -axis when magnetic field is applied alongthe b -direction [1, 26]. However, the observed polar-ization along a -direction is smaller because of the lackof complete flipping of bc cycloidal phase due to highdomain wall formation energy which is determined bythe competition between Zeeman energy and magneticanisotropy[27–29]. In the present case, the polycrstallineTMO shows only a small decrease in polarization (∆ P ≈−
12% at 80 kOe) with magnetic field as shown in insetof Fig. 3c. In contrast, a dramatic change of polarizationis observed in the two mixed rare-earth manganites, asshown in the insets of FIg. 3a and 3b. The magnitude ofthe polarization at zero field is fairly large (almost fourtimes that of TMO) in EDMO and it increases with mag-netic field drastically as shown in the inset of the fig. 3a.Remarkably, the effect of magnetic field on polarizationin GDMO is very large ( > C increases with magnetic field. We sug-gest that the large enhancement of polarization is due tothe coexistence of ab and bc -cycloidal phase at 0 kOe andchange of ab cycloidal into bc cycloidal phase in appliedmagnetic field. At zero field, we observe a net polariza-tion of the two components i.e. along a and c directions.Besides, we propose that the bc -cycloidal regions can actas seed for changing the rotation plane of ab cycloidal sothat the rotation of cycloidal plane becomes easier.Fig. 4 shows the polarization obtained by integratingthe zero bias magnetoelectric current measured isother-mally at 7 K by sweeping the magnetic field at 100 Oe/secfrom 80 to 0 to 80 kOe for six cycle after magnetoelectricpoling with E P = − ⊥ H P = 80 kOe from 30 to 7K for GDMO. We see a sequential flipping of polarizationwithout any decay from positive to negative and negativeto positive upon ramping up the magnetic field from 0to 80 kOe and then ramping down to 0 kOe. Thoughsimilar switching behavior is reported in other multifer-roics [30–33], it is not known in R MnO . The observedpolarization reversal in the present case is explained bythe sequential conversion of the cycloidal phases. As we
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10 15 20 250-5-10-15 I p y r o ( p A ) I p y r o ( p A ) I p y r o ( p A ) GDMO P % T (K) TMOE P = 8 kV/cmEDMO T (K) T (K) H (kOe) (c)(b) P ( C / m ) (a) H (kOe) P % P % H (kOe) T (K) FIG. 3. Polarization data of (a) Eu . Dy . MnO , (b)Gd . Dy . MnO and (c) TbMnO measured at various mag-netic field. Inset (right side) shows pyrocurrent data. Inset(left side) shows normalized △ P = [(P(H) − P(0)/P(0)) ∗ vs. magnetic field data. poled the sample with H P = 80 kOe, the polarizationat 7 K should be directed along c -direction (only bc cy-cloidal phase). Upon ramping down the field to zero, ab cycloidal phase grows and the polarization flips 90 ◦ ( a -direction) and the net polarization decreases to zero atH ∼
40 kOe where the oppositely aligned domains (along c -direction) are equally populated. When the field is fur-ther ramped down to zero, the polarization goes to theopposite (negative) direction. A complete switching ofpolarization with equal magnitude is obtained for a fieldrange of 0 to 80 kOe. The actual mechanism of switchingof polarization depends on the orientation of neighbour- Time (min) P ( C / m ) H ( k O e ) FIG. 4. Periodic change of polarization (left-axis ) and mag-netic field (right-axis) with time recorded at 7 K after polingthe sample from 30 to 7 K with −
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25 K 23 K 20 K (c)(b)
15 K I p y r o ( p A ) T C < T R < T N T R > T N T R < T C E P = 8 kV/cmRamp: 10-T R -10 K @ 4K/min (a) T (K)
35 K 30 K 40 K P ( C / m ) T (K)
70 K 90 K 80 K 60 K T (K)
50 K T (K) FIG. 5. Polarization data after integrating the pyrocurrent(inset), recorded after poling the sample (EDMO) from 30 to10 K with 8 kV/cm, 0 kOe and ramp the temperature from10 to T R to 10 K with zero bias. ing ab and bc cycloidal phases.Finally, we present the observation of memory ef-fect, the retention of polarized state when the sampleis warmed to the paraelectric state [16, 34, 35]. In thismemory experiment, first the sample was poled (E = 8kV/cm) from 30 K to 10 K. After poling the sample, theelectrode wires were short-circuited and the sample waswarmed up to a temperatures, called ramping temper-ature (T R ) and again cooled down to 10 K. After thisramping treatment, the pyrocurrent was recorded from10 to 35 K at 4 K/min rate (see the inset of Fig. 5).Fig. 5a shows the integrated polarization versus temper-ature for T R < T C (T R = 15, 20, 23 K). As expectedthe polarization is decreased gradually with increasingT R . Fig 5 (b) shows the polarization for T C < T R < T N (T R = 27.5, 30, 35 and 40 K). Though the polar-ization decreases with increasing T R , it is interesting tonote that the polarization survives even after warmingthe sample above T C . Fig 5(c) shows the polarization data obtained from similar measurement protocol for T R > T N (T R = 50, 60, 70, 80 and 90 K). Surprisingly, wesee that the polarization is memorized up to 80 K andvanishes at 90 K. To observe the memory effect aboveT N , it is very important to pole the sample just abovethe cycloidal ordering temperature to avoid the forma-tion of internal electric field [21]. In fact, we have shownthat if we pole the sample from slightly high tempera-ture (50 K) we do not see the memory effect above T N [19]. It is because of the poling temperature, the memoryeffect is not seen in Sm . Y . MnO [16]. The variationof polarization obtained at 10 K as a function of T R reveals the existence of three different slopes that corre-spond to temperatures below T C , T C ≤ T ≤ T N andabove T N [19]. To further confirm the memory effect,we poled ( − R . Inthis measurement, we observed depolarization and polar-ization current in each warming and cooling cycle for T R up to 80 K[19]. Similar memory effect is also observedin GDMO [19]. These results demonstrate the presenceof memory effect(cycloidal phase) at temperatures muchabove the ferroelectric transition. From the inset of Fig.5, we see that the two shoulders in the pyrocurrent peak,which are indicative of ab and bc cycloidal phases, grad-ually becomes one where the LT peak disappears withincreasing T R . This result suggests that the bc cycloidalphase (HT peak) is responsible for the memory effect.However, we suggest that this finding requires furtherstudy of dielectric response to explain how the cycloidalphase exists in the paramagnetic region also [34].In conclusion, we have shown the possible coex-istence of ab and bc cycloidal phases in the mixedrare-earth multiferroic manganits, Eu . Dy . MnO andGd . Dy . MnO . As a result, these materials exhibitlarge magnetic tunability of polarization and high mag-netocapacitance. More importantly, the electric polar-ization can be switched by ramping the magnetic field.Further, the electric polarization retains its memory evenin the paraelectric and paramagnetic region. We suggestthat these effects results from the coexistence of cycloidalphases.The authors acknowledge the Sheikh Saqr Laboratoryat the Jawaharlal Nehru Centre for Advanced ScientificResearch for experimental facilities. [1] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima,and Y. Tokura, Magnetic control of ferroelectric polar-ization, Nature , 55 (2003).[2] N. A. Spaldin and M. Fiebig, The Renaissance of Mag-netoelectric Multiferroics, Science , 391 (2005).[3] S.-W. Cheong and M. Mostovoy, Multiferroics: a mag-netic twist for ferroelectricity, Nat. Mater. , 13 (2007).[4] Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, Electric Control ofSpin Helicity in a Magnetic Ferroelectric, Phys. Rev.Lett. , 147204 (2007).[5] T. Kimura, Magnetoelectric Hexaferrites, Annu. Rev.Condens. Matter Phys. , 93 (2012).[6] Y. Tokura, S. Seki, and N. Nagaosa, Multiferroics of spinorigin, Rep. Prog. Phys. , 076501 (2014).[7] K. Noda, S. Nakamura, J. Nagayama, and H. Kuwa- hara, Magnetic field and external-pressure effect on ferro-electricity in manganites: Comparison between GdMnO and TbMnO , J. Appl. Phys. , 10C103 (2005).[8] T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y.Tokura, Ferroelectricity and Giant Magnetocapacitancein Perovskite Rare-Earth Manganites, Phys. Rev. Lett. , 257201 (2004).[9] I. A. Sergienko, C. ¸sen, and E. Dagotto, Ferroelectricityin the Magnetic E-Phase of Orthorhombic Perovskites,Phys. Rev. Lett. , 227204 (2006).[10] S. Picozzi, K. Yamauchi, B. Sanyal, I. A. Sergienko, andE. Dagotto, Dual Nature of Improper Ferroelectricityin a Magnetoelectric Multiferroic, Phys. Rev. Lett. ,227201 (2007).[11] N. Lee, Y. J. Choi,M. Ramazanoglu, W. Ratcliff, V.Kiryukhin and S.-W. Cheong, Mechanism of exchangestriction of ferroelectricity in multiferroic orthorhombicHoMnO single crystals, Phys. Rev. B , 020101(R)(2011).[12] S. M. Feng, Y. S. Chai, J. L. Zhu, N. Manivannan, Y. S.Oh, L. J. Wang, Y. S. Yang, C. Q. Jin, and K. H. Kim,Determination of the intrinsic ferroelectric polarization inorthorhombic HoMnO , New J. Phys. ,073006 (2010).[13] S. Ishiwata, Y. Kaneko, Y. Tokunaga, Y. Taguchi, T.-h. Arima, and Y. Tokura, Perovskite manganites hostingversatile multiferroic phases with symmetric and anti-symmetric exchange strictions, Phys. Rev. B , 100411(2010).[14] D. O’Flynn, C. V. Tomy, M. R. Lees, A. Daoud-Aladine,and G. Balakrishnan, Multiferroic properties and mag-netic structure of Sm − x Y x MnO , Phys. Rev. B ,174426 (2011).[15] T. Goto, Y. Yamasaki, H. Wantanabe, T. Kimura, andY. Tokura, Anticorrelation between ferromagnetism andferroelectricity in perovskite manganites, Phys. Rev. B , 220403R (2005).[16] I. Fina, V. Skumryev, D. OFlynn, G. Balakrishnan,and J. Fontcuberta, Phase coexistence and magneticallytuneable polarization in cycloidal multiferroics, Phys.Rev. B , 100403 (2013).[17] N. Zhang, S. Dong, Z. Fu, Z. Yan, F. Chang and J.Liu, Phase transition and phase separation in multifer-roic orthorhombic Dy − x Ho x MnO (0 ≤ x ≤ ,6506 (2014)[18] T. Aoyama, K. Yamauchi, A. Iyama, S. Picozzi, K.Shimizu, and T. Kimura, Giant spin-driven ferroelec-tric polarization in TbMnO under high pressure, Nat.Comm. , 4927 (2014).[19] See supplemental material at [URL will be inserted byAIP] for details of sample preparation, physical measure-ments, sketch of sample electrodes including electric andmagnetic field directions and some useful results of di-electric and pyrocurrent measurements.[20] In contrast to DyMnO , the magnetic ordering temper-ature in EDMO is decreased because of the fact thatthe magnetic Dy ions are diluted by the non magneticEu ions.[21] C. De, S. Ghara and A. Sundaresan, Effect of internalelectric field on ferroelectric polarization in multiferroicTbMnO , Solid State Commun. , 61 (2015).[22] J. Hemberger, F. Schrettle, A. Pimenov, P. Lunken- heimer, V. Yu. Ivanov, A. A. Mukhin, A. M. Balbashov,and A. Loidl, Multiferroic phases of Eu − x Y x MnO ,Phys. Rev. B , 035118 (2007).[23] N Abe, K Taniguchi, H Umetsu, S Ohtani, and T Arima,Control of the polarization flop direction in multiferroic R MnO ( R = Tb, Dy) by a tilted magnetic field, JPCS , 012001 (2010).[24] M. Mochizuki and N. Furukawa, Microscopic model andphase diagrams of the multiferroic perovskite mangan-ites, Phys. Rev. B , 134416 (2009).[25] X. Zhang, Y. G. Zhao, Y. F. Cui, L. D. Ye, D. Y. Zhao,P. S. Li, J. W. Wang, M. H. Zhu, H. Y. Zhang andG. H. Rao, Investigation on the pyroelectric property ofpolycrystalline GdMnO , App. Phys. Lett. , 062903(2014).[26] T. Kimura, T. Goto, Y. Tokura, A. P. Ramirez, G.Lawes, Magnetoelectric phase diagrams of orthorhombic R MnO ( R = Gd, Tb, and Dy), Phys. Rev. B , 224425(2005)[27] H. Murakawa, Y. Onose, F. Kagawa, S. Ishiwata, Y.Kaneko, and Y. Tokura, Rotation of an Electric Polar-ization Vector by Rotating Magnetic Field in CycloidalMagnet Eu . Y . MnO , Phys. Rev. Lett. , 197207(2008).[28] F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa,Y. Kaneko, N. Furukawa, and Y. Tokura, Dynamics ofmultiferroic domain wall in spin-cycloidal ferroelectricDyMnO , Phys. Rev. Lett. , 057604 (2009).[29] N. Abe, K. Taniguchi, H. Sagayama, H. Umetsu, and T.Arima, Correlation between the mobility of domain walland polarization flop direction in a slanted magnetic fieldin the helimagnetic ferroelectrics Tb − x Dy x MnO , Phys.Rev. B , 060403 (2011).[30] N. Lee, C. Vecchini, Y. Choi, L. Chapon, A. Bombardi, P.Radaelli, and S. Cheong, Giant tunability of ferroelectricpolarization in GdMn O , Phys. Rev. Lett. , 137203(2013).[31] N. Hur, S. Park, P. A. Sharma, J. S. Ahn, S. Guha andS-W. Cheong, Electric polarization reversal and mem-ory in a multiferroic material induced by magnetic fields,Nature , 392 (2004)[32] Kouji Taniguchi, Nobuyuki Abe, Shintaro Ohtani, Hi-roshi Umetsu and Taka-hisa Arima, Ferroelectric Polar-ization Reversal by a Magnetic Field in Multiferroic Y-type Hexaferrite Ba Mg Fe O , Appl. Phys. Express , 249902 (2006)[34] K. Taniguchi, N. Abe, S. Ohtani, and T. Arima, Mag-netoelectric Memory Effect of the Nonpolar Phase withCollinear Spin Structure in Multiferroic MnWO , Phys.Rev. Lett. , 147201 (2009).[35] T. Finger, D. Senff, K. Schmalzl, W. Schmidt, L. P. Reg-nault, P. Becker, L. Bohaty, and M. Braden, Electric-fieldcontrol of the chiral magnetism of multiferroic MnWO as seen via polarized neutron diffraction, Phys. Rev. B81