Evidence for large electric polarization from collinear magnetism in TmMnO3
V. Yu. Pomjakushin, M. Kenzelmann, A. Donni, A. B. Harris, T. Nakajima, S. Mitsuda, M. Tachibana, L. Keller, J. Mesot, H. Kitazawa, E. Takayama-Muromachi
EEvidence for large electric polarization from collinear magnetismin TmMnO V. Yu. Pomjakushin , M. Kenzelmann , , A. D¨onni , A. B. Harris , T. Nakajima , S.Mitsuda , M. Tachibana , L. Keller , J. Mesot , H. Kitazawa , E. Takayama-Muromachi (1) Laboratory for Neutron Scattering,ETH Z¨urich & Paul Scherrer Institute, CH-5232 Villigen, Switzerland(2) Laboratory for Solid State Physics,ETH Z¨urich, CH-8093 Z¨urich, Switzerland(3) National Institute for Materials Science (NIMS),1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan(4)Department of Physics and Astronomy,University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA(5) Department of Physics, Faculty of Science,Tokyo University of Science, 1-3 Kagurazaka,Shinjuku-ku, Tokyo 162-8601, Japan(6) National Institute for Materials Science (NIMS),1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan (Dated: November 13, 2018) a r X i v : . [ c ond - m a t . m t r l - s c i ] J a n bstract There has been tremendous research activity in the field of magneto-electric (ME) multiferroicsafter Kimura et al. [1] showed that antiferromagnetic and ferroelectric order coexist in orthorhom-bically distorted perovskite TbMnO and are strongly coupled. It is now generally accepted thatferroelectricity in TbMnO is induced by magnetic long range order that breaks the symmetry ofthe crystal and creates a polar axis [2]. One remaining key question is whether magnetic order caninduce ferroelectric polarization that is as large as that of technologically useful materials. We showthat ferroelectricity in orthorhombic (o) TmMnO is induced by collinear magnetic order, and thatthe lower limit for its electric polarization is larger than in previously investigated orthorhombicheavy rare-earth manganites. The temperature dependence of the lattice constants provides fur-ther evidence of large spin-lattice coupling effects. Our experiments suggest that the ferroelectricpolarization in the orthorhombic perovskites with commensurate magnetic ground states couldpass the 1 µ C / cm threshold, as suggested by theory [3, 4]. PACS numbers: 75.80.+q, 75.25.+z, 77.80.-e is an example of a mul-tiferroic material where the onset of ferroelectricity is completely unrelated to the onset ofmagnetism, and probably arises from geometrical effects [5]. Orthorhombic TbMnO is anexample of a multiferroic material where ferroelectricity arises from magnetic spiral order[1, 2, 6]. Ferroelectricity from magnetic order is related to competing magnetic interactions,whose competition at low temperatures is reduced through small lattice distortions thatresult in switchable electric polarization.Magnetically induced ferroelectricity has been observed for structurally very differentmaterials, most notably in rare-earth (R) manganites RMn O [7, 8], the kagome staircasemagnet Ni V O [9], and the triangular lattice antiferromagnet RbFe(MoO ) [10]. Thissuggests that the mechanism to obtain ferroelectricity from magnetic order is quite generaland should be present in many materials. In all these materials, ferroelectric polarizationarises, at least partly, from incommensurate spiral magnetic structures that lead to polarstructures. The ME interaction in these materials is believed to be mediated by spin-orbitinteractions, and so the ferroelectric polarization is relatively small.Much larger ferroelectric polarizations were predicted for materials where ferroelectricityarises from collinear magnetic order [3, 4]. In such materials, ME coupling may be mediatedby the symmetric exchange which is larger than spin-orbit related interactions. An exam-ple is orthorhombic (o) HoMnO where ferroelectricity arises from commensurate, collinearmagnetic order [11, 12]. However, the ferroelectric polarization in o-HoMnO was observedto be much smaller than predicted [4], and arises partly from rare-earth magnetic order [11].Here, we present the case of o-TmMnO for which we observed a ferroelectric polarizationthat arises from collinear Mn magnetic order, and that is at least 15 times larger thanobserved for o-HoMnO . We provide evidence for spin-lattice coupling effects that are largerthan in other magnetically-induced ferroelectrics.TmMnO crystallizes in the space group Pnma and has room-temperature lattice pa-rameters a = 5 .
809 ˚A, b = 7 .
318 ˚A and c = 5 .
228 ˚A. A projection of the crystal structure3nto the ac plane is shown in Fig. 1. The unit cell contains four Mn ions, located at r = (0 , , . r = (0 . , . , r = (0 . , , r = (0 , . , . ions is expected to result in appreciable antifer-romagnetic superexchange interactions along the a axis through pairs of oxygen anions [13]that compete with the ferromagnetic interactions in the ac plane.Our neutron diffraction data, shown in Fig. 2, feature new Bragg peaks below T Mn N = 42 Kand demonstrate that TmMnO adopts magnetic order below T Mn N . The ordering wave-vector is Q = ( q, ,
0) where q is the modulation wave-number along the a axis. The temper-ature dependence of the magnetic neutron Bragg peaks indicates a second-order transitionat T Mn N , as shown in Fig. 3, and an anomaly at T C = 32 K indicates a further transition.These two transitions coincide with peaks in the temperature dependence of the specific heat[14]. The temperature dependence of the magnetic peaks close to Q = (0 . , ,
0) (Fig. 3c)shows that the magnetic structure is incommensurate for T C < T < T Mn N and commensuratefor T < T C . In the incommensurate phase, the ordering wave-vector is Q = ( q, ,
0) with0 . < q ≤ . T = 35 K with an amplitude only on the Mn ions givenby m = [2 . , . , exp( iφ ) 0 . µ B , where φ is the relative phase between the a and c - components. Although we cannot experimentally determine φ , it can be shown thatbecause of the inversion center of the paramagnetic phase, exp( iφ ) = ± ions in the incommensurate phase. Thus the spins areamplitude modulated with moments collinear at an angle to the a axis, as shown in Fig. 1a.This is slightly different from the incommensurate order in HoMnO that is collinear [12].The commensurate structure at T = 2 K is described by two-dimensional order parameteras specified in Methods. The magnetic order is a E-type magnetic structure shown in Fig. 1b-c, with 3 . µ B magnetic moment ordered on the Mn sites along the a axis. The E-typemagnetic structure can have two independent basis vector for the moments along the a -axis: E = (1 , , − , −
1) and E = (1 , − , , −
1) in the order of the Mn ion as defined above -identical to the low-temperature Mn order in HoMnO [12]. In addition, we found thatTm has an ordered moment of 1 . µ B pointing along the c axis at 2 K. Because theTm moments are allowed only along the b -axis if they were magnetically polarized by theMn order, this implies that the Tm undergo independent spontaneous magnetic order,4s indicated by a peak in the specific heat at around T Tm N = 4 K [14].Fig. 4a shows that TmMnO has a macroscopic response to the onset of magnetic long-range order and develops spontaneous electric polarization P below 32 K, demonstrating thato-TmMnO has a multiferroic ground state. The observed value of P for a powder sample, P = 1500 µ C / m , is more than 15 times larger than that of o-HoMnO [11]. The value of P for a powder sample is half the intrinsic value for a single crystal, namely P = 0 . µ C / cm .Since we have not observed the saturation of P ( E ), as shown in the inset of Fig. 4a, P maybe substantially higher and our observation is a lower limit of the intrinsic polarization. Thereported electric polarization in o-HoMnO was much smaller, so our results suggest thatsample quality or the details of the crystal structure are decisive for the size of the electricpolarization in the orthorhombic rare earth manganites. The experimentally observed po-larization (which is merely a lower limit for the intrinsic electric polarization) is the highestobserved value for magnetically induced ferroelectricity to date, and is of the same orderas the values P = 0 . − µ C / cm [3] and 6 µ C / cm [4] predicted (but not observed)for HoMnO . This provides strong experimental evidence that the theoretically predictedmechanism of symmetric exchange, although not universal to all o-RMnO systems, doesapply in the case of TmMnO and can give rise to magnetically-induced ferroelectricity thatis large enough for applications.From the magnetic structures shown in Fig. 1 we propose a likely scenario for the magneticexchange interactions in TmMnO . These structures suggest that the interactions betweensecond neighbors are ferromagnetic along the c axis and are antiferromagnetic along the a and b axes. In the commensurate phase (for T < T C ) the distortion of the nearest neighborbonds is such that the straighter bonds have an interaction that is less ferromagnetic (ormore antiferromagnetic) than the bent bonds, thus removing the frustration that wouldoccur in the absence of the distortion. For T C < T , when the bonds are undistorted, thefrustration is removed by the incommensurate structure of Fig. 1a.The magnetic order is never strictly long-range, because magnetic Bragg peaks werefound to be always wider than the resolution-limited nuclear Bragg peaks. Fig. 3d showsthat the magnetic correlation length does never exceed 600 nm, and most probably arisesfrom ferroelectric domains. Picozzi et. al. [4] showed that ferroelectric polarization inHoMnO is generated mostly through movements of the Mn and O − positions, so themagnetic structure E and E (shown in Fig. 1) favor opposite ferroelectric polarization,5s can be seen from the phenomenological formula P ∝ ( E − E ). Thus the magneticstructure E and E must be separated by a magnetic domain walls, limiting the magneticcorrelation length to the size of the ferroelectric domains. Our measurements thus suggestthat the magnetic domains can be controlled by electric fields.The temperature dependence of the real part of the dielectric susceptibility, shown inFig. 4c provides evidence for the ferroelectric transition at T C = 32 K, in agreement withthe pyroelectric measurements. The imaginary part of the dielectric constant, shown inFig. 4d, shows a two-peak feature as a function of temperature, and relatively high valuesbetween T Tm N = 4 K and T C = 32 K that suggest substantial energy dissipation. The energydissipation in this temperature range may result from slow switching behavior associatedwith the magnetically polarized Tm magnetic moments that are only loosely coupled tothe rapidly switching Mn . Below T Tm N = 4 K, the Tm moments are spontaneouslyordered and therefore not directly connected to the electric order, so that dielectric constantshows no dissipation, as shown in Fig. 4d. This scenario is also consistent with a flatteningoff of the electric polarization stops below T Tm N = 4 K, suggesting that the Tm ordercompetes with the Mn order and thereby limits the size of the electric polarization.Independent evidence for strong coupling between the chemical and magnetic lattice isalso seen in the temperature dependence of the lattice constants, shown in Fig. 5. Thesespin-lattice effects are larger than in any other heavy rare-earth o-RMnO , suggesting thatthe magnetic order has a stronger effect on the chemical lattice of o-TmMnO than in otherheavy rare-earth manganites. Our results can be understood phenomenologically as follows.Because the incommensurate magnetic order is described by only a single one-dimensionalorder parameter, there can be no magnetically-induced ferroelectricity in accordance withour experiment [15]. In the commensurate phase the ME interaction is of the form given inRef. 3. However, the fourth order terms in the magnetic free energy cause either E · E = 0or | E | = | E | , depending on the sign of the fourth order spin anisotropy[16]. Thus the higherorder ME interaction in Ref. 3 is generally inoperative and the polarization is restricted tolie along the c axis with magnitude P c ∝ ( E − E ), where E E = 0 is selected. Thetemperature dependence of P is only qualitatively consistent with this, possibly because theresults are somewhat modified by the sample not being a single crystal.In summary, we have shown that TmMnO has a magnetically-induced electric polar-ization that is substantially higher than in any other heavy rare-earth manganites with6ommensurate magnetic order. We observed anomalies in the temperature dependence ofthe lattice constants at the magnetic phase transitions that are evidence for strong couplingeffects between the chemical and magnetic lattices. Theoretical calculations have predicteda large spontaneous electric polarization in HoMnO , at variance with current experimentalresults [4]. Since we have found such a large polarization in TmMnO , it is of great interestto have such calculations made for this system and hopefully to understand the differencebetween HoMnO and TmMnO .We acknowledge valuable discussions with R. A. Cowley, N. A. Spaldin, and D. Khomskii.This work was supported by the Swiss NSF (Contract No. PP002-102831). This work isbased on experiments performed at the Swiss spallation neutron source SINQ, Paul ScherrerInstitute. Methods
Polycrystalline samples of perovskite TmMnO were prepared under high pressure asdescribed in Ref. 14. Neutron powder diffraction measurements were performed on a largeamount (5 . sample using the HRPT and DMC diffractometers at thePaul Scherrer Institute, and incident neutrons with a wave-length of 1 .
89 ˚A and 4 . . covered with an area 3 . · − m of silver epoxy. The samplewas cooled from 50 K to 2 K in poling electric fields of up to E = 3750 kV / m, after whichthe electric field was reduced to zero and the sample was allowed to discharge for 5 minutes.After the discharge at 2 K the residual current was reduced to 10 − A, which suggests thattrapped charges did not affect the pyroelectric measurement. Then the sample was heatedat different constant rates between 0 .
85 and 4 .
86 K / min and the pyroelectric current wasmeasured using a Keithley 6517A electrometer, resulting an nearly identical estimates of theferroelectric polarization. Pyroelectric measurements at different ramping speeds and a stop-and-go ramp result in a nearly identical temperature dependent electric polarization, showing7he thermal excitation of trapped charges does not affect the pyroelectric measurements.These measurements therefore allow the determination of the lower limit of the electricpolarization. Real and imaginary part of the dielectric constant were measured using aAgilent E4980A LCR meter, making sure that the Maxwell-Wagner effect does not affect themeasurements. The magnetic susceptibility was measured in an external field H = 100 Oeon a small (5 . , wherethe superscript corresponds to Kovalev’s notation [18], and is defined by the following char-acters: χ ( I ) = 1, χ (2 a ) = − α , χ ( m ab ) = − α and χ ( m ac ) = 1, with α = exp( iπq ). Here2 a is a two-fold screw axis rotation, while m ab and m ac are ab / ac -mirror planes followedby a (0 . , , .
5) or (0 , . ,
0) lattice translation, respectively. The commensurate structureat T = 2 K is described by the two-dimensional irreducible representation Γ accordingto Kovalev’s notation and defined by the following non-zero characters: χ ( I ) = 2 and χ ( m ac ) = − [1] Kimura, T. et al. Magnetic control of ferroelectric polarization.
Nature , 55 (2003).[2] Kenzelmann, M. et al.
Magnetic inversion symmetry breaking and ferroelectricity in TbMnO . Phys. Rev. Lett. , 087206 (2005).[3] Sergienko, I. A., Sen, C. & Dagotto, E. Ferroelectricity in the magnetic e-phase of orthorhom-bic perovskites. Phys. Rev. Lett. , 227204 (2006).[4] Picozzi, S. et al. Dual nature of improper ferroelectricity in a magnetoelectric multiferroic.
Phys. Rev. Lett. , 227201 (2007).[5] Van Aken, B. B., Palstra, T. T. M., Filippetti, A. & Spaldin, N. A. The origin of ferroelectricityin magnetoelectric YMnO . Nature Materials
164 (2004).[6] Mostovoy, M. Ferroelectricity in spiral magnets.
Phys. Rev. Lett. , 067601 (2006).[7] Hur, N. et al. Electric polarization reversal and memory in a multiferroic material induced bymagnetic fields.
Nature , 392 (2004).[8] Harris, A. B. , Aharony, A. & Entin-Wohlman, O. Order parameters and phase diagrams ofmultiferroics.
J. Phys. Condens. Mat. , 434202 (2008).[9] Lawes, G. et al. Ferroelectricity through Magnetic Inversion Symmetry Breaking on a Kagome taircase. Phys. Rev. Lett. , 087205 (2005).[10] Kenzelmann, M. et al. Direct transition from a disordered phase to an incommensurate mul-tiferroic on a triangular lattice.
Phys. Rev. Lett. , 267205 (2007).[11] Lorenz, B., Wang, Y. Q., Chu, C. W., Ferroelectricity in perovskite HoMnO and YMnO . Phys. Rev. B , 104405 (2007).[12] Munoz, A. et al. Complex magnetism and magnetic structures of the metastable HoMnO perovskite. Inorg. Chem. , 1020 (2001).[13] Kimura, T., Ishihara, S., Shintani, H., Arima, T., Takahashi, K. T., Ishizaka, K. & Tokura,Y. Distorted perovskite with e configuration as a frustrated spin system. Phys. Rev. B ,060403(R) (2003).[14] Tachibana, M., Shimoyama, T., Kawaji, H., Atake, T. & Takayama-Muromachi, E. Jahn-Teller distortion and magnetic transitions in perovskite RMnO (R=Ho, Er, Tm, Yb, andLu). Phys. Rev. B , 144425 (2007).[15] Harris, A. B. Landau analysis of the symmetry of the magnetic structure and magnetoelectricinteraction in multiferroics. Phys. Rev. B , 054447 (2007).[16] Harris, A. B., Aharony, A. & Entin-Wohlman, O. Order parameters and phase diagram ofmultiferroic RMn O . Phys. Rev. Lett.
The FullProf Suite
Representations of the Crystallographic Space Groups , edited by H. T. Stokes& D M. Hatch, Gordon and Breach, London (1993). IG. 1: Chemical structure of TmMnO , showing Mn in red and O − in blue. (a) Incommen-surate amplitude-modulated Mn spin order in the paraelectric phase for 32 K < T <
40 K.(b-c) Commensurate Mn spin order of E and E type, respectively, in the ferroelectric phasefor T (cid:28)
32 K. The large arrows show the direction of the spontaneous polarization along the c axis that arises from a movement of the Mn and O − positions (shown here schematically) toadjust the Mn-O-Mn angle for parallel and antiparallel nearest-neighbor alignment, thereby lower-ing symmetry through the creation of a polar axis. (a-c) The moments in the neighboring planesare oriented in the opposite direction. Q
20 40 60 80 100 I n t en s i t y ( a r b . un t s ) -202468101214 Q
20 40 60 80 100 I n t en s i t y ( a r b . un t s ) Q
40 60 80 100 I n t en s i t y ( a r b . un t s ) Q
40 60 80 100 I n t en s i t y ( a r b . un t s ) (a)(b) (c)(d) FIG. 2: Part of the neutron scattering patterns measured using HRPT, as a function of scatteringangle 2Θ at (a) T = 50 K showing only nuclear scattering, and (b) T = 2 K showing additionallymagnetic scattering. (c-d) Bragg peak powder patterns measured using DMC at T = 35 K and T = 2 K. (a-d) The vertical bars indicate magnetic and nuclear (upper row) Bragg peaks. Thebottom solid line indicates the difference between the experiment and the model. (K) I n t en s i t y ( a r b . un i t s ) T (K) c o rr . l eng t h ( n m ) T (K) h (r . l . u . ) Q = (0.5,1,0) Q = (h,1,0), h=0.5 T (K) I n t en s i t y ( a r b . un i t s ) Q = (h,1,0) Q = (1+h,0,1) Q = (h,1,1) HRPTTmMnO (a) (b)(c) (d) Q = (h,1,0), h=0.5 Q = (0.5,1,0) Int 50 • FIG. 3: (a) Temperature dependence of the magnetic Bragg peak intensity at Q = (0 . , ,
0) in thecommensurate phase, or the added intensities at the Q = ( q, ,
0) and Q = (1 − q, ,
0) Bragg peakpositions for 0 . < q ≤ .
5. (b) Comparison of the temperature dependence of different magneticBragg peaks, showing that they have the same temperature dependence in the commensuratephase. The Q = (1 . , ,
1) Bragg peak is only present in the commensurate phase, and is evidenceof the ordering of Tm magnetic moments. (c) Temperature dependence of the a-component, h ,of the magnetic Bragg peak Q = ( h, , h = q or h = 1 − q . (d) Temperature dependenceof the magnetic correlation length as deduced from the width of the magnetic Bragg peaks. (K) P o l a r i z a t i on ( m C / m ) T (K) d i e l e c t r i c e '' T (K) d i e l e c t r i c e ' T (K) c ( e m u / m o l ) polycrystallineTmMnO (a) (b)(c) (d) E (V/mm) P ( m C / m ) T (K) d c / d T -0.08-0.06-0.04-0.020.00 T N FIG. 4: (a) Electric polarization of a pressed powder sample of o-TmMnO as a function of tem-perature, determined using pyroelectric measurements after cooling an electrically poled sample.Inset: Electric polarization at T = 2 K as a function of poling electric field with which the samplewas cooled. (b) Magnetic susceptibility as a function of temperature measured on cooling. Inset:Temperature derivative of the magnetic susceptibility indicating the onset of spontaneous Tm magnetic order at T Tm N = 4 K. (c) Real and (d) imaginary part of the dielectric susceptibility as afunction of temperature, measured at a frequency of f = 100 kHz. (K) a ( A ) T (K) b ( A ) T (K) c ( A ) T (K) V ( A ) b ( A ) T (K) V ( A ) T (K) a ( A ) T (K) c ( A ) (a) (b)(c) (d) FIG. 5: Temperature dependence of the lattice constants for
T <
50 K. The insets show additionaltransitions below 4 K. The vertical dotted lines at T Mn N and T C indicate magnetic transitions,while the vertical dotted line at T Tm N = 4 K indicates the onset of spontaneous Tm magneticorder.magneticorder.