Incompatible Magnetic Order in Multiferroic Hexagonal DyMnO3
C. Wehrenfennig, D. Meier, Th. Lottermoser, Th. Lonkai, J.-U. Hoffmann, N. Aliouane, D. N. Argyriou, M. Fiebig
aa r X i v : . [ c ond - m a t . s t r- e l ] M a y Incompatible Magnetic Order in Multiferroic Hexagonal DyMnO C. Wehrenfennig, D. Meier, Th. Lottermoser, Th. Lonkai, J.-U.Hoffmann, N. Aliouane, D. N. Argyriou, and M. Fiebig , ∗ HISKP, Universit¨at Bonn, Nussallee 14-16, 53115 Bonn, Germany Ganerben-Gymnasium, M¨uhlbergstraße 65, 74653 K¨unzelsau, Germany and Helmholtz-Zentrum Berlin f¨ur Materialien und Energie,Glienicker Straße 100, 14109 Berlin, Germany (Dated: Dated June 8, 2018)
Abstract
Magnetic order of the manganese and rare-earth lattices according to different symmetry representationsis observed in multiferroic hexagonal (h-) DyMnO by optical second harmonic generation and neutrondiffraction. The incompatibility reveals that the 3 d –4 f coupling in the h- R MnO system ( R = Sc, Y, In, Dy– Lu) is substantially less developed than commonly expected. As a consequence, magnetoelectric couplingeffects in this type of split-order parameter multiferroic that were previously assigned to a pronounced 3 d –4 f coupling have now to be scrutinized with respect to their origin. PACS numbers: 75.85.+t, 75.30.Et, 75.25.-j, 42.65.Ky joint-order-parameter multiferroics the mag-netic and the ferroelectric order are related to the same order parameter [3]. Although this leads tovery pronounced magnetoelectric interactions the improper spontaneous polarization is extremelysmall ( ≪ m C/cm ). In the split-order-parameter multiferroics magnetic and ferroelectric or-der emerge independently. Therefore, they display a technologically feasible proper spontaneouspolarization of 1 − m C/cm . Aside from the ambient multiferroic BiFeO [4] a split-order-parameter system at the center of intense discussion is hexagonal (h-) R MnO with R = Sc, Y, In,Dy–Lu [5]. The system displays a variety of multiferroic phases and a “giant” magnetoelectriceffect [6]. The availibility of as many as nine h- R MnO compounds is ideal for investigating therole played by magnetic 3 d –4 f interactions in the manifestation of magnetoelectric effects, a keyquestion of multiferroics research.Thus far, it is assumed that the 3 d –4 f interaction in the h- R MnO system is strong with a rigidcorrelation between the magnetic Mn + and R + order [7–11]. The Mn + – R + exchange paths areaffected by the ferroelectric distortion of the unit cell so that it is expected that, reminiscent of theorthorhombic manganites [3], the 3 d –4 f interaction has substantial impact on the magnetoelectricbehavior, including giant magnetoelectric [6] and magnetoelastic [12, 13] effects.In this Letter we show that the 3 d –4 f coupling in h- R MnO is substantially less developedthan assumed up to now. This is concluded from optical second harmonic generation (SHG) andneutron-diffraction data revealing that the Mn + spins and the Dy + spins in h-DyMnO orderaccording to different symmetry representations unless magnetization fields are present. Thishas extensive consequences for the magnetic structure and the magnetoelectric interactions in themultiferroic h- R MnO system that are discussed in detail.The h- R MnO compounds display ferroelectric ordering at T C = −
990 K, antiferromag-netic Mn + ordering at T N = −
130 K [5], and, for R = Dy–Yb, magnetic R + ordering andreordering at T N and 4 − m C/cm and directed along z . Frustration leads to a variety of triangular antiferromagneticstructures of the Mn + spins in the basal xy plane. In contrast, the R + sublattices order Ising-like along the hexagonal z axis. The possible magnetic structures of the Mn + and Dy + latticescorrespond to four one-dimensional representations [15] that are compared in Table I. An exten-2ive investigation of the magnetic R + order commenced only recently [7, 9, 14, 16] and revealedthat in h-HoMnO and h-YbMnO the Mn + and the R + ordering occurs according to the samemagnetic representation.The compound with the smallest R + ion in the h- R MnO series is h-DyMnO which wasgrown for the first time only recently [17]. The magnetic structure of the Dy + lattice was in-vestigated by resonant x-ray diffraction and magnetization measurements [14, 17]. Its magneticpoint group was found to be P cm in the interval 10 K < T < T N (“high-temperature range”). At T <
10 K (“low-temperature range”) or above a critical magnetic field applied along z it changesto P cm . In this work we focus on the determination of the complementary Mn + order, but forconfirmation the Dy + order is also verified.SHG is described by the equation P i ( w ) = e c i jk E j ( w ) E k ( w ) . An electromagnetic light field ~ E at frequency w is incident on a crystal, inducing a dipole oscillation ~ P ( w ) , which acts assource of a frequency-doubled light wave of the intensity I SHG (cid:181) | ~ P ( w ) | . The susceptibility c i jk couples incident light fields with polarizations j and k to a SHG contribution with polarization i . The magnetic and crystallographic symmetry of a compound uniquely determines the set ofnonzero components c i jk [18, 19]. In turn, observation of c i jk = samples were obtained by the floating zone technique and verified for the ab-sence of twinning and secondary phases by Laue diffraction. SHG reflection spectroscopy with120-fs laser pulses was conducted on polished z -oriented crystals in a He-operated cryostat gen-erating magnetic fields of up to 8 T [19]. Neutron diffraction in the ( h l ) plane was conducted atthe E2 beamline of the Helmholtz-Zentrum at a wavelength of 2.39 ˚A with the sample mounted ina He/ He dilution insert.In Table I the calculated selection rules identifying the magnetic structure of the Mn + andDy + lattice are listed. SHG is only sensitive to the Mn + order with c xxx and c yyy as independenttensor components [18]. Neutron diffraction can probe the magnetic moments of Mn + and Dy + .The (100) and (101) reflections lead to very clear selection rules so that we restrict the discussionto them. The contributions by the Mn + and Dy + lattice to these reflections were separated bysetting the magnetic moment of the other lattice, respectively, to zero in the computations donewith Simref 2.6 [9].We first focus on the high-temperature range and measurements at zero magnetic field. Figure 1shows the analysis of the magnetic structure of the Mn + lattice by SHG spectroscopy. Because of3he large optical absorption the SHG data on h-DyMnO cannot be taken with the standard trans-mission setup and ns laser pulses [19] — in contrast to all other h- R MnO compounds. Instead thereflected SHG signal was measured with a fs laser system. With fs laser pulses, higher-order SHGcontributions, incoherent multiphoton processes, and ultrafast nonequilibrium effects can easilyobscure any magnetically induced SHG [19, 20]. In the first step we therefore had to verify towhat extent SHG is still a feasible probe for the magnetic structure. We chose h-HoMnO forthis test since it allows us to compare transmission and reflection data. Figure 1(a) shows theSHG transmission spectrum taken at two different temperatures with a fs laser system. Aside froma minor decrease of resolution the fs laser pulses lead to the same SHG spectra as the ns laserpulses [19]. With SHG from c xxx at 50 K and from c yyy at 10 K we identify the P cm and the P cm structure, respectively, on the basis of Table I. Note that the spectral dependence is alsocharacteristic for the respective phases [21]. Figure 1(b) shows the corresponding SHG reflectionspectra. Aside from a 98% decrease of the SHG yield the result remains unchanged. Hence, the fsreflection data are well suited for identifying the magnetic phase of h- R MnO by SHG.Figures 1(c) and 1(d) show the spectral and temperature dependence of the SHG signal in h-DyMnO in a fs reflection experiment. Comparison with Fig. 1(b) and Table I clearly reveals P cm as magnetic symmetry of the Mn + lattice in the high-temperature range up to T N =
66 K.This is an utterly surprising result because P cm does not match the P cm symmetry of the Dy + lattice proposed in Ref. 14. We therefore sought additional confirmation by neutron diffraction.In Fig. 2 we show the temperature dependence of the (101) and (100) reflections of h-DyMnO .Note that while the (101) reflection is magnetically induced the (100) reflection in the high-temperature range is entirely due to crystallographic contributions — its magnetic intensity iszero. According to Table I, this is only possible if the magnetic symmetry of the Mn + lattice iseither P cm or P cm of which the latter corresponds to a ferromagnetic state which is ruled outby magnetization measurements [8, 14, 17]. Table I further shows that the magnetic symmetry ofthe Dy + lattice can only be P cm which confirms the magnetic structure proposed earlier [14].We thus conclude that three independent experimental parameters, i.e., SHG polarization, SHGspectrum, and neutron diffraction intensity, confirm P cm as magnetic symmetry of the Mn + lattice in the high-temperature range of h-DyMnO . This is in striking contrast to the known [14] P cm symmetry of the Dy + lattice which is confirmed by our neutron data. Hence, the Mn + andthe Dy + order are “incompatible” in the sense of belonging to different magnetic representations.Although it is not unusual that magnetic order is parametrized by more than one representation4t is most remarkable that this occurs in the h- R MnO system. Up to now, research on this systemwas based on the assumption that a pronounced coupling between the Mn + and R + lattices isa central mechanism in determining its magnetoelectric and multiferroic properties [6–12]. Ac-cordingly, ordering of the 3 d and 4 f lattices according to a single representation was implied to becompulsory. However, the incompatibility observed here shows that the 3 d –4 f coupling must bedistinctly less developed than commonly assumed: It competes with other effects of comparablemagnitude that can be associated to a different magnetic structure.Consequently, a variety of phenomena that were related to a pronounced 3 d –4 f coupling haveto be scrutinized. This includes the P cm → P cm reorientation of the Mn + lattice in HoMnO [5, 22], which plays a role in the emergence of a giant magnetoelectric effect [6]. Supplementary(or alternative) to Mn + –Ho + exchange the temperature dependence of the magnetic anisotropyor magnetoelastic effects [13] may be responsible for the reorientation. As another issue, R + ordering in the high-temperature range cannot be due to straightforward induction by the Mn + order since this would inevitably lead to compatible Mn + and R + order. Finally, we cannotconfirm that the Mn + order is directly determined by the size of the R + ion and, thus, by the R + –O − –Mn + bond angle [23]. If this were the case, the Mn + spins in DyMnO with thesmallest R + ion of the h- R MnO system would order according to the P cm structure alreadyobserved in HoMnO and YMnO . Likewise, it can be excluded that the unusual magnetic phasediagram and magnetoelectric properties established for HoMnO [5, 22, 24] continue towardsrare-earth h- R MnO compounds with a smaller R + radius than Ho + . These observations, too,corroborate the relative independence of the Mn + and R + lattices.In the low-temperature range and in a magnetic field applied along z the magnetic order of theDy + spins changes from P cm to P cm [14, 17]. In the following the effect of this transitionon the Mn + spins is investigated. The emerging intensity of the (100) peak in Fig. 2 reflectsthe transition of the Dy + lattice to the P cm phase in agreement with Table I. However, it alsoobscures the Mn + -related contributions so that we revert to SHG measurements for a uniqueidentification of the Mn + order.Figure 1(d) and Fig. 3(c) show that the SHG intensity is quenched in the low-temperature rangeand in a magnetic field. According to Table I this indicates a transition to either the P cm or the P cm phase. According to Figs. 3(a) and 3(b) the P cm → P cm transition passes througha state with P c symmetry for which c xxx = c yyy = P cm → P cm transitionpasses through a state with P c xxx = c yyy = R MnO with R = Er, Tm, Yb, all of which exhibit a P cm → P cm transition of the Mn + lattice in a magnetic field whereas the phase diagram of h-HoMnO ,in which this transition does not occur, is different. We conclude that in the low-temperature rangeand in a magnetic field along z the magnetic symmetry of the Mn + lattice in h-DyMnO is P cm and, thus, compatible to the magnetic symmetry of the Dy + lattice.Nevertheless this compatibility is not a compulsory indication for an enhanced 3 d –4 f exchangein the low-temperature range. P cm is a ferromagnetic point group and the observation that amagnetic field supports the transition into this state indicates that the magnetic field energy ratherthan Mn + –Dy + exchange coupling may be responsible for the P cm → P cm transition of theMn + lattice. The field is generated internally by the ferromagnetic order of the Dy + lattice andsupported externally by the applied magnetic field. Accordingly, the gray area in Fig. 3(d) doesnot show the hysteresis of a first-order transition of the Mn + lattice but rather the response ofthe Mn + lattice to the magnetizing field exerted by the Dy + lattice when it is ferromagneticallyordered.We thus observed that the magnetic order of the manganese and the rare-earth sublattices in theh- R MnO system can be incompatible from the point of view of symmetry. In h-DyMnO Mn + ordering according to the P cm symmetry and Dy + ordering according to the P cm symmetryis revealed. The incompatibility demonstrates that the 3 d –4 f interaction in the h- R MnO series isdistinctly less developed than assumed up to now. Even when the incompatibility is overcome byan internal or external magnetization field, pronounced Mn + –Dy + exchange does not have to beinvolved.As a consequence, a variety of magnetoelectric coupling effects in the h-RMnO system thatwere previously assigned to pronounced 3 d –4 f coupling have now to be scrutinized with respectto their origin. Apparently, interactions within the Mn + or R + lattices as well as separate crys-tallography, anisotropy, and frustration effects play a greater role than expected up to now. Inparticular, externally induced polarization [6] or magnetization [22] fields rather than the Mn + – R + exchange may contribute substantially to the magnetoelectric response.C.W., D.M., Th.L., and M.F. thank the DFG (SFB 608) for subsidy. D.N.A. thanks the DFGfor financial support under Contract No. AR 613/1-1.6 *] Email address: fi[email protected][2] M. Fiebig, J. Phys. D , 123 (2005).[3] S.-W. Cheong and M. Mostovoy, Nat. Mater. , 13 (2007).[4] R. 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Birss, Symmetry and Magnetism , (North Holland, Amsterdam, 1966).[19] M. Fiebig, V. V. Pavlov, and R. V. Pisarev, J. Opt. Soc. Am. B , 96 (2005).[20] B. Hillebrands, J. Phys. D: Appl. Phys. , 160301 (2008).[21] T. Iizuka-Sakano, E. Hanamura, and Y. Tanabe, J. Phys.: Condens. Matter , 3031 (2001).[22] M. Fiebig, Th. Lottermoser, and R. V. Pisarev, J. Appl. Phys. , 8194 (2003).[23] D. P. Kozlenko et al. , J. Phys.: Condens. Matter , 156228 (2007).[24] O. P. Vajk et al. , Phys. Rev. Lett. , 087601 (2005). ABLE I: Selection rules for SHG and neutron diffraction distinguishing between the four one-dimensionalsymmetry representations of the crystallographic space group P cm of h- R MnO [15].Representation G , A G , A G , B G , B Symmetry P cm P cm P cm P cm SHG c xxx = + ) c yyy = + ) (101) 17% 100% 17% 93%Neutron (100) 0 100% 0 75%(Dy + ) (101) 100% 0 2% 0 Symmetries refer to the magnetic structure of the Mn + or Dy + sublattice ; the overall sym-metry is determined by the intersection of the sublattice symmetries. Sketches of the magneticstructures of the Mn + and Dy + sublattices are given in Refs. 6 and 14. SHG selection rules werederived from Ref. 18. The neutron diffraction yield contributed by the Mn + and the Dy + order,respectively, was calculated as described in the text. The largest value obtained for each sublatticecorresponds to 100%. 8 igure , C. Wehrenfennig et al., Physical Review Letters
10 20 30 40 50 60 700 2.2 2.3 2.4 2.5 2.6 2.7 0 (cid:1) c xxx c yyy S H G i n t en s i t y Temperature (K)
DyMnO Reflection (d) (cid:2) c yyy : c xxx : (cid:1) (cid:2) c yyy : c xxx : K50 K S H G i n t en s i t y SHG energy (eV) (a)
HoMnO Transmission c yyy : c xxx : (cid:1) (cid:2) c yyy : c xxx : K50 K HoMnO S H G i n t en s i t y SHG energy (eV)
Reflection (b)
Reflection S H G i n t en s i t y SHG energy (eV)
DyMnO (c) c yyy : c xxx : (cid:1) K FIG. 1: Spectral, polarization, and temperature dependence of SHG in h- R MnO compounds. A “0” indi-cates zero SHG intensity. (a, b) SHG spectra of h-HoMnO measured in (a) transmission and (b) reflectionwith a fs laser. (c) SHG spectra of h-DyMnO measured in reflection with a fs laser. (d) Temperaturedependence of the signal in (c).
10 20 30 40 50 60 700 I n t en s i t y Temperature (K)
Figure , C. Wehrenfennig et al., Physical Review Letters
FIG. 2: Temperature dependence of the (101) and (100) reflections of h-DyMnO measured in a coolingrun on the sample from Fig. 1. The dashed line marks the offset due to crystallographic contributions. igure , C. Wehrenfennig et al., Physical Review Letters m H z (T) T e m pe r a t u r e ( K ) m H z (T) S H G i n t en s i t y P6 cm P3 P6 cm c xxx c yyy c xxx c yyy P3c P6 cm S H G (r e l . ) S H G (r e l . ) (a) (b)(c) (d) P6 cmP6 cm c yyy c xxx (c) P6 cm T N FIG. 3: Phase diagram of the magnetic Mn + order in h-DyMnO exposed to a magnetic field along z . (a,b) Sketch of the SHG tensor contributions in the course of the spin reorientation towards the (a) P cm and(b) P cm phase. (c) Exemplary field dependence of the SHG signal at 32 K measured in a field-increasingrun. (d) Phase diagram derived from measurements as in (c). Temperature-increasing and -decreasing runsyield the boundaries on the right- and left-hand side of the gray area, respectively. The boundary valuescorrespond to observation of 50% of the SHG yield of the P cm phase.phase.