ARTICLE IN PRESS
Physica B 385–386 (2006) 405–407 www.elsevier.com/locate/physb
Multiferroic behavior and two-dimensional magnetism of hexagonal manganites Seongsu Leea, Misun Kanga, Changhee Leeb, A. Hoshikawac, M. Yonemurac, T. Kamiyamac, J.-G. Parka, a
Department of Physics and Institute of Basic Science, SungKyunKwan University, Suwon 440-746, Republic of Korea b Neutron Physics Laboratory, Korea Atomic Energy Research Institute, Daejon 305-600, Republic of Korea c Institute of Materials Science, KEK, Tsukuba-shi, Ibaraki 305-0801, Japan
Abstract Hexagonal manganites are currently under intensive investigations because of their interesting multiferroic behavior. Here, we show that all the atomic positions exhibit drastic anomalies at the antiferromagnetic transition temperature, which we interpret as evidence of strong coupling between spin and lattice. This coupling, we argue, leads to further coupling to electric dipole moments. Our neutron diffraction data also show that there is strong frustration effect among Mn moments. This frustration gives rise to diffuse scattering, i.e. short-ranged spin correlations. We also discuss doping effects on the magnetic structure. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50.Ee; 77.90.+k; 61.12.Ld Keywords: Hexagonal manganites; Multiferroic compound; Neutron diffraction; Spin–lattice coupling
1. Introduction Although there are numerous systems with either ferromagnetic or ferroelectric transitions, surprisingly enough there are very few systems with both transitions in a single compound in nature. These so-called multiferroic compounds have promising applications once one can control an interplay between two order parameters of the ground states: spin moment and electric dipole moment. Recent pioneering works have shown that in fact such a control of the order parameters may be possible . Among the small class of multiferroic materials, hexagonal manganite RMnO3 is the one most intensively studied. Apart from the interesting multiferroic phenomenon, there is another interesting aspect in rare-earth hexagonal manganites: they have a natural two-dimensional structure with a triangular network, which makes
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(J.-G. Park). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.084
them an ideal system to explore the two dimensional magnetism. As regards the ferroelectric transition of hexagonal manganites, it is interesting to note that according to recent structural studies together with theoretical calculations electric polarization arises from the buckling of MnO5 polyhedra accompanied by the displacements of rare-earth ions . Below the antiferromagnetic transition near 80290 K, Mn moments are aligned on the ab plane with a 120 structure. Interestingly enough, all the known magnetic structures of hexagonal manganites without doping belong to either G1 =G3 or G2 =G4 representations . For example, YMnO3 has the magnetic structure compatible with G1 or G3 with an ordered moment of 3:3mB at 10 K, much smaller than the ionic value of 4mB . This reduction in the ordered moment is believed to be due to combined effects of geometrically frustrated triangular Mn network and strong two dimensionality of the magnetic order. The spin wave of the ordered moments is consistent with theoretical calculations based on a 2D Heisenberg model Hamiltonian according to recent inelastic neutron scattering experiments [5,6].
ARTICLE IN PRESS S. Lee et al. / Physica B 385–386 (2006) 405–407 0.308
Details of sample preparation can be found elsewhere [7,8]. We performed high resolution neutron diffraction experiments of RMnO3 (R ¼ Y, Er, and Lu) to study the temperature dependence of crystal and magnetic structure. In order to determine the magnetic structure, we made neutron powder diffraction experiments from 300 to 10 K using a neutron wavelength of l ¼ 1:835 A˚ using a high resolution powder diffractometer (HRPD) at Korea Atomic Energy Research Institute. Data were reﬁned using Fullprof program. For the study of crystal structure, we used a time-of-ﬂight diffractometer, SIRIUS, at the neutron scattering facility (KEKS) of the High Energy Accelerator Research Organization (KEK). We reﬁned the data using Rietan program.
0.306 O(1) z
2. Experimental details
0.302 O(1) x O(1) z
O(2) z O(2) x (c)
(d) (f) 0.344
In the crystal structure of hexagonal manganites, there are six formula units per unit cell and six Mn atoms are located on the z ¼ 0 and z ¼ 12 planes. Each Mn ion occupies the center of a triangular bipyrimid whose vertices are occupied by oxygen ions. According to our reﬁnement results of the data taken at KEK, all the crystal structure parameters of the hexagonal manganites show a clear anomaly at the antiferromagnetic transition temperature. For example, YMnO3 has the positions of Y(1), Y(2), O(3), and O(4) atoms moved along the positive direction of the caxis with decreasing temperatures while apical oxygens O(1) and O(2) move in the same direction on the ac plane below TN . (See Fig. 1.) This drastic temperature dependence near TN is an unmistakable piece of evidence suggesting that there is a strong coupling between lattice and Mn spin. A further interesting point is that when we calculated the electric dipole moment using nominal charge valences: Y ð3þÞ, Mn ð3þÞ, and O ð2Þ, we too found a similarly strong temperature dependence in the calculated electric dipole moment . Furthermore, we found very similar temperature dependence for the ordered moment, the induced electric dipole moment, and the difference between Mn-O3 and Mn-O4 bond distances: they all seem to follow the prediction of theoretical mean ﬁeld calculations. Therefore, this implies that through the rather strong spin-lattice coupling the spin moment is coupled to the electric dipole moment, the so-called magneto-electric effect. Finally, we note that using our structure parameters one can get theoretical estimate of electric polarization ð4:6 mC=cm2 Þ at room temperature, which fares well with the experimentally measured value of 5:5 mC=cm2 . As we noted above, rare-earth hexagonal manganites have different magnetic structures. For example, YMnO3 shows magnetic diffraction patterns that can be described in terms of G1 or G3 representations, while those of ErMnO3 can be ﬁtted using a magnetic model of either G2 or G4 representations. As there is a very small difference in the ionic radius of Y and Er, one can imagine that the
3. Data and analysis
0.272 Y(1) z Y(2) z
100 200 300 Temperature (K)
0.332 0.229 0 100 200 Temperature (K)
Fig. 1. Temperature dependence of atomic positions of Y1, Y2, Mn, O1, O2, O3, and O4 obtained for YMnO3 . 100 Φ
60 a 40
20 2.5 0 0.0 ErMnO3 Γ2
0.4 0.6 YxEr1-xMnO3 Γ1 + Γ2
1.0 YMnO3 Γ1
Fig. 2. It shows how the magnetic structure evolves with increasing Y concentrations. Inset shows the a model magnetic structure with an arbitrary angle ðFÞ between the magnetic moment and the b-axis. We have remade this ﬁgure for the beneﬁt of discussion from Fig. 8 of Ref. 8.
magnetic structures can be easily varied by external parameters. For example, one may expect that the magnetic structure of YMnO3 changes continuously to the magnetic structure of ErMnO3 with doping Er at the Y site. In fact, that is exactly what we found in our doping experiment of ðY; ErÞMnO3 . As shown in Fig. 2, the
ARTICLE IN PRESS S. Lee et al. / Physica B 385–386 (2006) 405–407
1400 ErMnO3 at 80K
Intensity (arb. units)
magnetic structure of YMnO3 evolves continuously from G1 of YMnO3 to G2 of ErMnO3 with increasing Er concentrations. It may be interesting to note that despite the gradual change in the magnetic structure the size of the ordered moment seems to remain almost unchanged. Our other doping experiments on ðY; LuÞMnO3 also showed very similar behavior of the magnetic structure and the ordered moment with doping. However, somewhat surprising results were found in our doping experiment on the Mn site. Although we could not dope more than 10% of any elements we tried, the magnetic structure is clearly seen to change to the mixed structure of G1 and G2 representations under doping at the Mn site. All these doping experiments indicate that there is so small a difference in the free energies of different magnetic structures that even tiny perturbations seem to produce some sizable effects on the magnetic structure. As one can expect from the antiferromagnetic structure, Mn moments are antiferromagnetically coupled to the nearest neighboring Mn moments. According to our investigation of YMnO3 , it has a Curie–Weiss temperature of YCW ’ 545 K, which corresponds to the exchange interaction integral of J3:8 meV between two nearest neighboring Mn moments. Because of a triangular network with such a strong antiferromagnetic interaction, Mn moments are frustrated as evidenced by a large ratio of YCW =TN . Another evidence of such frustration can be found in the neutron diffraction data. As shown in Fig. 3, all three compounds of RMnO3 exhibit strong diffuse scattering, indicative of short-ranged magnetic correlations. Using a typical Gaussian function, we obtained the total integrated intensity under the diffuse peaks are almost the same for the three compounds: 1033, 1077, and 1103 for ErMnO3 , LuMnO3 , and YMnO3 . Furthermore, we calculated the correlation length of the diffuse peaks using the Selyakov–Scherrer formula to ﬁnd that they are about ˚ These diffuse peaks show strong the same as 16 A. temperature dependence and the short-range magnetic ﬂuctuations seem to scatter off strongly acoustic phonon in the paramagnetic phase that carries thermal currents as demonstrated in our recent studies . To summarize, we have found that there is experimental evidence suggesting a coupling among spin and lattice and electric dipole moments. With the triangular network of Mn moments with strong antiferromagnetic interactions, all the hexagonal manganites show a 120 structure with strong frustration. Such a frustration produces diffuse scattering in neutron diffraction pattern that is seen in all the hexagonal manganites.
LuMnO3 at 95K
400 YMnO3 at 75K
18 2θ (degree)
Fig. 3. The magnetic diffuse scattering taken near TN for ErMnO3 , LuMnO3 , and YMnO3 after removing Bragg peaks. The lines are for Gaussian ﬁtting results. See the text.
Acknowledgments We acknowledge C.J. Fennie for useful discussion and the ﬁnancial supports by Center for Strongly Correlated Materials Research and the BAERI program of Ministry of Science and Technology.
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