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Synchrotron X-ray powder diffraction and convergent beam electron diffraction studies on the cubic phase of MgV2O4 spinel
Journal of Solid State Chemistry 215 (2014) 184–188
Contents lists available at ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Synchrotron X-ray powder diffraction and convergent beam electron diffraction studies on the cubic phase of MgV2O4 spinel Seiji Niitaka a,n, Soyeon Lee b, Yoshifumi Oshima c, Kenichi Kato d, Daisuke Hashizume e, Masaki Takata d, Hidenori Takagi a a
RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan c Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, Osaka, Ibaraki 567-0047, Japan d RIKEN SPring-8 Center, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan e RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2014 Received in revised form 24 March 2014 Accepted 27 March 2014 Available online 8 April 2014
The A V2O4 (A ¼Mg2 þ , Zn2 þ , Cd2 þ ) spinels are three-dimensional spin-1 frustrated systems with orbital degree of freedom, which have been known to possess intriguing orbital states causing releases of spin frustration at low temperatures. We have performed synchrotron X-ray and convergent beam electron diffraction measurements for one of these vanadates, MgV2O4 in order to clarify its crystal structure in the high temperature cubic phase, which is regarded as an important starting point for understanding the details of the low temperature phase. We have successfully observed that the [001] zone axis convergent beam electron diffraction pattern exhibits 4mm symmetry, suggesting the space group of Fd3m in the cubic MgV2O4. It has also been demonstrated that the crystal structure of the cubic MgV2O4 contains VO6 octahedra elongated along the threefold rotation axis. Based on our results, we discuss the orbital states of MgV2O4 as well as the other spinel vanadates. & 2014 Elsevier Inc. All rights reserved.
Keywords: MgV2O4 Spinel Crystal structure analysis Synchrotron X-ray diffraction Convergent beam electron diffraction
1. Introduction Geometrically frustrated magnetic systems have attracted a great deal of interest in condensed-matter science. The geometrical frustration causes macroscopic degeneracies of the ground-state manifold, leading to suppression of simple long-range spin ordering and alternative nontrivial magnetic phenomena. For instance, LiV2O4 [1], FeSc2S4 [2], and Ba3CuSb2O9 [3] exhibit spin liquid states down to the lowest temperatures measured and partially disordered antiferromagnetic (AFM) orderings occur in GeNi2O4 [4] and Ca3CoRhO6 [5]. When the spin sector in the frustrated system links closely with another sector such as an orbital degree of freedom or the crystal lattice, the system can lift the degeneracies by means of orbital ordering and/or lattice distortion, resulting in elaborate orderings of multiple degrees of freedom, which can result in useful functional materials such as multiferroics in some situations [6]. Understanding of the intriguing mechanisms of such degeneracy lifting, i.e., releases of spin frustration, can be greatly enhanced from the correct determination of crystallographic symmetry as well as precise atomic positions. As a good model material for systems where the geometrical frustration is entangled intimately with the orbital sector, trivalent
n
Corresponding author. E-mail address: [email protected] (S. Niitaka).
http://dx.doi.org/10.1016/j.jssc.2014.03.037 0022-4596/& 2014 Elsevier Inc. All rights reserved.
vanadium spinel oxides A V2O4 (A¼ Mg2 þ , Zn2 þ , Cd2 þ ) have been of particular interest [7]. A V2O4 (A¼Mg2 þ , Zn2 þ , Cd2 þ ) which adopt the cubic normal spinel structure at room temperature are Mott insulators with V3 þ ions coordinated octahedrally by six oxygens as shown in Fig. 1(a), resulting in their t 22g electron configuration. As shown in Fig. 1(b), the sublattice of the magnetic vanadium ions constitutes a three-dimensional (3D) network of corner-sharing regular tetrahedra called the pyrochlore lattice, giving rise to geometrical frustration. Therefore these vanadium spinel oxides can be regarded as 3D spin frustrated systems consisting of spin-1 with orbital degree of freedom in the t 2g orbitals. Previous investigations of these systems have revealed that they all exhibit similar structural and magnetic behaviors characterized by two successive phase transitions: an initial cubicto-tetragonal structural phase transition with contraction along the c-axis and subsequently AFM ordering with decreasing temperature [8–10]. Their AFM structures were found to be quite simple collinear ones with staggered AFM chains in the c-planes as observed in ordinary non-frustrated AFM compounds regardless of the expected spin frustration [11–13]. This simple AFM ordering together with the contradiction between the observed c-axis contraction and the expected exchange distortion of expansion along the c-axis for the ordering strongly suggests that the releases of spin frustration in these vanadates occur due to the changes of their orbital states through the structural transitions.
S. Niitaka et al. / Journal of Solid State Chemistry 215 (2014) 184–188
185
0.0034
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0.0036
M/H (emu/mol)
0.0034
0.0032
powder H=1T
0.0032 0.0030 0.0028 0.0026
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100
150
200
250
T (K)
0.0030
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MgV2O4 single crystal H=1T
0.0026
50
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150 200 Temperature (K)
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Fig. 2. Magnetic susceptibility of a MgV2O4 single crystal as a function of temperature with applied magnetic field of 1 T parallel to the [111] direction. The inset represents the temperature dependence of the magnetic susceptibility of a MgV2O4 powder sample under an applied magnetic field of 1 T, which was used in this investigation.
Fig. 1. (a) Crystal structure of spinel MgV2O4 at room temperature. The octahedra and tetrahedra represent VO6 and MgO4 polyhedra, respectively. Each VO6 octahedron connects with six others by edge-sharing. (b) V sublattice in the spinel structure, corresponding to a pyrochlore lattice.
This fact has stimulated many theoretical proposals on their orbital states relating closely to the release of spin frustration in the low temperature tetragonal (LTT) phase [14–18]. Needless to say, the crystal structure analysis of the LTT phases to reveal the orbital states of these materials is important for the elucidation of the mechanism to release their spin frustration, which has been reported in our recent article [19]; however, the crystal structure analysis of their high-temperature cubic (HTC) phases is also essential to a fundamental understanding of these systems because the crystal structure in the HTC phase is a starting point for the modulation to that in the LTT phase. From this viewpoint, in order to clarify the crystal structure of the HTC phase in one of the targeted vanadates, MgV2O4, precisely, we performed powder synchrotron X-ray diffraction (SXRD) and convergent beam electron diffraction (CBED) measurements. In this paper, we report the results for MgV2O4 and discuss the details of its orbital state in the HTC phase.
2. Experimental The polycrystalline MgV2O4 sample for powder SXRD measurements was synthesized by solid state reaction of MgO and V2O3.
Single crystals of MgV2O4 for the CBED measurements were prepared via the chemical vapor transport method [19]. We characterized our crystals using magnetization measurements. Fig. 2 shows the temperature dependence of the magnetic susceptibility of the as-grown single crystal measured under an applied magnetic field of 1 T with a SQUID magnetometer. The susceptibility undergoes a sharp drop at 62 K and followed by a small hump at 40 K, which corresponds well with those of MgV2O4 powder samples reported in Ref. [8] and also synthesized for our study as shown in the inset of Fig. 2. This demonstrated that the single crystal was of a quality high enough to be used for our study. The former and latter anomalies in the magnetic susceptibility reflect the cubic-to-tetragonal structural phase transition and the AFM ordering, respectively. CBED patterns were measured at room temperature with the incident beam along the [100] direction of the cubic spinel structure. Thin specimens for CBED experiments were prepared by crushing the single crystal of MgV2O4. Powder SXRD measurements were carried out on beam line BL02B02 at SPring-8. The diffraction data were collected using the powder sample sealed in a glass capillary (0.3 mm int. diam.) with a large Debye–Scherrer camera at 100 K in the HTC phase. The wavelength of the incident synchrotron X-ray beam was 0.5410 Å [20]. The structural parameters were refined by the Rietveld analysis of the powder diffraction data using RIETAN-FP [21].
3. Results and discussion First we show the result of the CBED measurement on the HTC phase of MgV2O4. Fig. 3(a) and (b) shows the [001] zone axis CBED pattern taken at an accelerating voltage of 80 keV and the enlarged view around the bright-field pattern, respectively. We can see that the zeroth-order Laue zone diffraction pattern shown in Fig. 3(b) and also the first-order Laue zone pattern emerging as a ring in Fig. 3(a) exhibit 4mm symmetry. Now let us consider the symmetries of the [001] zone axis CBED whole pattern (WP) in the cases of the space group Fd3m for the normal spinel structure and its three cubic subgroups of F43m (suggested as the space group of cubic MgV2O4 by Ref. [22]), F4132, and Fd3. Since the
S. Niitaka et al. / Journal of Solid State Chemistry 215 (2014) 184–188
Intensity (arb.unit)
3x10
MgV2O4, Measured temperature : 100 K, λ=0.5410 A
5
Intensity (arb.unit)
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12000 8000 4000 0
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60 64 2θ (degrees)
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0 5
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35 40 45 2θ (degrees)
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Fig. 4. Observed (cross) and calculated (solid line) diffraction patterns from the Rietveld analysis of the powder SXRD data for the HTC phase of MgV2O4 at 100 K. Tick marks represent the positions of allowed Bragg reflections for the space group Fd3m. The difference line, observed minus calculated, is located at the bottom of the figure. The inset shows the enlarged view of the patterns in the high 2θ region. In the Rietveld refinement, the intensity data in the narrow 2θ ranges around 8.511, 11.501, 12.581, 14.261, 17.081, and 18.421 were not used, where tiny diffraction peaks from the impurity phase of V2O3 appear. However, their ranges did not overlap with any diffraction peaks from MgV2O4, showing that this matter caused no problems for our analysis. Table 1 Lattice constant, fractional coordinates of ions and their isotropic atomic displacement parameters in MgV2O4 at 100 K from the Rietveld refinements of the powder SXRD patterns. The goodness-of-fit indicator for the refinement was 1.35.
Fig. 3. (a) The CBED pattern along the [001] zone axis for room-temperature cubic MgV2O4 and (b) the magnified view of the zeroth-order Laue zone disks.
crystallographic point groups of Fd3m, F43m, F4132, and Fd3 are m3m, 43m, 432, and m3, the expected symmetries of the WP correspond to 4 mm, 2 mm, 4, and 2 mm, respectively [23]. Therefore our result suggests that the space group of the HTC phase in MgV2O4 is Fd3m without any symmetry breaking from the normal spinel structure. This suggestion accords with the consequence of our recent observation of the Gjønnes–Moodie lines across the center of the disks for the 200 reflections [19]. Next let us turn to the result of the powder SXRD measurement. Fig. 4 shows the SXRD pattern of the polycrystalline MgV2O4 sample collected at 100 K in the HTC phase together with the result of the Rietveld refinement using a cubic normal spinel structure with the space group Fd3m. The refinement gave a good fit with the final reliability factors of Rwp ¼ 2:353%, Rp ¼ 1:645%, and Re ¼ 1:739%. We also performed the Rietveld refinement in consideration of cation inversion, acquiring no better fit. This result suggests no anti-site disorder in the sample. The refined structural parameters of the HTC phase of MgV2O4 at 100 K are listed in Table 1. We would like to emphasize here that the 200 reflection was not observed in the SXRD pattern, which is forbidden due to diamond-glide planes in Fd3m and by contrast allowed for F43m. We calculated the hypothetical powder diffraction pattern of MgV2O4 with the crystallographic symmetry of F43m for the same experimental conditions as our SXRD measurement, using the lattice constant and the atomic displacement
MgV2O4 100 K Fd3m a ¼8.4021(7) Å. Atom Site x y
z
B (Å2)
Mg V O
1/8 1/2 0.26024(2)
0.260(5) 0.181(2) 0.268(6)
8a 16d 32e
1/8 1/2 0.26024(2)
1/8 1/2 0.26024(2)
parameters from our results for the data at 100 K listed in Table 1 and using the atomic coordinates of Mg, V, and O ions from Ref. [22]. Our calculation indicated that the intensity of the 200 reflection was about four times as large as the observed variability of the background at its position, meaning that the 200 reflection should be clearly observed in our measurement at 100 K as a peak with the sufficiently large intensity relative to the background in this assumed case. This adds weight to our conclusion that the HTC phase of MgV2O4 has the crystallographic symmetry of Fd3m. The discrepancy in the space group of the HTC phase between Ref. [22] and our result might be due to the difference in the sample preparation. Further investigation is required in order to determine the cause of this discrepancy. Fig. 5 shows a schematic illustration of the VO6 octahedron in the HTC phase of MgV2O4 at 100 K using the structural parameters in Table 1. All of the V–O bonds in the octahedron have a length of 2.016 Å. With this bond distance, the bond-valence sum calculation [24] gave a valence of 2.852þ for the V ions, which is in good agreement with their formal valence of 3 þ in insulating MgV2O4. Meanwhile two kinds of O–O bonds exist with lengths of 2.728 and 2.976 Å, resulting in the elongated VO6 octahedron along the three-fold axis. This is ascribed to the larger spinel u-parameter showing the position of the oxygen ions in a spinel structure than 0.25 in the case of ideal cubic close packing of the anion sublattice. The angle between the three-fold axis and the V–O direction is 51.291, which is smaller than 54.741 for a regular octahedron. Now let us discuss the orbital state in the HTC phase of MgV2O4. First, the main contribution to the crystal field of the octahedron is of cubic symmetry, splitting the V 3d manifold into the lower lying t 2g and the higher lying eg states with a large energy difference of 2–3 eV. Additionally, the trigonal crystal field from the elongation distortion revealed in our study lifts the
S. Niitaka et al. / Journal of Solid State Chemistry 215 (2014) 184–188
V O
187
the LTT phases of A V2O4 (A¼Mg2 þ , Zn2 þ , Cd2 þ ) but also the relationship between them and the crystal structures in their HTC phases are interesting future subjects for detailed research.
4. Conclusion
O-O bonds 2.728Å 2.976Å Fig. 5. Schematic view of the VO6 octahedron at 100 K in the HTC phase, which was elucidated by the Rietveld refinement. The small and large circles represent vanadium and oxygen ions, respectively. The solid and dashed lines indicate the short and long bonds connecting between oxygen ions with the length of 2.728 and 2.976 Å, respectively. The octahedron was found to be elongated in the direction of its three-fold rotation axis.
degeneracy of the t 2g states, resulting in the further split into a single a1g and a doublet e0g . Note here that it is difficult to determine even the relative order of the a1g and e0g orbitals from only the results of the crystal structure analysis because the eg –e0g hybridization has the opposite effect on the a1g –e0g splitting to the crystal field effect [25] and another factors such as the kinetic energy depending heavily on the crystal structure can also have significant effects [26]. The quantitative evolution of the splitting remains to be solved, for which the information on the crystal structure of MgV2O4 obtained in our study could be of great benefit. Regardless of the a1g –e0g relative order, we can note the following two points. Firstly, the spatial distribution of the two 3d electrons under the trigonal crystal field is still isotropic in spite of the degeneracy lifting of the t 2g states, which results in the equivalent exchange interactions between the spins on the nearest neighboring V ions, inducing geometrical spin frustration. Secondly, and more importantly, their orbital moments are somewhat reduced compared with those in the case of the degenerate t 2g states. Hence the release of spin frustration in MgV2O4 by means of the orbital degree of freedom actually occurs with the orbital state in the HTC phase as a starting point, which could have an important effect on the nature of the resulting orbital state in the LTT phase. As for the other vanadates, ZnV2O4 and CdV2O4, the lattice parameters and positions of oxygen ions in A V2O4 (A¼ Mg2 þ , Zn2 þ , Cd2 þ ) should significantly depend on the radii of the nonmagnetic ions for the following reason based on the structural character of spinels. The larger radii of the A ion induce a longer A–O bond, resulting in a larger spinel u-parameter. In the consequently more elongated VO6 octahedron, the shorter O–O bonds create stronger Coulomb repulsion between the oxygen ions, bringing about the larger lattice constant. We can therefore expect that these vanadates have different a1g –e0g splittings under the respective trigonal crystal fields of the VO6 octahedra. As mentioned in the introduction, various orbital models for the LTT phases have been theoretically proposed, including one in which the spin–orbit coupling plays an important role. This theoretical situation could suggest that the proposed models have almost the same intrinsic energies in the actual materials and that which model emerges as the ground state depends on subtle differences in some properties of materials, in which the a1g –e0g splitting in the HTC phases is highly likely included. So A V2O4 (A ¼Mg2 þ , Zn2 þ , Cd2 þ ) might have the different orbital states in their LTT phases although they show similar structural and magnetic properties. The comprehensive understanding of not only the orbital states in
We have reported the results of the powder SXRD and CBED measurements for the HTC MgV2O4 which exhibits the release of spin frustration by means of an orbital degree of freedom in the LTT phase. The WP symmetry of the CBED taken at the [001] incidence was found to be 4 mm which was consistent only with the space group Fd3m among the space group for a cubic normal spinel structure and its cubic subgroups. The Rietveld refinement of the SXRD data of MgV2O4 at 100 K using a normal spinel structure with the space group of Fd3m was also successful. These results strongly support that the space group of the HTC phase of MgV2O4 is Fd3m, which was indicated by the observation of the Gjønnes–Moodie lines [19]. The refined structural parameters indicates that the VO6 octahedron in the HTC phase is stretched along its three-fold rotation axis, inducing a trigonal crystal field for the V cation. This additional field causes the splitting of its t 2g orbitals into the a1g and the e0g states, state, reducing the orbital moment of the V3 þ ion. This could influence the orbital state in the LTT phase of MgV2O4, taking into account many theoretical suggestions for the orbital model.
Acknowledgments We are grateful to Y. Motome for valuable discussions. This work was financially supported by Grant-in-Aid for Young Scientists (B) (No. 18760022). The synchrotron radiation experiments were performed on BL02B2 at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2007B1524).
Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version, at http://dx.doi.org/10.1016/j.jssc.2014.03.037. These data include MOL file and InChiKeys of the most important compounds described in this article. References [1] Y. Shimizu, H. Takeda, M. Tanaka, M. Itoh, S. Niitaka, H. Takagi, Nat. Commun. 3 (2012) 981. [2] V. Fritsch, J. Hemberger, N. Büttgen, E.-W. Scheidt, H.-A. Krug von Nidda, A. Loidl, V. Tsurkan, Phys. Rev. Lett. 92 (2004) 116401. [3] H.D. Zhou, E.S. Choi, G. Li, L. Balicas, C.S. Wiebe, Y. Qiu, J.R.D. Copley, J. S. Gardner, Phys. Rev. Lett. 106 (2011) 147204. [4] M. Matsuda, J.-H. Chung, S. Park, T.J. Sato, K. Matsuno, H. Aruga Katori, H. Takagi, K. Kakurai, K. Kamazawa, Y. Tsunoda, I. Kagomiya, C.L. Henley, S.H. Lee, Europhys. Lett. 82 (2008) 37006. [5] S. Niitaka, K. Yoshimura, K. Kosuge, M. Nishi, K. Kakurai, Phys. Rev. Lett. 87 (2001) 177202. [6] T. Kimura, Ann. Rev. Mater. Res. 37 (2007) 387. [7] H. Takagi, S. Niitaka, in: C. Lacroix, P. Mendels, F. Mila (Eds.), Introduction to Frustrated Magnetism: Materials, Experiments, Theory, Springer, Berlin, Heidelberg, 2011 (Chapter 7). [8] H. Mamiya, M. Onoda, T. Furubayashi, J. Tang, I. Nakatani, J. Appl. Phys. 81 (1997) 5289. [9] Y. Ueda, N. Fujiwara, H. Yasuoka, J. Phys. Soc. Jpn. 66 (1997) 778. [10] M. Onoda, J. Hasegawa, J. Phys.: Condens. Matter 15 (2003) L95. [11] S. Niziol, Phys. Status Solidi A 18 (1973) K11, and references therein. [12] M. Reehuis, A. Krimmel, N. Büttgen, A. Loidl, A. Prokofiev, Eur. Phys. J. B 35 (2003) 311. [13] Z. Zhang, Despina Louca, A. Visinoiu, S.-H. Lee, J.D. Thompson, T. Proffen, A. Llobet, Y. Qiu, S. Park, Y. Ueda, Phys. Rev. B 74 (2006) 014108. [14] H. Tsunetsugu, Y. Motome, Phys. Rev. B 68 (2003) 060405 (R).
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O. Tchernyshyov, Phys. Rev. Lett. 93 (2004) 157206. D.I. Khomskii, T. Mizokawa, Phys. Rev. Lett. 94 (2005) 156402. T. Maitra, R. Valentí, Phys. Rev. Lett. 99 (2007) 126401. V. Pardo, S. Blanco-Canosa, F. Rivadulla, D.I. Khomskii, D. Baldomir, Hua Wu, J. Rivas, Phys. Rev. Lett. 101 (2008) 256403. [19] S. Niitaka, H. Ohsumi, K. Sugimoto, S. Lee, Y. Oshima, K. Kato, D. Hashizume, T. Arima, M. Takata, H. Takagi, Phys. Rev. Lett. 111 (2013) 267201. [20] E. Nishibori, M. Takata, K. Kato, M. Sakata, Y. Kubota, S. Aoyagi, Y. Kuroiwa, M. Yamakata, N. Ikeda, Nucl. Instrum. Methods. Phys. Res., Sect. A 467 (2001) 1045.
[21] F. Izumi, K. Momma, Solid State Phenom. 130 (2007) 15. [22] E.M. Wheeler, B. Lake, A.T.M. Nazmul Islam, M. Reehuis, P. Steffens, T. Guidi, A.H. Hill, Phys. Rev. B 82 (2010) 140406 (R). [23] B.F. Buxton, J.A. Eades, J.W. Steeds, G.M. Rackham, Philos. Trans. R. Soc. Lond., Ser. A 281 (1976) 171. [24] N.E. Brese, M. O'Keeffe, Acta Crystallogr., Sect. B 47 (1991) 192. [25] S. Landron, M.-B. Lepetit, Phys. Rev. B 77 (2008) 125106. [26] G.R. Zhang, X.L. Zhang, T. Jia, Z. Zeng, H.Q. Lin, J. Appl. Phys. 107 (2010) 09E120.
Contents lists available at ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Synchrotron X-ray powder diffraction and convergent beam electron diffraction studies on the cubic phase of MgV2O4 spinel Seiji Niitaka a,n, Soyeon Lee b, Yoshifumi Oshima c, Kenichi Kato d, Daisuke Hashizume e, Masaki Takata d, Hidenori Takagi a a
RIKEN, 2-1, Hirosawa, Wako, Saitama 351-0198, Japan Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan c Research Center for Ultra-High Voltage Electron Microscopy, Osaka University, Osaka, Ibaraki 567-0047, Japan d RIKEN SPring-8 Center, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan e RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2014 Received in revised form 24 March 2014 Accepted 27 March 2014 Available online 8 April 2014
The A V2O4 (A ¼Mg2 þ , Zn2 þ , Cd2 þ ) spinels are three-dimensional spin-1 frustrated systems with orbital degree of freedom, which have been known to possess intriguing orbital states causing releases of spin frustration at low temperatures. We have performed synchrotron X-ray and convergent beam electron diffraction measurements for one of these vanadates, MgV2O4 in order to clarify its crystal structure in the high temperature cubic phase, which is regarded as an important starting point for understanding the details of the low temperature phase. We have successfully observed that the [001] zone axis convergent beam electron diffraction pattern exhibits 4mm symmetry, suggesting the space group of Fd3m in the cubic MgV2O4. It has also been demonstrated that the crystal structure of the cubic MgV2O4 contains VO6 octahedra elongated along the threefold rotation axis. Based on our results, we discuss the orbital states of MgV2O4 as well as the other spinel vanadates. & 2014 Elsevier Inc. All rights reserved.
Keywords: MgV2O4 Spinel Crystal structure analysis Synchrotron X-ray diffraction Convergent beam electron diffraction
1. Introduction Geometrically frustrated magnetic systems have attracted a great deal of interest in condensed-matter science. The geometrical frustration causes macroscopic degeneracies of the ground-state manifold, leading to suppression of simple long-range spin ordering and alternative nontrivial magnetic phenomena. For instance, LiV2O4 [1], FeSc2S4 [2], and Ba3CuSb2O9 [3] exhibit spin liquid states down to the lowest temperatures measured and partially disordered antiferromagnetic (AFM) orderings occur in GeNi2O4 [4] and Ca3CoRhO6 [5]. When the spin sector in the frustrated system links closely with another sector such as an orbital degree of freedom or the crystal lattice, the system can lift the degeneracies by means of orbital ordering and/or lattice distortion, resulting in elaborate orderings of multiple degrees of freedom, which can result in useful functional materials such as multiferroics in some situations [6]. Understanding of the intriguing mechanisms of such degeneracy lifting, i.e., releases of spin frustration, can be greatly enhanced from the correct determination of crystallographic symmetry as well as precise atomic positions. As a good model material for systems where the geometrical frustration is entangled intimately with the orbital sector, trivalent
n
Corresponding author. E-mail address: [email protected] (S. Niitaka).
http://dx.doi.org/10.1016/j.jssc.2014.03.037 0022-4596/& 2014 Elsevier Inc. All rights reserved.
vanadium spinel oxides A V2O4 (A¼ Mg2 þ , Zn2 þ , Cd2 þ ) have been of particular interest [7]. A V2O4 (A¼Mg2 þ , Zn2 þ , Cd2 þ ) which adopt the cubic normal spinel structure at room temperature are Mott insulators with V3 þ ions coordinated octahedrally by six oxygens as shown in Fig. 1(a), resulting in their t 22g electron configuration. As shown in Fig. 1(b), the sublattice of the magnetic vanadium ions constitutes a three-dimensional (3D) network of corner-sharing regular tetrahedra called the pyrochlore lattice, giving rise to geometrical frustration. Therefore these vanadium spinel oxides can be regarded as 3D spin frustrated systems consisting of spin-1 with orbital degree of freedom in the t 2g orbitals. Previous investigations of these systems have revealed that they all exhibit similar structural and magnetic behaviors characterized by two successive phase transitions: an initial cubicto-tetragonal structural phase transition with contraction along the c-axis and subsequently AFM ordering with decreasing temperature [8–10]. Their AFM structures were found to be quite simple collinear ones with staggered AFM chains in the c-planes as observed in ordinary non-frustrated AFM compounds regardless of the expected spin frustration [11–13]. This simple AFM ordering together with the contradiction between the observed c-axis contraction and the expected exchange distortion of expansion along the c-axis for the ordering strongly suggests that the releases of spin frustration in these vanadates occur due to the changes of their orbital states through the structural transitions.
S. Niitaka et al. / Journal of Solid State Chemistry 215 (2014) 184–188
185
0.0034
M/H (emu/mol)
0.0036
M/H (emu/mol)
0.0034
0.0032
powder H=1T
0.0032 0.0030 0.0028 0.0026
50
100
150
200
250
T (K)
0.0030
0.0028
MgV2O4 single crystal H=1T
0.0026
50
100
150 200 Temperature (K)
250
Fig. 2. Magnetic susceptibility of a MgV2O4 single crystal as a function of temperature with applied magnetic field of 1 T parallel to the [111] direction. The inset represents the temperature dependence of the magnetic susceptibility of a MgV2O4 powder sample under an applied magnetic field of 1 T, which was used in this investigation.
Fig. 1. (a) Crystal structure of spinel MgV2O4 at room temperature. The octahedra and tetrahedra represent VO6 and MgO4 polyhedra, respectively. Each VO6 octahedron connects with six others by edge-sharing. (b) V sublattice in the spinel structure, corresponding to a pyrochlore lattice.
This fact has stimulated many theoretical proposals on their orbital states relating closely to the release of spin frustration in the low temperature tetragonal (LTT) phase [14–18]. Needless to say, the crystal structure analysis of the LTT phases to reveal the orbital states of these materials is important for the elucidation of the mechanism to release their spin frustration, which has been reported in our recent article [19]; however, the crystal structure analysis of their high-temperature cubic (HTC) phases is also essential to a fundamental understanding of these systems because the crystal structure in the HTC phase is a starting point for the modulation to that in the LTT phase. From this viewpoint, in order to clarify the crystal structure of the HTC phase in one of the targeted vanadates, MgV2O4, precisely, we performed powder synchrotron X-ray diffraction (SXRD) and convergent beam electron diffraction (CBED) measurements. In this paper, we report the results for MgV2O4 and discuss the details of its orbital state in the HTC phase.
2. Experimental The polycrystalline MgV2O4 sample for powder SXRD measurements was synthesized by solid state reaction of MgO and V2O3.
Single crystals of MgV2O4 for the CBED measurements were prepared via the chemical vapor transport method [19]. We characterized our crystals using magnetization measurements. Fig. 2 shows the temperature dependence of the magnetic susceptibility of the as-grown single crystal measured under an applied magnetic field of 1 T with a SQUID magnetometer. The susceptibility undergoes a sharp drop at 62 K and followed by a small hump at 40 K, which corresponds well with those of MgV2O4 powder samples reported in Ref. [8] and also synthesized for our study as shown in the inset of Fig. 2. This demonstrated that the single crystal was of a quality high enough to be used for our study. The former and latter anomalies in the magnetic susceptibility reflect the cubic-to-tetragonal structural phase transition and the AFM ordering, respectively. CBED patterns were measured at room temperature with the incident beam along the [100] direction of the cubic spinel structure. Thin specimens for CBED experiments were prepared by crushing the single crystal of MgV2O4. Powder SXRD measurements were carried out on beam line BL02B02 at SPring-8. The diffraction data were collected using the powder sample sealed in a glass capillary (0.3 mm int. diam.) with a large Debye–Scherrer camera at 100 K in the HTC phase. The wavelength of the incident synchrotron X-ray beam was 0.5410 Å [20]. The structural parameters were refined by the Rietveld analysis of the powder diffraction data using RIETAN-FP [21].
3. Results and discussion First we show the result of the CBED measurement on the HTC phase of MgV2O4. Fig. 3(a) and (b) shows the [001] zone axis CBED pattern taken at an accelerating voltage of 80 keV and the enlarged view around the bright-field pattern, respectively. We can see that the zeroth-order Laue zone diffraction pattern shown in Fig. 3(b) and also the first-order Laue zone pattern emerging as a ring in Fig. 3(a) exhibit 4mm symmetry. Now let us consider the symmetries of the [001] zone axis CBED whole pattern (WP) in the cases of the space group Fd3m for the normal spinel structure and its three cubic subgroups of F43m (suggested as the space group of cubic MgV2O4 by Ref. [22]), F4132, and Fd3. Since the
S. Niitaka et al. / Journal of Solid State Chemistry 215 (2014) 184–188
Intensity (arb.unit)
3x10
MgV2O4, Measured temperature : 100 K, λ=0.5410 A
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Intensity (arb.unit)
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12000 8000 4000 0
1
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60 64 2θ (degrees)
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0 5
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35 40 45 2θ (degrees)
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Fig. 4. Observed (cross) and calculated (solid line) diffraction patterns from the Rietveld analysis of the powder SXRD data for the HTC phase of MgV2O4 at 100 K. Tick marks represent the positions of allowed Bragg reflections for the space group Fd3m. The difference line, observed minus calculated, is located at the bottom of the figure. The inset shows the enlarged view of the patterns in the high 2θ region. In the Rietveld refinement, the intensity data in the narrow 2θ ranges around 8.511, 11.501, 12.581, 14.261, 17.081, and 18.421 were not used, where tiny diffraction peaks from the impurity phase of V2O3 appear. However, their ranges did not overlap with any diffraction peaks from MgV2O4, showing that this matter caused no problems for our analysis. Table 1 Lattice constant, fractional coordinates of ions and their isotropic atomic displacement parameters in MgV2O4 at 100 K from the Rietveld refinements of the powder SXRD patterns. The goodness-of-fit indicator for the refinement was 1.35.
Fig. 3. (a) The CBED pattern along the [001] zone axis for room-temperature cubic MgV2O4 and (b) the magnified view of the zeroth-order Laue zone disks.
crystallographic point groups of Fd3m, F43m, F4132, and Fd3 are m3m, 43m, 432, and m3, the expected symmetries of the WP correspond to 4 mm, 2 mm, 4, and 2 mm, respectively [23]. Therefore our result suggests that the space group of the HTC phase in MgV2O4 is Fd3m without any symmetry breaking from the normal spinel structure. This suggestion accords with the consequence of our recent observation of the Gjønnes–Moodie lines across the center of the disks for the 200 reflections [19]. Next let us turn to the result of the powder SXRD measurement. Fig. 4 shows the SXRD pattern of the polycrystalline MgV2O4 sample collected at 100 K in the HTC phase together with the result of the Rietveld refinement using a cubic normal spinel structure with the space group Fd3m. The refinement gave a good fit with the final reliability factors of Rwp ¼ 2:353%, Rp ¼ 1:645%, and Re ¼ 1:739%. We also performed the Rietveld refinement in consideration of cation inversion, acquiring no better fit. This result suggests no anti-site disorder in the sample. The refined structural parameters of the HTC phase of MgV2O4 at 100 K are listed in Table 1. We would like to emphasize here that the 200 reflection was not observed in the SXRD pattern, which is forbidden due to diamond-glide planes in Fd3m and by contrast allowed for F43m. We calculated the hypothetical powder diffraction pattern of MgV2O4 with the crystallographic symmetry of F43m for the same experimental conditions as our SXRD measurement, using the lattice constant and the atomic displacement
MgV2O4 100 K Fd3m a ¼8.4021(7) Å. Atom Site x y
z
B (Å2)
Mg V O
1/8 1/2 0.26024(2)
0.260(5) 0.181(2) 0.268(6)
8a 16d 32e
1/8 1/2 0.26024(2)
1/8 1/2 0.26024(2)
parameters from our results for the data at 100 K listed in Table 1 and using the atomic coordinates of Mg, V, and O ions from Ref. [22]. Our calculation indicated that the intensity of the 200 reflection was about four times as large as the observed variability of the background at its position, meaning that the 200 reflection should be clearly observed in our measurement at 100 K as a peak with the sufficiently large intensity relative to the background in this assumed case. This adds weight to our conclusion that the HTC phase of MgV2O4 has the crystallographic symmetry of Fd3m. The discrepancy in the space group of the HTC phase between Ref. [22] and our result might be due to the difference in the sample preparation. Further investigation is required in order to determine the cause of this discrepancy. Fig. 5 shows a schematic illustration of the VO6 octahedron in the HTC phase of MgV2O4 at 100 K using the structural parameters in Table 1. All of the V–O bonds in the octahedron have a length of 2.016 Å. With this bond distance, the bond-valence sum calculation [24] gave a valence of 2.852þ for the V ions, which is in good agreement with their formal valence of 3 þ in insulating MgV2O4. Meanwhile two kinds of O–O bonds exist with lengths of 2.728 and 2.976 Å, resulting in the elongated VO6 octahedron along the three-fold axis. This is ascribed to the larger spinel u-parameter showing the position of the oxygen ions in a spinel structure than 0.25 in the case of ideal cubic close packing of the anion sublattice. The angle between the three-fold axis and the V–O direction is 51.291, which is smaller than 54.741 for a regular octahedron. Now let us discuss the orbital state in the HTC phase of MgV2O4. First, the main contribution to the crystal field of the octahedron is of cubic symmetry, splitting the V 3d manifold into the lower lying t 2g and the higher lying eg states with a large energy difference of 2–3 eV. Additionally, the trigonal crystal field from the elongation distortion revealed in our study lifts the
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V O
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the LTT phases of A V2O4 (A¼Mg2 þ , Zn2 þ , Cd2 þ ) but also the relationship between them and the crystal structures in their HTC phases are interesting future subjects for detailed research.
4. Conclusion
O-O bonds 2.728Å 2.976Å Fig. 5. Schematic view of the VO6 octahedron at 100 K in the HTC phase, which was elucidated by the Rietveld refinement. The small and large circles represent vanadium and oxygen ions, respectively. The solid and dashed lines indicate the short and long bonds connecting between oxygen ions with the length of 2.728 and 2.976 Å, respectively. The octahedron was found to be elongated in the direction of its three-fold rotation axis.
degeneracy of the t 2g states, resulting in the further split into a single a1g and a doublet e0g . Note here that it is difficult to determine even the relative order of the a1g and e0g orbitals from only the results of the crystal structure analysis because the eg –e0g hybridization has the opposite effect on the a1g –e0g splitting to the crystal field effect [25] and another factors such as the kinetic energy depending heavily on the crystal structure can also have significant effects [26]. The quantitative evolution of the splitting remains to be solved, for which the information on the crystal structure of MgV2O4 obtained in our study could be of great benefit. Regardless of the a1g –e0g relative order, we can note the following two points. Firstly, the spatial distribution of the two 3d electrons under the trigonal crystal field is still isotropic in spite of the degeneracy lifting of the t 2g states, which results in the equivalent exchange interactions between the spins on the nearest neighboring V ions, inducing geometrical spin frustration. Secondly, and more importantly, their orbital moments are somewhat reduced compared with those in the case of the degenerate t 2g states. Hence the release of spin frustration in MgV2O4 by means of the orbital degree of freedom actually occurs with the orbital state in the HTC phase as a starting point, which could have an important effect on the nature of the resulting orbital state in the LTT phase. As for the other vanadates, ZnV2O4 and CdV2O4, the lattice parameters and positions of oxygen ions in A V2O4 (A¼ Mg2 þ , Zn2 þ , Cd2 þ ) should significantly depend on the radii of the nonmagnetic ions for the following reason based on the structural character of spinels. The larger radii of the A ion induce a longer A–O bond, resulting in a larger spinel u-parameter. In the consequently more elongated VO6 octahedron, the shorter O–O bonds create stronger Coulomb repulsion between the oxygen ions, bringing about the larger lattice constant. We can therefore expect that these vanadates have different a1g –e0g splittings under the respective trigonal crystal fields of the VO6 octahedra. As mentioned in the introduction, various orbital models for the LTT phases have been theoretically proposed, including one in which the spin–orbit coupling plays an important role. This theoretical situation could suggest that the proposed models have almost the same intrinsic energies in the actual materials and that which model emerges as the ground state depends on subtle differences in some properties of materials, in which the a1g –e0g splitting in the HTC phases is highly likely included. So A V2O4 (A ¼Mg2 þ , Zn2 þ , Cd2 þ ) might have the different orbital states in their LTT phases although they show similar structural and magnetic properties. The comprehensive understanding of not only the orbital states in
We have reported the results of the powder SXRD and CBED measurements for the HTC MgV2O4 which exhibits the release of spin frustration by means of an orbital degree of freedom in the LTT phase. The WP symmetry of the CBED taken at the [001] incidence was found to be 4 mm which was consistent only with the space group Fd3m among the space group for a cubic normal spinel structure and its cubic subgroups. The Rietveld refinement of the SXRD data of MgV2O4 at 100 K using a normal spinel structure with the space group of Fd3m was also successful. These results strongly support that the space group of the HTC phase of MgV2O4 is Fd3m, which was indicated by the observation of the Gjønnes–Moodie lines [19]. The refined structural parameters indicates that the VO6 octahedron in the HTC phase is stretched along its three-fold rotation axis, inducing a trigonal crystal field for the V cation. This additional field causes the splitting of its t 2g orbitals into the a1g and the e0g states, state, reducing the orbital moment of the V3 þ ion. This could influence the orbital state in the LTT phase of MgV2O4, taking into account many theoretical suggestions for the orbital model.
Acknowledgments We are grateful to Y. Motome for valuable discussions. This work was financially supported by Grant-in-Aid for Young Scientists (B) (No. 18760022). The synchrotron radiation experiments were performed on BL02B2 at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2007B1524).
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