Observation of Quadrupole Helix Chirality and Its Domain Structure in Dyfe3(BO3)4
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ARTICLES PUBLISHED ONLINE: 6 APRIL 2014 | DOI: 10.1038/NMAT3942 Observation of quadrupole helix chirality and its domain structure in DyFe3(BO3)4 T. Usui1, Y. Tanaka2, H. Nakajima1, M. Taguchi2, A. Chainani2, M. Oura2, S. Shin2, N. Katayama3, H. Sawa3, Y. Wakabayashi1 and T. Kimura1* Resonant X-ray diraction (RXD) uses X-rays in the vicinity of a specific atomic absorption edge and is a powerful technique for studying symmetry breaking by motifs of various multipole moments, such as electric monopoles (charge), magnetic dipoles (spin) and electric quadrupoles (orbital). Using circularly polarized X-rays, this technique has been developed to verify symmetry breaking eects arising from chirality, the asymmetry of an object upon its mirroring. Chirality plays a crucial role in the emergence of functionalities such as optical rotatory power and multiferroicity. Here we apply spatially resolved RXD to reveal the helix chirality of Dy 4f electric quadrupole orientations and its domain structure in DyFe3(BO3)4, which shows a reversible phase transition into an enantiomorphic space-group pair. The present study provides evidence for a helix chiral motif of quadrupole moments developed in crystallographic helix chirality. t is well known that chirality often plays a critical role in various detect not only crystallographic helix handedness but also the disciplines, such as biology, organic chemistry and particle chirality ascribed to the periodic motif of multipole moments, such Iphysics1,2. In contrast, chirality in solid-state physics, which as magnetic dipoles and electric quadrupoles12–14. In the case of is largely concerned with crystals possessing periodic arrays of magnetic dipoles, the handedness of a `helical magnetic structure' atoms, has attracted less attention. This is partly because most of represents an example of chirality in magnetic crystals which can the physical properties of crystals are only weakly sensitive to their be identified by the RXD technique using circularly polarized chirality. In fact, Neumann's principle3 states that the symmetry X-rays15–17. Furthermore, recent extensive studies on magnetic of any physical property of a crystal must include the symmetry crystals revealed that the chirality (or the handedness) of complex element of the crystal's `point group', in which the screw rotation magnetic orderings, such as helical magnetic order, has a unique operation related to the helix chirality is neglected. Indeed, in impact on the dielectric and transport properties, leading to connection with this insensitivity, there are very few methods unusual phenomena such as multiferroicity18,19 and anomalous to detect and identify the handedness embedded in crystals magnetotransport20. Thus, during these years, the concept of (except for optical activity4 and X-ray diffraction using dispersion chirality has moved to the forefront of solid-state physics. corrections5). In recent years, however, resonant X-ray diffraction In this study, we show the chiral motif of quadrupole moments (RXD) with circularly polarized X-rays has developed as a valuable and its domain structure by means of the RXD technique using a technique to identify the handedness in helix chiral structures circularly polarized, micro-focused X-ray beam. For this purpose, through a coupling of X-ray helicity with an enantiomorphic screw we employed single-crystal specimens of DyFe3(BO3/4 having axis6,7. The first experimental demonstration to distinguish the dysprosium 4f quadrupole moments and enantiomorphs with crystallographic helix chirality by RXD with circularly polarized right-handed and left-handed helical structures21. This ferroborate 3C X-rays was carried out for α-quartz (SiO2/ with an enantiomorphic crystallizes in a trigonal space group, R32, in which a Dy ion 2− space-group pair, P3121 (right-handed screw; ref. 8) and P3221 (left- is surrounded by a trigonal prism of six O ions. On cooling, handed screw), and subsequently in berlinite (AlPO4/ and elemental it undergoes a first-order structural phase transition into an 9,10 Te with the same space-group pair . In crystals having the space- enantiomorphic space-group pair (P3121 and P3221), which is the group pair P3121 and P3221, reflections 00l (l 6D3n, nDinteger) are same as that in α-quartz, at Ts ≈ 285 K (refs 22,23). In the P3121 3C forbidden in non-resonant X-ray diffraction, but allowed in RXD or P3221 structure of DyFe3(BO3/4, not only Fe ions but also for certain X-ray energy ranges. By carefully examining the space- Dy3C ions are arranged in a right-handed or left-handed helical group forbidden reflections observed for the RXD with circularly manner along the three-fold c axis22. For our samples, we have polarized X-rays, one can identify the sign of the crystallographic clearly observed the structural transition at Ts as a sharp peak helix chirality6–10. More recently, using a highly focused X-ray anomaly in specific heat and the appearance of the Bragg reflection beam, this technique was applied to image chiral domain 204,N as shown in Fig. 1a. On further decreasing the temperature (T/, structures of CsCuCl3 with a P6122 and P6522 enantiomorphic the specific heat shows another anomaly at the Néel temperature 11 space-group pair . TN D 38 K, where an antiferromagnetic (AF) order for both Fe and 22 Compared with measurements of the optical activity and X-ray Dy moments develops . In the AF phase, DyFe3(BO3/4 exhibits a diffraction using dispersion corrections, RXD measurement with magnetoelectric effect accompanied by a spin flop24. In this work, we circularly polarized X-rays has the advantage of being able to show that chirality due to the orientation of the quadrupole moment 1Division of Materials Physics, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan, 2RIKEN SPring-8 Center, Sayo, Hyogo 679-5148, Japan, 3Department of Applied Physics, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan. *e-mail: [email protected] NATURE MATERIALS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturematerials 1 © 2014 Macmillan Publishers Limited. All rights reserved. ARTICLES NATURE MATERIALS DOI: 10.1038/NMAT3942 a b P3121 or P3221 R32 DyFe3(BO3)4 400 c*||κ crystal Integrated intensity (a.u.) ) −1 Reflection 204 Ψ mol ya* −1 θθ σ’ σ π ’ π 200 k (−) kf i (+) Specific heat (J K x b(||z) c 0 d Dy M5 Reflection 001 200 K displacement (×10 E = 1,292 eV Square of Dy position 4 0.2 2 Intensity (a.u.) X-ray absorption Reflection 001 2 1 −4 0.0 Å 2 ) Dy M4 Integrated intensity (a.u.) Integrated intensity (a.u.) 0 0 x3 0 100 200 300 1,290 1,310 1,330 Temperature (K) Photon energy (eV) Figure 1 | Characterization of the structural phase transition using specific heat, non-resonant diraction, and resonant diraction at the Dy M4,5 absorption edges. a, Specific heat and integrated intensity of reflection 204¯ as a function of T. Reflection 204¯ was taken using non-resonant X-ray diraction with Mo Kα X-rays. b, Schematic illustration of the scattering geometry for the present RXD measurements. Here ki and kf are the propagation vectors of the incident and diracted X-rays, respectively. The azimuthal and Bragg angles are denoted by Ψ and θ, respectively. The origin of Ψ D0 is 0 0 defined by the a* axis when it is parallel to −(ki C kf/. The σ (σ ) and π (π ) components are perpendicular and parallel to the scattering plane, respectively. c, T dependence of the integrated intensity of forbidden reflection 001 obtained by the RXD measurements with an incident X-ray energy of 1,292 eV. Open squares show the square of the displacement of the Dy position along the ξ axis from its position at 300 K (Supplementary Information). The inset shows a magnified region around Ts. d, The black line and red dots represent the spectra of the X-ray absorption and forbidden reflection 001, respectively, as a function of photon energy at 200 K. sets in at Ts ≈285 K and co-exists with the antiferromagnetic order helicity (C/ ((−)) is expressed by a sum of the σ and π linear below TN D38 K. polarizations, in which the σ component is advanced (behind) We prepared two crystals of DyFe3(BO3/4 (Sample 1 and in time by a quarter period with respect to the π component, as Sample 2) for the RXD measurements (Methods). The experimental illustrated in Fig. 1b. A photograph of Sample 1 is shown in Fig. 2a. set-up for the RXD measurements is illustrated in Fig. 1b, and is The two different positions are in the regions marked as α and explained in detail in the Methods. Figure 1d shows the resonance β. These RXD measurements were carried out at T D 200 K (<Ts/ ◦ enhancement of the forbidden reflection 001 at the Dy M4,5 and an azimuthal angle ' D 0 . Here, ' is the angle rotated with ◦ absorption edges and T D 200 K (<Ts/ for Sample 1. To show the respect to the scattering vector κ (k c*), and its origin (' D 0 ) resonant edges, we overlay the corresponding X-ray absorption is defined as the configuration in which the scattering plane is spectrum (XAS), in which three strong peaks and one weak parallel to the horizontal direction of the photo in Fig. 2a. As clearly peak appear around the Dy M5 and M4 edges, respectively. The seen in Fig. 2b,c, the sign change in the helicity of the circular three distinct features at the M5 edge in XAS are ascribed to the polarization yields substantially different intensities of the forbidden dipole selection rules: 1J D0 and ±1 transitions25 (Supplementary reflection 001 for both the sample positions. Moreover, the helicity- Information).