Charge disproportionation associated with spin ordering in delafossite CuFeO 2 as seen via resonant x-ray diffraction N. Terada, 1,2 T. Nakajima, 3 S. Mitsuda, 3 Y. Tanaka, 2 H. Mamiya, 1 and H. Kitazawa 1 1 National Institute for Materials Science, Sengen 1-2-1, Tsukuba, Ibaraki 305-0044, Japan 2 RIKEN SPring-8 Center, Harima Institute, Sayo, Hyogo 679-5148, Japan 3 Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo 162-8601, Japan Received 10 September 2009; revised manuscript received 12 January 2010; published 23 February 2010 We have performed the resonant x-ray diffraction measurements on the triangular lattice antiferromagnet CuFeO 2 near the Fe K absorption edge. The resonant enhancement of the space-group-forbidden superlattice 010 reflection was observed below the second Néel temperature T N2 =11 K at which the four-sublattice ground state is stabilized. The significant azimuthal angle dependence of the superlattice reflection was not observed. On the other hand, the energy spectrum can be explained by the charge disproportionation CD model, 2Fe 3+ ↔Fe 3++ +Fe 3-+ . We discuss the relationship between the unconventional collinear four-sublattice ground state and the CD state in CuFeO 2 . DOI: 10.1103/PhysRevB.81.064424 PACS numbers: 75.80.q, 77.84.s I. INTRODUCTION Cross correlation between different order parameters in solids, which is typified by magnetoelectric, piezoelectric, and magnetostrictive effect, is fertile ground for the appear- ance of novel physical phenomena. In magnetic materials, the discovery of magnetostriction more than 150 years ago has presented an important physical concept for understand- ing their physical phenomena. 1 Novel physical phenomena discovered recently, such as giant/colossal magneto- resistance 2–4 and magnetoferroelectrics, 5,6 are also under- stood with interplay between spin and the other degree of freedom. The delafossite CuFeO 2 is one of magnetic materi- als showing several cross-correlation phenomena of the spontaneous spin-lattice coupling, 7–9 magnetic field-induced ferroelectricity, 10 and multistep lattice changes. 11 CuFeO 2 has triangular lattice layered structure, which be- longs to space group R3 ¯ m. The magnetic ions Fe 3+ which make up the triangular lattice layers are characterized by an isotropic 3d orbital state of the electronic configuration with orbital singlet, S =5 / 2 and L = 0. Since the single-ion aniso- tropy of Fe 3+ is considered to be small, the Heisenberg spin behaviors are expected in CuFeO 2 . In a Heisenberg spin tri- angular lattice antiferromagnet TLA with weak anisotropy, a noncollinear magnetic ground state so-called 120° state is predicted by the theoretical study. 12 In CuFeO 2 , however, its ground state is the collinear four-sublattice ↑↑↓↓ 4SL state with the magnetic moments confined along the hexagonal c axis. 8,13,14 In magnetic fields along the c axis, multistep mag- netization changes occur, which is generally seen in frus- trated Ising antiferromagnets with a strong uniaxial aniso- tropy. Despite great efforts for understanding the unconventional spin behaviors, their origin has not been un- derstood thus far. The previous x-ray diffraction studies 7–9 have pointed out that the lattice distortion lifting the macro- scopic degeneracy of the frustrated spin system plays an im- portant role for the stabilization of the 4SL ground state in CuFeO 2 . However, no study to directly investigate the elec- tronic state below the Néel temperature in CuFeO 2 have been carried out. Therefore, the origin of the uniaxial anisotropy of the orbital singlet Fe 3+ in CuFeO 2 has not been clarified so far. In the present work, in order to obtain knowledge for the electronic state of Fe 3+ below Néel temperature, we have performed the resonant x-ray diffraction RXD experiment on CuFeO 2 near the Fe K absorption edge. A RXD measurement is one of the most powerful tech- niques for studying charge orderings, 15–17 orbital orderings 18 and magnetic orderings. 19 As for charge ordering/ disproportionation, the generalized scattering factor for a single atom/ion can be given by f ee  = e · e f T Q + f ee   E + if ee   E , 1 where e and e are unit vectors of polarization for the inci- dent and diffracted x-ray beams, respectively. The first term is the Thomson scattering factor which is independent of incident energy E and depends on the scattering vector Q. The terms f ee   and f ee   are the real and imaginary parts of the dispersion corrections, respectively, which are dependent on E. They vary significantly near the absorption edges for the elements of which the materials are composed. One can, therefore, detect resonant enhancement for a superlattice re- flection near the edge, which is caused by the difference in the scattering factor for different crystal sites. II. EXPERIMENTAL DETAIL A single crystal of CuFeO 2 , which was prepared by the floating zone technique, 20 was cut into a disk with a thick- ness of 2 mm and subsequently polished in air to remove the surface roughness. The RXD experiments were carried out with a standard four-circle diffractometer in BL29XU at SPring-8. The cut crystal was mounted in a liquid 4 He re- frigerator that can cool a sample down to 3 K. The incident x-ray beam had almost perfect horizontal polarization and its energy was tuned to near the Fe-K absorption edge E  7.112 keV The diffracted x-rays were analyzed using the 006 reflection of a pyrolytic graphite crystal. The azimuthal reference vector was chosen as the 001 direction. The x-ray absorption spectrum was measured at room temperature us- ing the powder sample. PHYSICAL REVIEW B 81, 064424 2010 1098-0121/2010/816/0644244 ©2010 The American Physical Society 064424-1