Session K2: Exotic Ordering in Spinels

Metal-insulator transition in CuIr$_2$S$_4$: XAS results, structure revisited, electronic structure proposed

Interestingly, the magnetism in the spinel compound Fe$_{3}$O$_{4}$ (loadstone), constitutes the correlated electron material/problem of the greatest antiquity known to man. The Verwy transition problem in Fe$_{3}$O$_{4}$ is, by comparison, young at only 67 years of age. Recently experimental and theoretical insights into such exotic magnetic, charge, and orbital orderings in transition metal (T) spinel compounds have been rapidly emerging. The leitmotifs in these works involve: frustrated tripartite crossing 1D chains of edge-sharing T-ligand octahedra; T-d(t$_{2g})$ orbital ordering onto subsets of these chains which involve d-d overlap; dimmer formation on these chains; and/or charge ordering on the chains dependent on band filling. Understanding the low temperature structural and metal (M) to insulator (I) transition in the spinel compound CuIr$_{2}$S$_{4}$ provides a key link in the generalization to other such systems. S $K$-edge X-ray absorption spectroscopy (XAS) measurements across this M-I transition reflect a dramatic Ir $d$-electronic state redistribution$^{1}$. These results stimulated a detailed re-evaluation of the of $I$-phase crystal structure in terms of: decoupled chains of IrS$_{6}$ octahedra along the (110)-type directions; and an Ir$^{3+}$ (Ir$^{4+}$-Ir$^{4+})$ Ir$^{3+}$ repeat pattern ordering, where the (Ir$^{4+}$-Ir$^{4+})$ pair forms a dimmer. Further, the electronic state changes, evidenced by the XAS, motivated a model in which the I-phase involves: an orbital ordering of the highest lying t$_{2g}$ electron into 1D chains; the 3/4 filling of this 1D band dictating the periodicity of the orbital/charge ordering; and the direct t$_{2g}$-t$_{2g}$ dimmer bonding production of an antibonding state prominent in the S-K edge spectrum. The generalization of these concepts to other transition metal spinels will be addressed. $^{1}$M. Croft, W. Caliebe, H. Woo, T. A. Tyson, D. Sills, Y. S. Hor, S-W. Cheong, V. Kiryukhin, and S-J. Oh, Phys. Rev. B 67 (Rapid Comm.), 201102 (2003)   

Charge carriers in spinel AlV$_{2}$O$_{4}$ order below 700K

AlV$_{2}$O$_{4}$ with the spinel structure shows some magnetic and electric anomalies around 700K, which originate from the formation of the charge ordered (CO) structure.[1,2] In this talk, we will report a structural model of the CO structure in AlV$_{2}$O$_{4}$, which was obtained by electron diffraction, synchrotron x-ray diffraction and magnetic measurements. The CO structure is characterized by the formation of V clusters ``heptamers'', each of which is consisting of 7 vanadium atoms and is in a spin- singlet state as a total. Note that the number of electrons per site is still fractional in this CO structure. In addition, theoretical consideration suggests that this unique molecular-like V heptamer is stabilized by a strong bonding of vanadium t$_{2g}$ orbitals. This work has been done in collaboration with Drs. S. Mori, T. Katsufuji, Y. Motome, N. Furukawa, H. Ishibashi, N. Ikeda and K. Kato. [1]K. Matsuno,et al., J. Phys. Soc. Jpn. \textbf{70}, 1456 (2001). [2]K. Matsuno et al., Phys. Rev. Lett. \textbf{90}, 096404 (2003).   

Orbital Superstructures in Spinels

Orbital degrees of freedom often lead to specific types of orbital and spin ordering. Complicated and interesting superstructures are observed in B-sublattice of spinels. This is connected with the geometric frustration of this lattice and with the interconnection of edge-sharing MO$_{6}$ octahedra, which is especially important for transition metals with partially-filled t$_{2g}$ levels. In some such systems (MgTi$_{2}$O4, CuIr$_{2}$S$_{4}$, AlV$_{2}$O$_{4})$ there appears strange superstructures with the formation of spin gap states. In other cases (ZnV$_{2}$O$_{4})$ structural transitions, apparently connected with orbital ordering, are followed by long-range magnetic ordering. Last but not least, the famous Verwey transition in magnetite Fe$_{3}$O$_{4}$ leads to a very complicated structural pattern, accompanied by the appearance of ferroelectricity. In this talk I will discuss all these examples, paying main attention to an interplay of charge, spin and orbital degrees of freedom. In particular, for MgTi$_{2}$O4, and CuIr$_{2}$S$_{4}$ we proposed the picture of orbitally-driven Peierls state [1]. Similar phenomenon can also explain situation in ZnV$_{2}$O$_{4 }$[2], although the corresponding superstructure has not yet been observed experimentally. Finally, I propose the model of charge and orbital ordering in magnetite [3], which uses the idea of an interplay of site- and bond-centered ordering [4] and which seems to explain both the structural data and the presence of ferroelectricity in Fe$_{3}$O$_{4 }$ below Verwey transition. \newline \newline [1] D.I.Khomskii and T.Mizokawa, Phys.Rev.Lett. \textbf{94}, 156402 (2005); \newline [2] Hua Wu, T.Mizokawa and D.I.Khomskii, unpublished; \newline [3] D.I.Khomskii, unpublished; \newline [4] D.V.Efremov, J.van den Brink and D.I.Khomskii, Nature Mater. \textbf{3}, 853 (2004)   

Probing spin correlations with phonons in the strongly frustrated magnet: ZnCr2O4

Geometrically frustrated magnets can resist magnetic ordering and remain in a strongly correlated paramagnetic state well below the Curie-Weiss temperature. The spin-lattice coupling can play an important role in relieving the frustration in these systems. In ZnCr2O4, an excellent realization of the Heisenberg antiferromagnet on the pyrochlore network, a lattice distortion relieves the geometrical frustration through a spin- Peierls-like phase transition at Tc=12.5 K with a lowering of the symmetry from cubic to tetragonal. Conversely, spin correlations strongly influence the elastic properties of a frustrated magnet. By using infrared spectroscopy and published data on magnetic specific heat, we demonstrate that the frequency of the Cr optical phonon triplet in ZnCr2O4 tracks the nearest-neighbor spin correlations above Tc.* Below Tc, the triplet splits into a singlet and a doublet, separated by 11 cm- 1. This splitting gives a direct measurement of the spin- Peierls order parameter. From analysis of the ion displacements in the phonon modes we can conclude that direct Cr-Cr exchange dominates in ZnCr2O4. These experiments result in a clear understanding of spin-phonon coupling in ZnCr2O4 in contrast to other oxide magnets. Recent ab initio calculations** confirm the magnetic origin of both the phonon splitting in ZnCr2O4 and the frequency shifts in the ferromagnetic insulating spinel CdCr2S4. *A.B. Sushkov et al., Phys. Rev. Letters 94 (2005) 137202. ** C.J. Fennie and K.M. Rabe, cond-mat/0508136 and Mar06 APS Meeting.   

Orbital ordering in transition-metal spinels

Transition-metal spinels (general formula \textit{AB}$_{2}X_{4})$ have been for many years the subject of intense experimental and theoretical activity. Structurally, the most interesting feature of these systems is the fact that the $B$ cation occupies the nodes of a pyrochlore lattice, which is known to be geometrically frustrated. Therefore, one can explore how their natural tendency to order in the charge, magnetic and orbital sectors is affected by geometrical frustration. Orbital Ordering (OO) occurs when the orbital degeneracy of an extended concentrated system is lifted, typically through a distortion of the lattice. This may result in either single orbital occupation or alternation/modulation of the orbital occupancy, with or without an associated charge ordering. The degree of charge localization is another important issue: in highly localized systems, one can speak of a cooperative Jahn-Teller (JT) effect, but this paradigm is no longer sufficient in the present of significant electronic hopping. Both e$_{g}$ and t$_{2g}$ orbitals are relevant for transition-metal spinels; e$_{g}$ systems, such as ZnMn$_{2}$O$_{4}$, tend to display the strongest JT effects, with direct coupling to the lattice. More recently, significant attention has been devoted to the possibility of orbital ordering in ions with partial t$_{2g}$ occupation, such as Ti$^{3+}$ and V$^{4+}$ (3d$^{1})$ and V$^{3+}$ (3d$^{2})$ and their electron/hole-symmetric counterparts. With respect to e$_{g}$ systems, t$_{2g}$ systems have a greater degeneracy and weaker coupling to the lattice, and can give rise to significant hopping, due to the direct overlap of the t$_{2g}$ orbitals along the $<$110$>$ crystallographic directions of the spinel structure. Recent results on Ti, V, Fe and Ir spinels will be discussed, with particular reference to the relation between the complex crystallographic superstructures and the changes in transport (metal-insulator transitions) and magnetic (paramagnetic-diamagnetic transitions) properties at the ordering temperatures.