Orbital order in vanadium spinels

Abstract

Motivated by recent theoretical and experimental controversy, we present a theoretical study to clarify the orbital symmetry of the ground state of vanadium spinel oxides AV2O4 (A=Zn, Mg, Cd). The study is based on an effective Hamiltonian with spin-orbital superexchange interaction and a local spin-orbit coupling term. We construct a classical phase-diagram and prove the complex orbital nature of the ground state. Remarkably, with our new analysis we predict correctly also the coherent tetragonal flattening of oxygen octahedra. Finally, through analytical considerations as well as numerical ab-initio simulations, we propose how to detect the predicted complex orbital ordering through vanadium K edge resonant x-ray scattering.PACS numbers: 75.10. Jm, 75.30.Et Vanadium and titanium spinels, AB 2 O 4 (B=Ti 3+ , or V 3+ ), belong to a class of frustrated antiferromagnets where magnetic B-ions are characterized by orbital degeneracy due to partial occupancy of t 2g -orbitals (n t2g =1 for titanates and n t2g =2 for vanadates). Recently these spinels were thoroughly studied from both experimental [1,2,3] and theoretical [4,5,6] points of view. While the ground state of Ti-based spinels can be explained in terms of orbitally-driven superexchange interactions on the frustrated pyrochlore lattice [6], the situation seems not so fluid for vanadium spinels, as two conflicting theoretical works appeared to explain their structural and magnetic properties [4,5].In AV 2 O 4 , magnetically active V 3+ -ions form a pyrochlore lattice and are characterized by two 3d electrons in t 2g -orbitals, while A is a divalent ion like Cd 2+ , or Zn 2+ , or Mg 2+ . All compounds show qualitatively similar structural and magnetic behavior with a structural transition at a higher temperature T S and an antiferromagnetic (AFM) transition at a slightly lower temperature T N [7]. These findings have been interpreted by Tsunetsugu and Motome [4] as an interplay of ddσ superexchange (SE) interaction and geometrical frustration: they showed that ordering of orbitals can partially remove magnetic frustration and explain the experimentally observed magnetic structure which is composed of AFM chains running in [110] and [110] directions. The ground state orbital ordering suggested in Ref.[4] consists of stacked ab planes with alternating d xz and d yz vanadium hole orbitals (hereafter referred to as ROO).On the other side Tchernyshyov [5] pointed out that the ground state symmetry I4 1 /a of ROO solution seems at odds with x-ray and neutron diffraction data, indicating a I4 1 /amd space symmetry. Thus, he proposed a purely ionic model where spin-orbit (SO) coupling plays the major role and the V hole occupies (predetermining the sign of Jahn-Teller (JT) distortion) a complex linear combination of xz and yz orbitals: (d xz ± id yz )/ √ 2. (We shall refer to this orbital order as COO).Actually, the correct space group of the system is still elusive. The tetragonal I4 1 /amd space group was found in Ref.[1], while the authors of the neutron scatter...

Classical Dimers and Dimerized Superstructure in an Orbitally Degenerate Honeycomb Antiferromagnet

“…For the full expressions of the exchange constants in terms of hopping integral t, on-site Coulomb repulsion U and Hund's coupling J H we refer reader to Refs. [15,16]. To the leading order in small parameter η = J H /U , the coupling constants are given…”

“…The effective spin-orbital Hamiltonian for such a system been reported in Refs. [15,16]. It has the following form:…”

Theory of Successive Transitions in Vanadium Spinels and Order of Orbitals and Spins

“…Hence, this mean-field type analysis for the ground state tells that the model with superexchange interactions alone fails to reproduce the experimental results. 13) There is, however, one caveat -the energy difference between the ground state (b) and the next lowest state (a) is small compared to the relevant energy scale in experiments. The energy difference between (a) and (b) per site is given by…”

“…4) by their mean value in high-temperature regime, that is, S i → S i = 0. The resultant Hamiltonian for the orbital degree of freedom reads 13) up to irrelevant constants, where…”

Variety of elastic anomalies in an orbital-active nearly itinerant cobalt vanadate spinel

“…For AV 2 O 4 (A = Zn, Mg, Cd, Mn, and Fe), the structural phase transition is considered to arise from a longrange ordering of the V t 2g orbitals, where the lowering of the lattice symmetry should result in the release of frustration (magnetic ordering). The orbital order to explain the structural and magnetic orders for AV 2 O 4 is still under debate both theoretically [ [25][26][27][28][29][30][31] and experimentally [ 4,7,12,15 ]; it is considered to be driven by the competition among Jahn-Teller coupling, Kugel- ) is a unique vanadate spinel with its highest electrical conductivity among the insulating or semiconducting AV 2 O 4 , which is considered to arise from the nearly-itinerant character of the V 3d electrons [ [33][34][35][36][37][38][39]. CoV 2 O 4 exhibits a ferrimagnetic order below T C ∼ 150 K, which is similar to AV 2 O 4 with magnetic A = Mn (T C = 57 K) and Fe (T C = 110 K).…”