Suppression of spin frustration due to orbital selection

Abstract

In order to clarify a crucial role of orbital degree of freedom in geometrically frustrated systems, we investigate both ground-and excited-state properties of the eg-orbital degenerate Hubbard model on two kinds of lattices, ladder and zigzag chain, by using numerical techniques. In the ladder, spin correlation extends on the whole system, while the zigzag chain is decoupled to a double chain and spin excitation is confined in one side of the double chain due to the selection of a specific orbital. We envision a kind of self-organization phenomenon that the geometrically frustrated multi-orbital system is spontaneously reduced to a one-orbital model to suppress the spin frustration. 71.10.Fd, 75.30.Et, 75.40.Mg Recently strongly correlated electron systems with geometrical frustration have attracted much attention in the research field of condensed-matter physics, since a subtle balance among competing interactions leads to a variety of cooperative phenomena such as exotic superconductivity and novel magnetism. In particular, the discovery of superconductivity in layered cobalt oxyhydrate Na 0.35 CoO 2 ·1.3H 2 O [1] has triggered intensive investigations of superconductivity on the triangular lattice. Concerning magnetism on geometrically frustrated lattices, properties of antiferromagnets with the trianglebased structure have been discussed for a long time [2]. In low-dimensional systems, the combined effects of geometrical frustration and strong quantum fluctuation cause peculiar behavior in low-energy physics, as typically observed in the Heisenberg zigzag chain with spin S=1/2. With increasing the strength of frustration, the ground state is changed from a critical spin-liquid to a gapped dimer phase [3,4,5,6]. In the dimer phase, neighboring spins form a valence bond to gain the local magnetic energy, while the correlation among the valence bonds is weakened to suppress the effect of spin frustration.Another important ingredient in actual materials is orbital degree of freedom, when electrons partially fill degenerate orbitals, as frequently observed in d-and felectron compounds. In such a system, the interplay of spin and orbital degrees of freedom yields the possibility of orbital ordering. It is an intriguing issue to clarify the influence of orbital ordering on magnetic properties in geometrically frustrated systems. In fact, significance of t 2g -orbital degree of freedom has been discussed to understand the mechanism of two phase transitions in spinel vanadium oxides AV 2 O 4 (A=Zn, Mg, and Cd) [7,8,9]. It has been proposed that orbital ordering brings a spatial modulation in the spin exchange and spin frustration is consequently relaxed. Similarly, for MgTi 2 O 4 , the formation of a valence-bond crystal due to orbital ordering has been also suggested [10].In general, since d-and f -electron orbitals are spatially anisotropic, there always exist easy and hard directions for electron motion. Then, it is reasonable to expect that the effect of geometrical frustration would be reduced due to orbital...

Multipoles in -Pu

“…Here we note that O 3g quadrupoles indicate orbital degrees of freedom in the 8 state. In general, orbitals tend to arrange themselves so as to gain the kinetic energy [20], but in 3D environment, ferro orbital order does not easily occur, since the optimal shape of the orbital cannot be determined only from the viewpoint of kinetic energy. Then, orbital (quadrupole) fluctuations significantly remain.…”

Spin-orbital gap of multiorbital antiferromagnet with geometrical frustration

“…When the Hund's rule interaction is small, the ground state is found to be paramagnetic, 19,20 which is relevant to a geometrically frustrated antiferromagnet. Here, we study the property of the paramagnetic phase and simply ignore the Hund's rule interaction, but the results do not change qualitatively for quarter filling case.…”

“…In fact, we have found that orbital ordering actually relaxes the frustration effect in the exchange interaction due to the spatial anisotropy of relevant orbital, even though the lattice originally exhibits a geometrically frustrated structure. 19,20,21 After the occurrence of orbital ordering, one may naively expect that the system is described by an effective spin system on the frozen background of orbital arrangement. It is true that we can intuitively understand what kind of magnetic correlation develops in the static orbital ordering.…”

Orbital Ordering Phenomena in D‐ and F‐Electron Systems

“…Here we refer only the result for J=0, but readers should consult with Ref. [230] about the results for J =0. In Figs.…”