Orbital ordering and one-dimensional magnetic correlation in vanadium spinel oxides AV2O4 (A = Zn, Mg, or Cd)

We present our theoretical results on the mechanism of two transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) in which magnetic V cations constitute a geometrically-frustrated pyrochlore structure. We have derived an effective spin-orbital-lattice coupled model in the strong correlation limit of the multiorbital Hubbard model, and applied Monte Carlo simulation to the model. The results reveal that the higher-temperature transition is a layered antiferro-type orbital ordering accompanied by tetragonal Jahn-Teller distortion, and the lower-temperature transition is an antiferromagnetic spin ordering. The orbital order lifts the magnetic frustration partially, and induces spatial anisotropy in magnetic exchange interactions. In the intermediate phase, the system can be considered to consist of weakly-coupled antiferromagnetic chains lying in the perpendicular planes to the tetragonal distortion.Comment: 2 pages, 1 figure, submitted to SCES'0

Orbital and magnetic transitions in geometrically-frustrated vanadium spinels -- Monte Carlo study of an effective spin-orbital-lattice coupled model --

We present our theoretical and numerical results on thermodynamic properties and the microscopic mechanism of two successive transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) obtained by Monte Carlo calculations of an effective spin-orbital-lattice model in the strong correlation limit. Geometrical frustration in the pyrochlore lattice structure of V cations suppresses development of spin and orbital correlations, however, we find that the model exhibits two transitions at low temperatures. First, a discontinuous transition occurs with an orbital ordering assisted by the tetragonal Jahn-Teller distortion. The orbital order reduces the frustration in spin exchange interactions, and induces antiferromagnetic correlations in one-dimensional chains lying in the perpendicular planes to the tetragonal distortion. Secondly, at a lower temperature, a three-dimensional antiferromagnetic order sets in continuously, which is stabilized by the third-neighbor interaction among the one-dimensional antiferromagnetic chains. Thermal fluctuations are crucial to stabilize the collinear magnetic state by the order-by-disorder mechanism. The results well reproduce the experimental data such as transition temperatures, temperature dependence of the magnetic susceptibility, changes of the entropy at the transitions, and the magnetic ordering structure at low temperatures. Quantum fluctuation effect is also examined by the linear spin wave theory at zero temperature. The staggered moment in the ground state is found to be considerably reduced from saturated value, and reasonably agrees with the experimental data.Comment: 22 pages, 23 figure

Theory of successive transitions in vanadium spinels and order of orbitals and spins

We have theoretically studied successive transitions in vanadium spinel oxides with (t_2g)^2 electron configuration. These compounds show a structural transition at ~ 50K and an antiferromagnetic transition at ~ 40K. Since threefold t_2g orbitals of vanadium cations are occupied partially and vanadiums constitute a geometrically-frustrated pyrochlore lattice, the system provides a particular example to investigate the interplay among spin, orbital and lattice degrees of freedom on frustrated lattice. We examine the models with the Jahn-Teller coupling and/or the spin-orbital superexchange interaction, and conclude that keen competition between these two contributions explains the thermodynamics of vanadium spinels. Effects of quantum fluctuations as well as relativistic spin-orbit coupling are also discussed.Comment: 30 pages, 23 figures, proceedings submitted to YKIS200

Non-Fermi liquid, unscreened scalar chirality and parafermions in a frustrated tetrahedron Anderson model

We investigate a four-impurity Anderson model where localized orbitals are located at vertices of a regular tetrahedron and find a novel fixed point in addition to the ordinary Fermi liquid phase. That is characterized by unscreened scalar chirality of a tetrahedron. In this phase, parafermions emerges in the excitation spectrum and quasiparticle mass diverges as 1/|T log^3 T| at low temperatures (T). The diverging effective mass is a manifestation of singular Fermi liquid states as in the underscreened Kondo problem. Between the two phases, our Monte Carlo results show the existence of a non Fermi liquid critical point where the Kondo effects and the intersite antiferromagnetic interactions are valanced. Singular behaviors are prominent in the dynamics and we find that the frequency (omega) dependence of the self-energy (Sigma) is the marginal Fermi liquid like, -Im Sigma \sim |omega|.Comment: 7 pages, 4 figures, 1 table, published versio