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Interplay between orbital and spin degrees of freedom is theoreticallystudied for the phase transition to the spin-singlet state with latticedimerization in pyroxene titanium oxides ATiSi2O6 (A=Na, Li). For the quasione-dimensional spin-1/2 systems, we derive an effective spin-orbital-latticecoupled model in the strong correlation limit with explicitly taking account ofthe t_2g orbital degeneracy, and investigate the model by numerical simulationas well as the mean-field analysis. We find a nontrivial feedback effectbetween orbital and spin degrees of freedom; as temperature decreases,development of antiferromagnetic spin correlations changes the sign of orbitalcorrelations from antiferro to ferro type, and finally the ferro-type orbitalcorrelations induce the dimerization and the spin-singlet formation. As aresult of this interplay, the system undergoes a finite-temperature transitionto the spin-dimer and orbital-ferro ordered phase concomitant with theJahn-Teller lattice distortion. The numerical results for the magneticsusceptibility show a deviation from the Curie-Weiss behavior, and wellreproduce the experimental data. The results reveal that the Jahn-Teller energyscale is considerably small and the orbital and spin exchange interactions playa decisive role in the pyroxene titanium oxides.Comment: 13 pages, 9 figures; final version. Text, Fig.1, and references are  revised. To appear in Phys. Rev.

physical review. b, condensed matter and materials physics

Orbital and spin interplay in spin-gap formation in pyroxene<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Ti</mml:mi><mml:msub><mml:mi mathvariant="normal">Si</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:…

Orbital and spin interplay in spin-gap formation in pyroxeneATiSi2O6(A