Orbital-Spin Structure and Coupling to Lattice in RTiO${}_3$ with R=La,Pr,Nd and Sm

The origin of the G-type antiferromagnetism (AFM(G)) and puzzling properties of RTiO${}_3$ with R=La are studied. We clarify that the crystal field from La caused by the GdFeO${}_3$-type distortion lifts the $t_{2g}$ degeneracy at Ti 3d orbitals. The lift stabilizes the AFM(G) with spin-exchange constant in agreement with neutron scattering results. The orbital-spin structures for R=Pr, Nd and Sm are also consistent with experiments. We propose that the GdFeO${}_3$-type distortion has a universal mechanism of controlling orbital-spin structure competing with the Jahn-Teller (JT) mechanism.