Orbital-spin structure and lattice coupling in [formula presented] where [formula presented], [formula presented], [formula presented], and [formula presented]

The origin of the G-type antiferromagnetism [AFM(G)] and puzzling properties of [Formula presented] with [Formula presented] are studied. We clarify that the crystal field from La caused by the [Formula presented]-type distortion lifts the [Formula presented] degeneracy at Ti [Formula presented] orbitals. The lift stabilizes the AFM(G) with spin-exchange constant in agreement with neutron-scattering results. The orbital-spin structures for [Formula presented], Nd, and Sm are also consistent with experiments. We propose that the [Formula presented]-type distortion has a universal mechanism of controlling orbital-spin structure competing with the Jahn-Teller (JT) mechanism.