  Antiferromagnetic resonance (AFMR) of BaCu2Si2O7 and a microscopic theory of
the magnetic anisotropy of spin 1/2 chain compounds with folded CuO3 geometry
being in good agreement with the available data are presented. The AFMR studies
at 4.2 K show the existence of two gaps (40 and 76 GHz) at zero magnetic field
and of two spin re-orientation transitions for H||c. The microscopic origin of
the two gaps is shown to be Hund's rule coupling which leads to a "residual
anisotropy" beyond the compensation of the Dzyaloshinskii-Moriya term by the
symmetric anisotropy which would be valid without Hund's coupling.
