  We have discovered a new antiferromagnetic phase in TmNi2B2C by neutron
diffraction. The ordering vector is Q_A = (0.48,0,0) and the phase appears
above a critical in-plane magnetic field of 0.9 T. The field was applied in
order to test the assumption that the zero-field magnetic structure at Q_F =
(0.094,0.094,0) would change into a c-axis ferromagnet if superconductivity
were destroyed. We present theoretical calculations which show that two effects
are important: A suppression of the ferromagnetic component of the RKKY
exchange interaction in the superconducting phase, and a reduction of the
superconducting condensation energy due to the periodic modulation of the
moments at the wave vector Q_A.
