  Three independent contributions to the magnetically induced spontaneous
polarization of multiferroic TbMn2O5 are uniquely separated by optical second
harmonic generation and an analysis in terms of Landau theory. Two of them are
related to the magnetic Mn3+/4+ order and are independent of applied fields of
up to 7 T. The third contribution is related to the long-range
antiferromagnetic Tb3+ order. It shows a drastic decrease upon the application
of a magnetic field and mediates the change of sign of the spontaneous electric
polarization in TbMn2O5. The close relationship between the rare-earth
long-range order and the non-linear optical properties points to isotropic
Tb-Tb exchange and oxygen spin polarization as mechanism for this rare-earth
induced ferroelectricity.
