In strong magnetic fields up to 20 T the magnetoelectric effect (ME) has be
en measured in the tetragonal antiferromagnets R2CuO4, R = Gd, Sm, and Nd w
hich are parent compounds for high-T-c superconductivity. For the Gd2CuO4 a
nd Sm2CuO4 compounds a symmetry analysis yields that the ME effect is assoc
iated with the antiferromagnetically ordered rare earth subsystem. From the
magnetic field and temperature dependence of the ME effect in Gd2CuO4 some
very detailed conclusions can be drawn about the nature of the magnetic or
dering which appear to be in agreement with the magnetic structure revealed
in this compound. For Sm2CuO4 in addition to the ME effect a distinct ferr
oelectric behaviour has been observed which is only compatible with a lower
crystal symmetry than it has been thought to be. It raises a question of w
hether superconductivity in the Ce doped Sm2CuO4 coexists with ferroelectri
city. The ME-effect data in high magnetic fields show evidence for magnetic
phase transitions, associated with a rearrangement of the intrinsic rare e
arth magnetic structure. From the obtained (H,T)-phase diagrams of Gd2CuO4
and Sm2CuO4 critical exponents (beta(Gd) approximate to 0.4 and beta(Sm) x
0.5) were found and it can be concluded that the intrinsic ordering of the
rare earth magnetic subsystem is of 3-dimensional character. In the case of
Nd2CuO4, the adopted crystal and magnetic structure of this compound rules
out any kind of ME-effect. Nevertheless, we have observed some weak but di
stinct ME response, which suggests the existence of a spontaneous structura
l distortion within the CuO2 planes.