We discuss new types of nonlinear time-noninvariant optical susceptibi
lities that arise in crystals due to magnetic ordering. We show that d
ifferent contributions to the nonlinear optical susceptibilities may c
oexist in magnetic materials that lead to a number of unusual optical
effects. Experimental data are given for magnetoelectric antiferromagn
et Cr2O3, piezomagnetic alpha-Fe2O3 and ferroelectric antiferromagnet
YMnO3. We developed a novel method to study antiferromagnetic domains
by use of nonlinear spectroscopy. With use of the novel technique we c
onfirm that in Cr2O3 in the spin-flop phase the antiferromagnetic vect
or is oriented along the twofold axis. in YMnO3 we observed an unusual
behaviour of antiferromagnetic domains which we explain by the entrop
y contribution to the domain wall energy.