  The space and time symmetry breaking at magnetic phase transitions in
multiferroics results in a number of strongly pronounced optical effects. Our
high-resolution spectroscopic study of 3d- excitons in a complex
multi-sublattice magnetoelectric CuB2O4 demonstrates that, among those, a large
antiferromagnetic linear dichroism is observed which is highly
sublattice-sensitive to subtle changes in the spin subsystems. We prove that
the discovered linear dichroism is related microscopically to the magnetic
Davydov splitting of the exciton states. We announce a novel magnetic phase
transition and argue that an elliptical spiral structure rather than a simple
circular helix is realized in the incommensurate phase, these findings being
overlooked in previous studies by optical and other techniques. We claim that
this spectroscopic method can be effectively applied to other materials for
revealing hidden features of magnetic structures and phase transitions.
