Inelastic neutron scattering measurements have been performed on high
quality single crystals of La2-xSrxCuO4 in order to study the spin dyn
amics of this compound. In addition to the well-established incommensu
rate magnetic response, we show the existence of a new set of low ener
gy excitations present in the whole superconducting region of the phas
e diagram. This new feature of the dynamical cross section is characte
rized; below about 10 K, by very short range (similar to 3 lattice spa
cing) antiferromagnetic correlations and by a low energy scale of simi
lar to 1 meV. At higher temperatures these fluctuations become nearly
Q-independent. Different possible origins of these new spin correlatio
ns are discussed.