We performed magnetic inelastic neutron-scattering experiments on La1.93Sr0
.07CuO4 over a wide range of omega and T; 2 less than or equal to omega les
s than or equal to 44meV and 1.5 less than or equal to T < 300 K. The dynam
ic susceptibility <chi>" (q, omega) of this underdoped high-T-c superconduc
tor (T-c = 17K) is characterized by broad, incommensurate peaks. Here, the
incommensurate wavevector delta (omega) is approximately 0.07 reciprocal la
ttice units at low T and omega. The superconducting phase does not possess
an observable gap in the spin excitation spectrum down to at least 2 meV. S
caling behavior is demonstrated for the Q-integrated energy spectrum chi "(
omega)(T) with respect to (omega /k(B)T). This scaling establishes a connne
ction between the magnetic excitations of the compositions on either side o
f the insulator-superconductor boundary in the La2-xSrxCuO4 phase diagram.
We note a possible cross-over from an incommensurate to a commensurate resp
onse for omega > 20 meV or T > 300 K.