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We report high-resolution resonant inelastic x-ray scattering (RIXS)measurements of the collective spin fluctuations in three compositions of thesuperconducting cuprate system La2-xSrxCuO4. We have mapped out the excitationsthroughout much of the 2-D (h,k) Brillouin zone. The spin fluctuations inLa2-xSrxCuO4 are found to be fairly well-described by a damped harmonicoscillator model, thus our data allows us to determine the full wavevectordependence of the damping parameter. This parameter increases with doping andis largest along the (h, h) line, where it is peaked near (0.2,0.2). We haveused a new procedure to determine the absolute wavevector-dependentsusceptibility for the doped compositions La2-xSrxCuO4 (x=0.12,0.16) bynormalising our data to La2CuO4 measurements made with inelastic neutronscattering (INS). We find that the evolution with doping of the intensity ofhigh-energy excitations measured by RIXS and INS is consistent. For the dopedcompositions, the wavevector-dependent susceptibility is much larger at(1/4,1/4) than at (1/2,0). It increases rapidly along the (h,h) line towardsthe antiferromagnetic wavevector of the parent compound (1/2,1/2). Thus, thestrongest magnetic excitations, and those predicted to favour superconductivepairing, occur towards the (1/2,1/2) position as observed by INS.

Anisotropic damping of the spin fluctuations in doped La2-xSrxCuO4 studied by resonant inelastic x-ray scattering