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The band structures of pure and hole doped La$_2$CuO$_4$ withantiferromagnetic (AFM) spin-fluctuations are calculated and compared tospectral weights of ARPES. It is shown that observations of coexisting Fermisurface (FS) arcs and closed FS pockets are consistent with modulated AFM spinfluctuations of varying wave lengths. Large variations of strong spinfluctuations make the outer part of the FS break diffuse at low doping. Thispart of the FS is suppressed at high doping when spin fluctuations are weak.The resulting superimposed spectral weight has features both from FS arcs andclosed pockets. A connection between results of ARPES, neutron scattering, andband results for the modulated AFM spin wave state, suggests that spin-phononcoupling is an important mechanism for the %pseudogap and other properties ofthe cuprates.

Bands, spin fluctuations and traces of Fermi surfaces in angle-resolved photoemission intensities for high-$T_C$ cuprates