Angle-resolved photoemission spectroscopy (ARPES) is one of most powerful techniques to unravel the electronic properties of layered materials and in the last decades it has lead to a significant progress in the understanding of the band structures of cuprates, pnictides and other materials of current interest. On the other hand, its application to Mott-Hubbard insulating materials where a Fermi surface is absent has been more limited. Here we show that in these latter materials, where electron spins are localized, ARPES may provide significant information on the spin correlations which can be complementary to the one derived from neutron scattering experiments. Sr$_2$Cu$_{1-x}$Zn$_x$O$_2$Cl$_2$, a prototype of diluted spin $S=1/2$ antiferromagnet (AF) on a square lattice, was chosen as a test case and a direct correspondence between the amplitude of the spectral weight beyond the AF zone boundary derived from ARPES and the spin correlation length $xi$ estimated from $^{35}$Cl NMR established. It was found even for correlation lengths of a few lattice constants a significant spectral weight in the back-bended band is present which depends markedly on $xi$. Moreover the temperature dependence of that spectral weight is found to scale with the $x$ dependent spin-stiffness. These findings prove that ARPES technique is very sensitive to short-range correlations and its relevance in the understanding of the electronic correlations in cuprates is discussed.
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