A measurement of spin correlation in tt¯ production is presented using data collected with the ATLAS detector at the Large Hadron Collider in proton-proton collisions at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 20.3 fb-1. The correlation between the top and antitop quark spins is extracted from dilepton tt¯ events by using the difference in the azimuthal angle between the two charged leptons in the laboratory frame. In the helicity basis the measured degree of correlation corresponds to Ahelicity=0.38±0.04, in agreement with the standard model prediction. A search is performed for pair production of top squarks with masses close to the top quark mass decaying to predominantly right-handed top quarks and a light neutralino, the lightest supersymmetric particle. Top squarks with masses between the top quark mass and 191 GeV are excluded at the 95% confidence level.