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We investigate the entanglement entropy of a massive scalar fieldnonminimally coupled to spacetime curvature, assuming a static, sphericallysymmetric background. We discretize the field Hamiltonian by introducing alattice of spherical shells and imposing a cutoff in the radial direction. Wethen study the ground state of the field and quantify deviations from area lawdue to nonminimal coupling, focusing in particular on Schwarzschild-de Sitterand Hayward spacetimes, also discussing de Sitter spacetime as a limiting case.We show that large positive coupling constants can significantly alter theentropy scaling with respect to the boundary area, even in case of small fieldmass. Our outcomes are interpreted in view of black hole entropy production andearly universe scenarios.

Entanglement area law violation from field-curvature coupling