Type-D solutions of the Einstein-Euler-Heisenberg nonlinear electrodynamics with a cosmological constant

We establish the Einstein-Euler-Heisenberg system of field equations with cosmological constant (EEH-?) for type -D metrics within the null tetrad formalism. Then we determine all type -D solutions to the EEH-? equations; among the derived solutions are the Einstein-Euler-Heisenberg-? generalizations of the Bertotti-Robinson, Reissner-Nordstrom, Newman-Unti-Tamburino-B (NUT-B)(+), and Kerr-Newman solutions. Moreover it is shown that the (static) C-metric is not compatible with the Euler-Heisenberg electrodynamics.