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The magnetic Laplacian with a step magnetic field has been intensivelystudied during the last years. We adapt the construction introduced byBonnaillie-No\"el, Fournais, Kachmar and Raymond to prove the existence ofbound states of a new effective operator involving a magnetic step field on adomain with an almost flat magnetic barrier. This result emphasizes the factthat even a small non-smoothness of the discontinuity region can cause theappearance of eigenvalues below the essential spectrum. We also give an examplewhere this effective operator arises.

Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers