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Tunnelling of electrons in graphene-based junctions is studied theoretically.Graphene is assumed to be deposited either directly on a ferromagneticinsulator or on a few atomic layers of boron nitride which separate graphenefrom a metallic ferromagnetic substrate. Such junctions can be formed byappropriate external gating of the corresponding system. To describe low-energyelectronic states near the Dirac points, certain effective Hamiltoniansavailable in the relevant literature are used. These Hamiltonians includestaggered potential and exchange interaction due to ferromagnetic substrates.Tunnelling in the systems under consideration is then spin-dependent. The mainfocus is on Klein tunnelling and also on the group delay and the associatedHartman effect. The impact of a gap induced in the spectrum at the Dirac pointson tunnelling is analysed in detail.

Klein tunnelling and Hartman effect in graphene junctions with proximity exchange field