The magnetic molecular conductor lambda-(BETS)(2)FeCl4 shows metal-insulator (MI) transition and antiferromagnetic (AF) transition simultaneously at T-MI similar to 8.3 K. In its metallic phase, two Fermi surfaces coexist, and the one has good nesting, and the other has bad nesting. Although a scenario of the MI transition by the formation and stabilization of a spin-density-wave (SDW) AF order is likely, it is not straightforward due to the existence of the bad nesting Fermi surface. In this paper, we propose a novel mechanism for the MI transition motivated by this material. Our proposal is based on the square-lattice two-band t - t' - U Hubbard model at half-filling, and we examine this mechanism in the ground state. As the key part of our mechanism, we incorporate the interband exchange interaction between the band A with good nesting Fermi surface and the band B with bad nesting Fermi surface. We analyze B, incorporating the electronic correlation effect into the quasi-particle weight by the slave-rotor approach. In this model, as the value of U/t increases, the SDW state in A induces another SDW state in B via the interband exchange interaction. As a result, this exchange interaction significantly decreases the value of U/t required for the MI transition.
