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We investigate the effect of the micromagnetic exchange tensor on the magnetization switching in bi-layer rectangular dots. The micromagnetic model adopted in this work is used to calculate the in-plane and out-of-plane hysteresis loops based on the fundamental magnetic parameters of hcp CoCrPt for a wide range of elemental compositions corresponding to magnetically hard and semi-hard cases. The exchange interaction term in micromagnetic energy functional is constructed to capture the results of the first principles calculations that show large difference between the in-plane and out-of-plane constants of the micromagnetic exchange tensor for hcp Co. In our calculations we compare two cases for in-plane and perpendicular exchange constants: (a) A|| = A⊥ and (b) A|| = 0.5 A⊥, and find that the athermal coercive force for 30×30 nm bi-layer rectangular dots differs for these two cases. Further, we find that the magnetization switching changes from curling mode in the case (a) to the vortex formation in the case (b). We also find that these differences in magnetization switching become more pronounced if interface exchange between hard and soft layers is increased to the bulk value.