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The effect of the crystallinity and the grain texturing of CoPt hard layers on exchange coupled Fe/CoPt soft/hard magnetic systems was studied using gradient thickness multilayer thin films. We have studied the hard layer structures by transmission electron microscopy and x-ray diffraction, and characterized the exchange coupling interaction through magnetization loops obtained by the magneto-optical Kerr effect measurement. We found that exchange coupling strongly depends on the crystalline characteristics of the CoPt hard layer. There is correlation between the mixture of different grain orientations of the CoPt hard layer and coupling efficiency. In particular, interlayer coupling is enhanced when there is only one orientation, namely, the L10 CoPt structure with its c-axis inclined at 45° with respect to the substrate plane. An increased degree of mixture of the latter with the in-plane-c-axis L10 CoPt structure is detrimental to obtaining one-phase-like magnetization loops. The present work points to the importance of controlling the crystalline properties of the hard layer in order to enhance the maximum energy product (BH)max in hard/soft nanocomposite magnets.