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Micromagnetic simulation results on Co-based recording media are presented which examine the impact of a modified near-neighbor exchange interaction between grains of the form J z (Mi z Mj z), reflecting the hexagonal crystal symmetry. Both out-of-plane and in-plane M-H loops are calculated, with an emphasis on a model fit to data reported by Wang . [IEEE Trans. Magn, vol. 43, p. 682 (2007)] on exchange coupled composite perpendicular media. The principle effect of J z is to increase the coercivity and slope of both hard and soft layers. Improved agreement with experimental data for the in-plane loops is achieved by assuming a substantial value for J z . Possibilities for measurement of Jz through spin-wave excitations are discussed. Thermal fluctuation effects are also examined through simulations of the magnetization vs temperature.