High-quality, insulating antiferromagnetic thin films and multilayers offer possibilities for new studies of exchange mechanisms at surfaces and across interfaces between dissimilar magnetic materials. Using a microscopic theory, we study long-wavelength spin waves to answer two questions: ͑1͒ Can we determine accurate values for surface and interface exchange from spin-wave frequencies and ͑2͒ can we obtain an effectivemedium description which properly reproduces all the spin-wave excitations

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... f the antiferromagnetic structure. We find that the frequencies of surface and interface modes are particularly sensitive to interface exchange values, even when the spin-wave frequencies for the two materials are far apart and little coupling is expected. We also present a method for calculating the dynamic magnetic response of a superlattice structure that avoids a serious approximation made in conventional effective-medium theory. Our effective-medium formulation gives results in excellent agreement with microscopic calculations and will be useful for characterizing thin antiferromagnetic films as well as large multilayers. Susceptibilities are derived which can be directly applied to calculations for infrared reflectivity experiments.