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A magnetic dipole moving parallel to a ferromagnetically interacting surface is subject to a friction force due to the conversion of kinetic energy into spin excitations. This phenomenon is studied in the framework of the classical anisotropic Heisenberg-model, using the stochastic Landau-Lifshitz-Gilbert equation. The friction force is calculated from dissipation rates, which are obtained directly from energy functions. For small velocities, magnetic friction increases linearly (like Stokes' law for laminar flow). The characteristic low- and high-temperature behavior is analyzed and explained by a relaxation time ansatz.