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The study of microscopic effects on the dispersion of surface magnetoplasmon polaritons is important. We use the collisionless Vlasov equation and Maxwell’s equations to evaluate the dielectric tensor for evaluating the dispersion relations of surface magnetoplasmon polaritons. We treat the case in the Voigt geometry assuming a semi-infinite dielectric medium. The direction of the magnetic field is considered parallel to the surface and perpendicular to the propagation vector k. The analysis shows the influence of additional microscopic kinetic effects. Standard Drude model results are retrieved in the absence of these effects.