There is weak bulk but strong surface coupling between the electron and phonons for polar crystals in a magnetic field. In this paper

the influences of the electron interaction with both the weak-coupling bulk longitudinal optical phonons and the strong coupling surface optical phonons on the properties of the surface magnetopolaron are studied. the cyclotron-resonance frequency and the cyclotron-resonance mass of the surface polaron are derived by using improved linear combination operator method. As an example

the numerical calculation for AgCl crystal has been carried. The results show that the cyclotrou-resonance frequency and the cyclotron-resonance mass of the surface magnetopolaron will be increased with increasing magnetic field.