There is weak bulk but strong surface coupling between the electron an
d phonons for polar crystals in a magnetic field. In this paper, the i
nfluences 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 polaron in a magnetic field a
re studied. The effective Hamiltonian of the surface polaron is derive
d by using a linear-combination operator method. Numerical calculation
s on the AgCl crystal, as an example, are performed, and some properti
es of the vibration frequency and the effective interaction potential
of the surface polaron in a magnetic field are discussed.