The cyclotron resonance is a standard technology that determines the conductive electron and hole mass in solids. Usually the effective mass of electron is decided according to the cyclotron-resonance frequency confirmed by experiment. It should be noted that the split of cyclotron-resonance spectrum is strongly affected by the coupling of electron-phonon. Many scholars have paid much attention to the cyclotron resonance of polaron. Many investigations on the properties of the magnetopolaron were performed by means of Feynman’s route integration

Larsen’s original operator

Green function

linear combination operator

variation

bound Landau state and perturbation method. At investigating the properties of the crystals

many methods was only confined to the one LO phonon branch

however

in the polyatomic crystals containing three and more atoms

with several atoms per unit cell

there are more than one LO phonon. The polar problem of the crystals containing many LO slab has been investigated. In recent years

the polaron problem with many LO phonon branches has been investigated also. However

the magnetopolaron in polyatomic polar crystals has rarely been investigated. Recently Hu

et al

. discussed the properties of the surface magnetopolaron and bulk magnetopolaron in polyatomic polar crystals by means of a linear combination operator.But the properties of polaron of polyatomic crystals in magnetic field has not investigated so far. In this paper

the vibrational frequency and effective mass of the weak-coupling magnetopolaron in the polyatomic semi-infinite polar crystals were studied through a linear combination operator and unitary transformation and by using Lagrange’s multiplier. When the electron is approaching infinitely to the surface of crystals

the vibrational frequency and effective mass of the magnetopolaron is identical with the surface magnetopolaron. When the electron is situated in the depth of crystals

the vibrational frequency of the magnetopolaron is not changed

but effective mass of the magnetopolaron related to its depth as well as the coupling constant of LO-electron.