In recent years

the properties of magnetopolaron in polar crystals have been of considerable

interest.Larsen proposed a fourth-order perturbation method to calculate the ground state energy of two-dimensional polaron in a magnetic field.Kandemir et aL.discussed the ground-state and first-excited-state energy of two-dimensional large magnetopolaron by using recently introduced squeezed Landau states.Wei

et al

.studied the cyclotron resonance mass and resonance frequency of the interface magnetopolaron using the Green’s function method.Xiu

et al

.using the variational method

studied the property of strong coupling magnetopolaron in a polar crystal slab.The energies of the ground state and the excited state were presented and the electron-surface optical (SO) phonon interactions at ground state and excited state were studied emphatically.Using Huybretch’s variational method and unitary transformation

the strong coupling between electron and surface optical (SO) phonons and the weak coupling between electron and bulk longitudinal optical (LO) phonons were studied systematically by Xia

et al

..Wang

et al

.investigated the magnetic field and temperature dependence of the properties of a magnetopolaron at the interface of polar-polar crystals in an external magnetic field by using the generalized Haga perturbation method.The properties of surface polaron in a magnetic field have been further discussed by the present authors and co-workers.Tokuda studied the property of the mean number of the optical and the piezoelectric polarons and the mean number of the acoustic and optical polarons via deformation potential by using improved variational method.However

the mean number of optical phonon of surface magnetopolarons has not been studied so far.In this paper

the properties of surface magnetopolaron which is a strong-and weak-coupling of optical phonon was discussed by using Tokuda’s improved linear combination operator and the Lagrange multiplier and the variational method.The ground state energy and the mean number of optical phonons of the strong-and weak-coupling magnetopolaron were calculated.Numerical calculations for AgCl and ZnS crystals

as an example

were performed.The relational of the vibration frequency

the ground energy and the mean number of optical phonon to magnetic field

B

and Lagrange multiplier

u

were discussed.The result illustrates that the vibration frequency λ of surface magnetopolaron will increase with increasing magnetic field

B

and Lagrange multiplier

u

the ground state energy E will increase with increasing

u

and decreasing

B

the mean number of optical phonon N will increase with increasing

u

.