With the development of solid science theory and experimental technology

the properties of surface magnetopolaron in crystals have been of considerable interest. Many investigators studied the properties of surface magnetopolaron by means of various theoretical methods. Larsen proposed a novel fourth-order perturbation method to investigate the properties of 2D magnetopolaron. Wei and co-workers calculated the induced potential and the self-energy of an interface magnetopolaron interacting with bulk LO phonons as well as interface-optical phonons using the Green-function method. The properties of surface magnetopolaron in semiconductor CdF

2

and CdTe were investigated by means of a linear combination operator and a perturbation method by one of the authors.Most polar crystals are diatomic and cubic and their crystal structure belongs to NaCl

CsCl or ZnS type. In these crystals there is one mode of the longitudinal optical(LO) phonon. The properties of crystals have been studied by a great variety of techniques

in the case

of crystals having only one LO phonon branch. However

a large number of polar crystals

with several atoms per unit cell

have more than one LO phonon branch. For example

in cuprite such as CuO

2

GaAs

1-x

P

x

and a large number of perovskites (SrTiO

3

BaTiO

3

LiNbO

3

) there are more than two modes. In recent years

the problem with many LO phonon branches has been investigated. The ground state energy of surface magnetopolaron in polyatomic polar crystals are calculated using linear combination operator method by one of the authors.In the early 1970s

Huybrechts investigated the internal excited state of the bulk optical polaron by using linear combination operator method. Gu

et al

. apply the Larsen method to investigate the properties of the ground-and excited-state energies of a magnetopolaron in a quantum well and in a slab of polar crystal. Kandemir

et al

. discussed the ground-state and first-excited state energy of two-dimensional large magnetopolaron by using recently introduced squeezed Landau states. The energy of the first internal excited state of the magnetopolaron were calculated by using linear combination operator method by one of the authors. However

the internal excited state of surface magnetopolaron in polyatomic polar crystals has not been investigated so far. In this paper

the properties of internal excited state of the surface magnetopolaron in polyatomic polar crystals are studied by using linear combination operator and unitary transformation methods.The results show that in a strong magnetic field the ground state energy

E

0

the first internal excited state energy

E

1

and the excited energy △

E

for the strong-coupling surface magnetopolaron in polyatomic polar crystals increases with increasing magnetic field

B

whereas for the weak magnetic field the ground state energy

the first internal excited energy and the excited energy contain an extra contribution due to crossed terms between the different phonon branches.