With the development of the theory of the solid science and experimental technology

the research the properties of magnetopolaron in crystals has been of considerable interest.Peeters and Devreese studied the properties of magnetopolaron using a Feynman’s path integral method.Wei and co-workers studied the induced potential and the self-energy of an interface magentopolaron interacting with bulk LO phonons as well as interface optical phonons using the Green function method.Zorkani

et al

.calculated the ground state energy of bound magnetopolaron using variational method.If consider the interaction between phonons of different wave vectors in the recoil process

the magnetic field dependence of cyclotron resonance frequency

induced potential

the effective interaction potential

and the cyclotron-resonance mass of the surface magnetopolaron is obtained by using a linear combination operator and perturbation method by one of the authors.The magnetic field and temperature dependence of the mass of a surface magnetopolaron in polar crystals has been discussed by a linear combination operator method by present authors.Most polar crystals are diatomic and cubic and their crystal structure belongs to NaCl

CsCl or ZnS type.The research of these methods only was restricted to the case of crystals having only one mode of the longitudinal optical(LO)phonon.The properties of crystals have been studied by a great variety 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

there are two LO phonon modes.SiO

2

GaAs

1-

x

P

x

and a large number of perovskites(SrTiO

3

BaTiO

3

LiNbO

3

etc

.)have more than two modes.The polaron problem with many LO phonon branches has been studied.The properties of polaron and magnetopolaron in polyatomic polar crystals are discussed by the method of a linear combination operator by one of the authors.However

the influences of magnetic field on the properties of ground state and excited state of a polaron in polyatomic crystals has not been investigated so far.In this paper

the excitation energy and the mean number of phonons in the cloud around the electron of magnetopolaron in a polyatomic crystal studied for the first time by a linear combination operator and a simple unitary transformation methods.The results show that the excitation energy and the mean number of phonons of a magnetopolaron in polyatomic crystals not only includes the coupling contribution between the electron and the different LO phonon branches

but also exists an extra contribution due to crossed terms between the different phonon branches.