With the development of magneto-optical technology

the properties of the Polaron in magnetic field have been of considerable interest.Larsen proposed a novel operator method to investigate the properties of 2D Polarons.Peeters et al discussed the properties of the magnetopolaron using the Feynmann path-integral approach.Wei and co-workers studied the induced potential and the self-energy of an interface magnet-opolaron using the Green-function method.The properties of the surface magnetopolaron have been discussed by the method of a linear-combination operator and a perturbation by the present authors and co-workers.In fact

so far research on the polaron has been restricted to approximation and calculation where the electron spin and the interaction between phonons of different wave vectors in the recoil process are neglected.There is weak bulk but strong surface coupling between the electrons and phonons for semi-infinite TIBr crystal in a magnetic field.So far

research into this has been very scarce.The purpose of this present paper is to explore the effects of the electron spin and the interaction between phonons of different wave vectors in the recoil process on the properties of the surface polaron in magnetic field.With both the weak coupling between the electron and bulk LO phonon and the strong coupling between the electron and SO phonon included

an expression for the effective Hamiltonian of the surface magetopolaron is obtained.With considering the electron spin and the corresponding interaction

the influence on the effective Hamiltonian

vibration frequency

induced potential and effective interaction potential of the surface magnetopolaron in semi-infinite TIBr crystal are investigated by a linear combination operator and perturbation method.Numerical calculations for a TIBr crystal

as an example

are performed

and some properties of the vibration frequency and the induced potential of the surface magnetopolaron are discussed.