Symmetry of molecular wavefunction in BaBiO3 determined by q-resolved EELS

Abstract

Momentum-transfer (q) resolved electron energy loss spectroscopy is a unique technique to investigate the symmetry of electronic excitations in materials. Under small momentum-transfer conditions, the dielectric function derived from electron energy loss spectrum (EELS) is comparable to the dielectric function obtained by optical measurement. However, relatively large momentum-transfer conditions, which optical spectroscopy cannot achieve, can be met with high energy electrons and such q-resolved EELS data can provide dynamic information of the excitations as well as possible location of optically forbidden transitions.According to the Born approximation, the differential cross section of inelastic scattering can be written as:(1)where Ψo and Ψf are the initial- and final-state wave functions with energies as Eo and Ef, respectively, q is the momentum transfer. If rc is the effective radius of the excitation, then for q<1/rc, one can write:(2)For small q, the second term dominates the integral, permitting dipole-allowed transitions. For large q, the third term, which contains monopole and quadrupole transitions, increases in strength relative to the dipole transitions.