Dipole-forbidden excitations in electron-energy-loss spectroscopy

Is magnetic chiral dichroism feasible with electron vortices?

“…Here, we discuss the dichroic L 2,3 dipole transitions in the 3d ferromagnets -a standard for EMCD experiments in the electron microscope [12] -mediated by an incident electron with topological charge.The most dominant contributions to the electron energy loss spectrometry (EELS) signal are electric dipole transitions. Higher multipole transitions have low transition amplitudes contributing less than 10 % at the scattering angles of < 20 mrad relevant in EELS [13][14][15].In case of an L edge dipole transition which changes the magnetic quantum number of an atom located at the vortex center by µ, an incident electron ψ m (r) = e imϕ f (r) with topological charge m transforms into an outgoing wave [16] ψ m,µ (r) = e i(m+µ)ϕr f µ (r)f (r),where ϕ r is the azimuthal angle, and(2) with j 1 (Q) ELSj the matrix element of the spherical Bessel function between initial and final radial atomic wave functions, and Q 2 = q 2 + q 2 E . Here, q is the transverse scattering vector that relates to the experimental scattering angle θ as q = k 0 θ, andhq E is the scalar difference of linear momenta of the probe electron before and after inelastic interaction, also known as the characteristic momentum transfer in EELS [17].When there are several transition channels at the same energy, the outgoing probe electron is in a mixed state, described by a reduced density matrix.…”

Some effects of electron channeling on electron energy loss spectroscopy

“…This is consistent with the observations of electric monopole transitions by Ritsko et al [37] and calculations using the mixed dynamic form factor for large angle scattering by Nelhiebel et al [38] (a small channeling peak is an accumulation of large incident angles producing large angle scattering into a on-axis detector). Auerhammer and Rez [39] have also calculated non-dipole transitions (including the monopole term) in the Silicon L 23 edge produced by large momentum transfer. For small angle scattering (smallq) and plane wave incidence, the matrix element expðiq ÁrÞ $ 1 þ iq Á r þ Á Á Á is vector-like which leads to dipole selection rules (Section 3.5d of Ref.…”

High Resolution Optical and Vibrational Spectroscopy with Low Loss EELS

“…While it is possible to perform subatomic resolution electron energy loss spectroscopy (EELS) at unprecedented energy resolution, with ever improving aberration correctors and monochromators, it is argued that low loss features can be severely delocalized (up to hundreds of Ångstroms for optical excitations and millions of Ångstroms for vibrational states) which would suggest poor prospects for atomic resolution imaging [1]. Here, we go beyond the traditional multipole expansions and construct an exact treatment of the near-field inelastic scattering that predicts atomic-scale resolution for monopolar optical and vibrational excitations.While the dipole approximation succeeds for high loss, large probe experiments, very-low loss experiments enter a regime where multipole expansions converge poorly and no longer hold [2,3]. By removing the multipole approximation and implementing the exact transition potential, we show that it is possible to image surprisingly low loss transitions at the Ångstrom scale.…”