Rotating exchange field effect on the electron energy loss spectrum of black phosphorene: anisotropic blue and red shift phenomena

Abstract

How to tune optical transitions via physical perturbations is an intriguing fundamental question on the optical properties of materials. We theoretically present interesting blue and red shifts for the interband electron energy loss spectrum (EELS) in black phosphorene coupled to a magnetic material with a rotating magnetization. Employing the two-band Hamiltonian model in the presence of the rotating exchange field and the Kubo formalism, we obtain the band gap changes and the corresponding EELS functions at a certain temperature. We show that the EELS amplitude behavior is inversely proportional to the band gap changes induced by the rotating exchange field, while the specific position of the peaks in EELS function takes place at optical energies equal to the modified band gaps. We further show that depending on the polar and azimuth angles of the magnetization vector, regular and irregular blue and red shifts can emerge. Our findings report that manipulating anisotropic interband optical excitations in phosphorene through magnetic perturbations are the key for various optoelectronic applications.

Electron-phonon coupling, spin-polarized Zeeman field, and exchange field effects on the electronic properties of monolayer h-BP

“…In this section, we intend to immediately turn to the effects of proximity coupling and Zeeman magnetic field on the electronic DOS of monolayer h-BP [40,56]. In the case of the exchange field M z , the proximity effect of h-BP into a ferromagnetic semiconductor is studied.…”

“…Considering the imaginary part of the Green's function components, the electronic DOS can be calculated [7,56,[62][63][64]. Therefore, by summing over all quantum numbers which label the Hamiltonian, the normalized DOS of the system per unit cell would be expressed as…”