3.3 Optical properties

For a detailed work of Rh2MnX alloys, we have also calculated the variation of the several optical properties versus the photon energy e.g. the dielectric function, optical conductivity, refractive index, loss function, absorption and reflectance. Present optical calculations were performed along with the [100] polarization under energies up to 30 eV.
Fig. 5 denotes complete optical properties of Rh2MnTi alloy where other optical spectra of remaining alloys are displayed together to make a benchmark between all computed alloys. The absorption spectrum of any material signifies the region at which the maximum photo excitation occurs [48,49]. As well, it provides useful data on the optimum solar energy conversion efficiency. The variation of absorption in Fig. 5 for Rh2MnTi and Fig.6 for other alloys exhibit identical absorption nature under incident energy. The absorption peaks of all computed alloys give two substantial maxima around 5 eV and 25 eV and imply slight or rapid falls after their last maximum.
Reflectivity offers the part of the incident energy of a wave reflected from the surface of any material [48,49]. The reflectivity peaks for Rh2MnTi in Fig. 5 and other alloys in Fig.7 show similarities again for their first maximum peaks at 5 eV. Further, under increasing energy, second maximums of the reflectivity peaks of Rh2MnTi, Rh2MnZr and Rh2MnSc appear around 22.5 eV. Unlike them, second maximum reflectivity peaks of Rh2MnHf arise at 20 eV and Rh2MnZn at 27.5 eV in Fig.7. Hence, we can easily state that the reflectivity characteristics of studied alloys strongly depend on the alloying elements.
As being another key optical property, the complex dielectric function ε(ω) with the relation ε(ω) = εr(ω) + εi(ω) explains the optical properties of a medium under different photon energies where εr(ω) stand for the real part (Re) and εi(ω) denotes the imaginary (Im) part of the dielectric function [48,49]. Fig. 8 shows the Re and Im parts of the dielectric function of all studied alloys. Including the dielectric function of Rh2MnTi in Fig.5, real and imaginary parts of dielectric functions of Rh2MnHf and Rh2MnZn alloys begin with the negative values where the peak positions are different and have discrete height positions. In other words, real and imaginary parts of these alloys are smaller than zero under 2.5 eV. This specific result indicates the presence of metallic behavior. After the energy values bigger than 2.5 eV, they become positive and follow the unity for the entire energy range. On the other side, real and imaginary parts of the dielectric function of Rh2MnSc and Rh2MnZr alloys keep their positive character from beginning to end with different peak positions and track the unity under energy range up to 30 eV.
The optical conductivity of any material closely relates to dielectric function. It is also an effective tool to measure the electronic states of the material that proposes information about the optical excitations in a given material [48,49]. Fig. 9 represents the variation of real and imaginary parts of the optical conductivity with a change in the energy up to 30 eV for studied alloys. In general, with different peak positions, all addressed alloys show analogous conductivity behavior where real and imaginary parts of the conductivity always appear in the positive region for all alloys.
Fig. 10 illustrates the refractive indexes (n and k) of considered alloys as a function of energy. Both the real part of the refractive index (n) and the imaginary part of the refractive index (also known as extinction coefficient (k)) located at different peak positions show diverse characteristics under energy. For example, Rh2MnTi (Fig.5) and Rh2MnHf alloys always preserve their positive tendency along with the whole energy range. Unlike, other alloys (Rh2MnSc, Rh2MnZn and Rh2MnZr) experience a sluggish drop to zero for energies bigger than 20 eV and subsequently follow the positive regime after this energy value.
The electron energy loss function is a noteworthy feature of materials associates with the energy loss of a moving electron in a material [48,49]. The existing peaks in the electron energy loss function symbolize the resonance frequency which is also recognized as plasma frequency. For any material, the material acts like a dielectric above resonance frequency and below this limit it behaves like a metal. Fig. 11. implies the variation of the electron energy loss function against photon energy for computed alloys. Except for the fluctuating loss function of Rh2MnHf alloy, all other alloys exhibit a clear and sharp peak after 20 eV. This energy region above 20 eV also relates to the cooperative vibration of valance electrons and proves the plasma oscillations of Rh2MnTi (Fig.5), Rh2MnSc, Rh2MnZn and Rh2MnZr alloys.