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.