Electronic band profiles and magneto-electronic properties of ternary XCu₂P₂ (X = Ca, Sr) compounds: insight from ab initio calculations

3.1 Structural properties

In this section XCu₂P₂ (X = Ca, Sr) compounds are optimized in the tetragonal structure with space group I4/mmm (139). Along with this section we have purposed in addition to GGA, the GGA+U formalism in the FM phase. We have optimized our studied compounds in three different phases, namely paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM). Interestingly, the studied compounds stabilize in the FM phase as predicted from Figure 2. To further determine the material structure performance, we have computed the structural parameters such as lattice parameter a (Å), bulk modulus, B (GPa), and pressure derivative (B^p) through the volume optimization process in the Birch Murnaghan's equation of state [25] in Table 1. The lowest energy state is called the ground state (stable state) energy and the volume correspond to this energy is called optimized volume. It is seen from Table 1 that the computed lattice constants and bulk moduli increases if we move down the group from Ca to Sr, which means that the size of the unit cell increases and the substitution of Ca with Sr forced the hardness of the materials. The negative values of the energy difference between ferromagnetic and anti-ferromagnetic phase predicted in Table 1 also support the ferromagnetic phase of these compounds. To the date there is no experimental/theoretical data available in the literature for the studied compounds to be compared with our present results, therefore further experiment could test these results.

Figure 2:

Optimization plots showing energy verses volume for XCu₂P₂ (X = Ca, Sr).

3.2 Electronic properties

The electronic nature of XCu₂P₂ (X = Ca, Sr) compounds are investigated by computing the electronic band structure and density of states (DOS). For the analyses of band structure of these compounds GGA+U scheme in the ferromagnetic phase were adopted. The electronic energy band structure of XCu₂P₂ (X = Ca, Sr) compounds in the tetragonal structure of both spin channels with optimized lattice parameters along with the high symmetry points within the first Brillion zone are exhibited in Figures 3a and 3b respectively. Majority (spin up) and minority (spin dn) spin states in both figures are indicated on left side and right side respectively. In view of Figure 3a, the conduction band (CB) minimum and valance band (VB) maximum of CaCu₂P₂ crosses the Fermi level E_f along Γ and H direction in both spin channels. While in Figure 3b for SrCu₂P₂ compound many of them just cross the Fermi level in both spin channels. Moreover, the conduction bands overlap with the valence band near the Fermi level for both compounds. As a result, clearly no noticeable band gap are examined and these compounds behave as a metal, in the ferromagnetic phase. The gross features of the band structures of CaCu₂P₂ and SrCu₂P₂ are nearly same.

Figure 3:

a. Band structure of CaCu₂P₂ in spin polarized calculations in both modes calculated using GGA+U. b. Band structure of SrCu₂P₂ in spin polarized calculations in both modes calculated using GGA+U.

To further extend the electronic properties of these compounds we have evaluated the total (TDOS) and partial (PTDOS) densities of states of XCu₂P₂ (X = Ca, Sr) compounds. The TDOS and PTDOS of XCu₂P₂ are shown in Figure 4. As can be seen form Figure 4 that the TDOS has a fixed value at the Fermi level E_f, around 1.0 and 1.8 states per electron volt per unit cell, for CaCu₂P₂ and SrCu₂P₂ compound respectively. CaCu₂P₂ is small contribution as compared to SrCu₂P₂ at the E_f. The DOS at the E_f increases considerably due to the substitution of Ca by Sr. The facts of the peak structures in the TDOS and PDOS for CaCu₂P₂ and SrCu₂P₂ are nearly comparable. One remarkable difference is that the relative heights in the DOS at the VB and Fermi level E_f for SrCu₂P₂ are dominated as compared to CaCu₂P₂. The dominant states in these compounds are due to Ca-d, Cu-d, P-p and Sr-d, Cu-d, P-p states for CaCu₂P₂ and SrCu₂P₂ respectively in both spin channels (up and down). Cations (Ca, Sr) and anion (P) are situated in CB and VB dominantly in both spin types. The occupied valence bands (VB) usually spread from −7.8 eV to the Fermi level E_f for CaCu₂P₂ compound, while for SrCu₂P₂ compound the VB spreads from −6 eV to −4 eV dominantly in both spin types.

Figure 4:

DOS plots for ternary compound CaCu₂P₂ and SrCu₂P₂ in both the spin directions using GGA+U.

The TDOS are not symmetrical due to exchange splitting occur in both of the compounds. The contributions of d (Cu) states are dominantly buried in VB for both compounds which are not the same like the DOS of rare earth metal (Ca, Sr). High sharp peaks of d (Cu) states are observed in VB in both compounds. In the VB regime, we determine the existence of hybridization occur between Cu 3d and P 3p states. Examination of the PDOS shows that the DOS for XCu₂P₂ at the Fermi level originates mainly from the hybridized contributions from the Cu 3d and P 3p electronic orbitals. Hybridization for FM is important for partial d-band filling on account of the super or double exchange. In these FM states super exchange couplings occur due d states which are isolated from the E_f level [15]. These plots show metallic character in both spin directions.

3.3 Magnetic properties

To get more information about the magnetic properties of XCu₂P₂ (P = Ca, Sr) compounds, we have computed the total and atomic magnetic moments of XCu₂P₂ (P = Ca, Sr) in Table 2. Here we have used GGA+U scheme, so the function of the U parameter appears to improve the localization of transition-metal element (Cu). It is evident from Table 2 that in both compounds, CaCu₂P₂ and SrCu₂P₂ the most important regions of the total magnetic moments are due to d (Cu), p (P) and d (Sr), p (P) orbitals respectively. To obtain insight into the atomic magnetic moments, it can be seen that the magnetic moments of the Cu and P atoms in CaCu₂P₂ are 0.10940 μ_B and 0.00546 μ_B, respectively which are parallel to the magnetic moments of Ca atom, and SrCu₂P₂ compound the magnetic moment of Cu atom is −0.00286 μ_B, which is anti-parallel to the magnetic moments of Ca and P atoms. As a result of the magnetic moment analysis given in Table 2. The total magnetic moment of each cell, m_c, for each of the compound, as well as their individual atomic magnetic moments, are given in Table 2. The magnetic moments of these compounds show weak Ferromagnetic behavior.

Moreover, it is clear from FM phase that magnetism are mostly arises in the DOS plots due to the strong spin coupling of the Cu-d and P-p states near the Fermi level. To get insight into the Cu exposed that it is the unfilled 3d (e_g) orbitals that play significant role in the magnetic nature of these compounds. The d-orbitals of these commonly split into e_g(dz², dx²-y²) states. For CaCu₂P₂ and SrCu₂P₂ the electronic configuration will lead to valence electrons filling the lower d-orbitals, giving rise to a total magnetic moment of 0.17 and 0.1 μ_B for both compounds respectively.

3.4 Formation energy

From thermodynamic point of view there is no inclusive experimental work on XCu₂P₂ compounds. Therefore, we required to check their thermodynamic stability by determining the energy of formation and cohesion energy [26], [27] of these compounds like in our previous work [28]. The formation energy (E_f) is defined as a required energy quantum which dissociates the links between atoms to form the solid. From the computed negative values of E_f in Table 3, we can predict that these compounds are thermodynamically stable.

3.5 Cohesive energy

The cohesion energy (E_C) determines the value of the strength of the force that holds atoms together in the materials, which predict the structural stability in the ground state. The cohesion energy E_C of these compounds is computed using the following relation [29].

where ECaCu2P2           total and ESrCu2P2          total are the equilibrium total energy per formula unit of XCu₂P₂ (P = Ca, Sr) compounds respectively determined by first principles and E    Caisol, E    Srisol, E    Cuisol and E    Pisol, are the energies of isolated Ca, Sr, Cu and P atoms, respectively. This is the energy needed to dissociate the crystal in to fragments, which is not only an indicator of the bond strengths but also an indicator of the mobility of atoms in the crystal. The computed values of E_C are −127 eV and −124 eV for the CaCu₂P₂ and SrCu₂P₂ respectively. The high value of cohesion energies of these compounds predict the strong chemical binds in these compounds.

3.6 Curie temperature

The Curie temperature (TC) of XCu₂P₂ compounds are also calculated for XCu₂P₂ compounds by the method introduced in our previous work [30].The Curie temperature was evaluated having in hands the total magnetic moments μ_B, using the following expression [31], [32].

where

The calculated values of Curie temperature for CaCu₂P₂ and SrCu₂P₂ are 54.70 K and 40.49 K respectively. The higher value of Curie temperature for CaCu₂P₂ shows strong interaction among the magnetic atoms as compared to SrCu₂P₂.