The ground state structures and magnetic properties of ZrₙNi (n = 1-9) clusters are studied by using first principles calculation. Firstly, we find the ground state configurations of ZrₙNi (n = 1-9) clusters. Secondly, the magic clusters (Zr₂Ni and Zr₇Ni) of ZrₙNi clusters are found by the comparisons of average binding energies, the second-order energy difference and energy gaps between the highest occupied orbital and the lowest unoccupied orbital of the ground state of ZrₙNi clusters. Thirdly, the calculated results show that magnetic moment of ZrₙNi (n = 1-2) clusters is 4 μ_{B}; however, the magnetic moment of ZrₙNi clusters is about 2 μ_{B} for n = 3-9 (exception for n = 7). Finally, it is found that the magnetic moment of ZrₙNi cluster mainly comes from Zr atom and Ni atom is the electron acceptor from the Mulliken population analysis.
First-principles calculations have been used to study the structural, electronic, magnetic, and thermal properties of the Cr doped Ge₆Mn₂Te₈ and Ge₆Fe₂Te₈ systems. The calculations were performed using the full-potential linearized augmented plane wave plus local orbitals (FP-LAPW + LO) method based on the spin-polarized density functional theory. Additionally, the electronic exchange-correlation potential is approximated using the spin generalized gradient approximation. The structural properties of the Ge₅Mn₂CrTe₈ and Ge₅Fe₂CrTe₈ alloys are indicated by their corresponding lattice constants, values of the bulk moduli and their pressure derivatives. An analysis of the band structures and the densities of states indicate that for both alloys, they present nearly half-metallic ferromagnetism character. The band structure calculations are used to estimate the spin-polarized splitting energies, Δp_{x}(d) and Δp_{x}(pd) produced by the 3d Mn, 3d Fe and 3d Cr doped states as well as the s(p)-d exchange constants, N₀α (conduction band) and N₀β (valence band). It is observed that the p-d hybridization reduces the magnetic moment of the Mn and Fe atoms from their atomic charge values and create small local magnetic moments on the nonmagnetic Ge and Te sites. Furthermore, the calculations of the charge density indicate that both compounds have ionic bonding character. Through the quasi-harmonic Debye model, the effects of pressure P and temperature T on the bulk modulus B, the primitive cell volume V/V₀, the Debye temperature θ_{D}, the Grüneisen parameter γ, the heat capacity C_{V}, the entropy S, as well as the thermal expansion coefficient, α of the Ge₆Mn₂Te₈, Ge₅Mn₂CrTe₈, Ge₆Fe₂Te₈ and Ge₅Fe₂CrTe₈ alloys are predicted.
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