First-Principles Study of the Structural, Electronic, Magneticand Thermal Properties of the Cr Doped Ge6Mn2Te8 and Ge6Fe2Te8 Systems

F. Semaria, N. Bakib, H. Khachaib, A. Yakoubib, S. Méçabihc, R. Khenataa,∗,A. Shankard, D.P. Raieand A. Bouhemadouf

aLaboratoire de Physique Quantique de la Matiére et de Modélisation Mathématique (LPQ3M),Université de Mascara, 29000 Mascara, Algeria


Received June 6, 2016; in final form May 22, 2017

First-principles calculations have been used to study the structural, electronic, magnetic, and thermal proper-ties of the Cr doped Ge6Mn2Te8and 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 den-sity 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. Ananalysis 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,∆x(d) and ∆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 thatboth compounds have ionic bonding character. Through the quasi-harmonic Debye model, the effects of pressure P and temperatureT on the bulk modulus B, the primitive cell volume V/V0, the Debye temperature θD, the Grüneisen parameterγ, the heat capacity CV, the entropy S, as well as the thermal expansion coefficient,αof theGe6Mn2Te8, Ge5Mn2CrTe8, Ge6Fe2Te8 and Ge5Fe2CrTe8 alloys are predicted.

 http://przyrbwn.icm.edu.pl/APP/PDF/132/app132z4p06.pdf

 3.3. Magnetic properties 

3.3.1. Exchange coupling constants 

From the band structure spectra, we calculate the p−d exchange splitting and the TMd-spin exchange splitting energy (∆xd), which is defined as the separation between the corresponding spin-up and spin-down peaks where our results are listed in Table II. The significant param-eters determining the magnetic properties of the DMS are the s−d exchange constant (N0α) and the p−d ex-change constant (N0β), where N0 is the concentration of the cations. These parameters describe how the valence and conduction bands contribute to the process of exchange and splitting. From the band structure calculations of the ferromagnetic (FM) Ge5Mn2CrTe8andGe5Fe2CrTe8alloys, we estimated these exchange cou-pling constants by assuming the usual Kondo interac-tions, and N0α and N0β are defined as [30]:

 

 where ∆Ev and ∆Ec are the band edge spin splitting of the valence band maxima (VBM) and the conduction band minima (CBM),x is the concentration of the Mn(Cr, Fe) dopants and〈s〉is one-half of the magnetization per TM atom. Our calculated values of N0α and N0β aregiven in Table II where we found a negative value of N0β, hence we can deduce that the p−d exchange interaction in the Ge5Mn2CrTe8 alloy is antiferromagnetic. Conversely, N0β is found to be –1.16 for the Ge5Mn2CrTe8 alloy.

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On the other hand, we found that the TM-3d spin exchange splitting energy (∆xd), which is defined asthe separation between the corresponding spin up and spin down peaks, are 4.12 eV and 4.03 eV for the Ge6Mn2Te8 and Ge6Fe2Te8 alloys, respectively. In addi-tion, the (∆xd) values are 4.09, 3.24, and 2.65, 3.06 eV forthe Ge5Mn2CrTe8and Ge5Fe2CrTe8 alloys, respectively.

 Another important exchange splitting parameter, which illustrates the nature of the attraction in these alloys is the p−d exchange splitting parameter at the maxima ofthe valence bands for the spin up and spin down cases given by