Physica B 406 (2011) 4612–4619 Contents lists available at SciVerse ScienceDirect Physica B journal homepage: www.elsevier.com/locate/physb Structural, electronic and magnetic properties of Mn, Co, Ni in Gen for (n ¼1–13) Neha Kapila a, V.K Jindal a, Hitesh Sharma b,n a b Department of Physics, Center of Advanced Studies in Physics, Punjab University, Chandigarh 160014, India Department of Physics, Punjab Technical University, Jalandhar, Kapurthala 144601, Punjab, India a r t i c l e i n f o a b s t r a c t Article history: Received March 2011 Received in revised form August 2011 Accepted 12 September 2011 Available online 17 September 2011 The structural, electronic and magnetic properties of TMGen (TM ¼Mn, Co, Ni; n ¼1–13) have been investigated using spin polarized density functional theory The transition metal (TM) atom prefers to occupy surface positions for n o and endohedral positions for n Z The critical size of the cluster to form endohedral complexes is at n ¼9, 10 and 11 for Mn, Co and Ni respectively The binding energy of TMGen clusters increases with increase in cluster size The Ni doped Gen clusters have shown higher stability as compared to Mn and Co doped Gen clusters The HOMO–LUMO gap for spin up and down electronic states of Gen clusters is found to change significantly on TM doping The magnetic moment in TMGen is introduced due to the presence of TM The magnetic moment is mainly localized at the TM site and neighbouring Ge atoms The magnetic moment is quenched in NiGen clusters for all n except for n ¼ 2, and & 2011 Elsevier B.V All rights reserved Keywords: Density functional theory Doped germanium clusters Magnetic semiconductors Introduction In recent years transition metal (TM) doped group IVA semiconductor clusters have been investigated extensively in view of their fundamental understanding and possible technological applications as possible dilute magnetic semiconductors (DMS) in nanoelectronics The TM doping has proven to be effective to tune the opto-electronic, magnetic properties and stability of the host clusters [1–4] Among the group IV clusters, silicon clusters doped with TM dopants (Cr, Mo, W, Mn, Cu, Zn) [5–10] have been studied extensively both theoretically and experimentally to explore the possibility of incorporating magnetism in semiconducting clusters When TMs are encapsulated into large sized silicon cages some interesting phenomena appears such as tunability of HOMO (highest occupied molecular orbital)–LUMO (lowest unoccupied molecular orbital) gap The TM dopants have shown to enhance the symmetry (related geometric stability) of the host cluster and tune the HOMO–LUMO gap The magnetic moment of a few TM dopants is completely quenched in Si [11–13] Therefore, search for group-IV based DMSs has been extended to higher mass congeners such as Ge and Sn [10,14,15] The experimental information related to metal doped group IVA clusters except Si is relatively in scarce n Corresponding author Tel.: þ91 9501109031; fax: þ 91 1822 662523 E-mail address: dr.hitesh.phys@gmail.com (H Sharma) 0921-4526/$ - see front matter & 2011 Elsevier B.V All rights reserved doi:10.1016/j.physb.2011.09.038 In the recent past, room temperature ferromagnetism (FM) has been reported in Ge1Àx Mnx nanocolumns [16] The FM has also been observed up to 115 K in MnGe prepared using molecular beam epitaxy (MBE) growth [17] Further, FM at Tc ¼ 285 K [18] is also reported in high Mn doped Ge single crystals obtained by solid solutions The magnetic moment (MM) does not show signs of quenching for Co doped Gen clusters [19] Ferromagnetism has been reported in Mnx Ge1Àx and Crx Ge1Àx single crystals grown by MBE [18,20] and Cr, Fe doped bulk Ge single crystals These developments have created a strong interest in search for room temperature Ge based compounds [2] However, despite various attempts based on different theoretical calculations, the origin of observed magnetism in TM doped Gen clusters is still debated The isolated investigations reported in the literature fail to explain comprehensively the magnetic behavior due to TM doping Moreover, most of the theoretical studies on TM doped Ge clusters have been carried using density functional theory (DFT) using localized basis sets In the literature the results using localized basis sets are reported to depend strongly on the choice of the basis sets due to superposition error The plane wave basis does not exhibit such error therefore investigation of nanoclusters using such formulation may lead to accurate description of their properties We have investigated the electronic and magnetic properties of Cr doped Gen cluster for n ¼1–13 [21] In this paper, we have extended our work to other TMs (Mn, Co and Ni) in Gen clusters using DFT with plane wave basis sets to understand the origin of magnetism N Kapila et al / Physica B 406 (2011) 4612–4619 4613 Computational details The calculations are performed using density functional theory (DFT) within the pseudopotential plane wave method as implemented in VASP (Vienna Ab initio Simulation Package) [22] The projector augmented wave method with PW-91 exchange correlation function is used for spin polarized generalized gradient approximation (GGA) The valence shell electronic configuration used for potential generation of Ge is 4s2, 4p2 and for Mn, Co and Ni it is 4s13d6, 4s13d8 and 4s13d9 respectively The energy cut-off 300 eV is used for the expansion of plane wave basis set The reciprocal space integration is carried out at the gamma point Symmetry unrestricted geometry and spin optimizations are done using conjugate gradient and quasi-Newtonian methods until all ˚ The cubic supercell with the forces are less than 0.01 eV/A dimension of 15 A˚ is used to create sufficient vacuum space to eliminate the image interactions The test calculations are performed on pure Gen and Mnn clusters and our results are in good agreement with reported ab initio calculations [23,24] For Ge2 and Ge3 the binding energy per atom is 1.92 eV and 2.73 eV respectively which is in agreement to 2.0 eV and 2.50 eV as obtained by Wang et al and it is 1.89 eV/A˚ and 2.78 eV/A˚ as reported in the literature [23] The binding energy per atom and magnetic moment for Mn2 and Mn3 are 0.52 eV, 10mB and 0.81 eV, 15mB respectively which is in agreement with Kabir et al [24] In order to obtain the lowest energy structures, we considered all possible isomeric structures by (a) considering all the possible structures reported in the previous papers [13,16,19]; (b) substituting one Ge atom by TM atom from isomers of optimized Gen þ clusters; (c) adopting known structures for TM doped Gen and Sin clusters such as Gen Mn, Gen Co, Sin Ni and Sin Co; (d) handmade geometries, taking into consideration basic chemical properties Results and discussion Using the computational procedure described above we optimized a large number of low-lying isomers and determined the ground state structures for TM doped Gen clusters up to n ¼13 as shown in Figs 1–3 for Mn, Co and Ni respectively To study the comparative stabilities of the clusters, binding energy per atom and the second difference of energies are plotted in Fig 3.1 Structural growth of TMGen clusters 3.1.1 MnGen For GeMn dimer, cluster with bond length 2.29 A˚ is found to be the ground state structure which is in agreement to Wang et al [25] For MnGe2 cluster, the planer triangular structure with C2v symmetry having bond lengths 2.36 A˚ (Ge–Mn) and 2.42 A˚ (Ge–Ge) is found to be the ground state structure The linear isomers (Mn–Ge–Ge, Ge–Mn–Ge) are found less stable by 1.3 eV and 2.13 eV respectively The Ge–Mn bond distance is higher than its dimer indicating comparatively weak interaction For MnGe3 cluster, the three dimensional (3D) geometry having C3v symmetry is found to be the ground state structure The rhombic structure is found to be less stable by 1.39 eV MnGe3 is the smallest cluster with three dimensional (3D) structure having a pyramidal geometry with MnGe and Ge–Ge bond lengths equal to 2.28 A˚ and 2.69 A˚ respectively The obtained optimized structure is similar to that reported in the literature [25,26] For MnGe4 cluster, a distorted rhombus geometry with Cs symmetry is found to be the ground state (GS) structure The obtained GS is in agreement with Wang et al [25] The calculated Fig The calculated lowest-energy structures for GenMn (n–1–13) clusters Pink circles represent germanium atoms, and green circles represent manganese atoms (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Ge–Mn and Ge–Ge bond lengths lie in between 2.49–2.65 A˚ and 2.51–2.84 A˚ respectively For MnGe5 cluster, a square bipyramidal geometry with C4v symmetry is found to be the ground state structure The Ge–Mn and Ge–Ge bond lengths are 2.35 A˚ and 2.64–2.68 A˚ respectively For MnGe6 cluster, a bicapped pentagonal geometry with C5v symmetry is found to be the GS structure The Ge–Mn and Ge–Ge bond-lengths are 2.59 A˚ and in the range 2.53–2.79 A˚ respectively The capped tetragonal bipyramid structure is less stable by 0.03 eV For MnGe7 cluster, a distorted cubic geometry with C3v symmetry is found to be the GS structure, which is in agreement to Ref [25] The Ge–Mn and Ge–Ge bond lengths lie in the range 2.45–2.85 A˚ and 2.60–2.72 A˚ respectively For MnGe8 cluster, a cage structure having C2v symmetry with Mn atom on the surface is obtained as GS structure The Ge–Mn and Ge–Ge bond lengths lie in the range 2.49–2.95 A˚ and 2.67–2.73 A˚ respectively The obtained optimized GS structure is in agreement to available literature [25,26] For MnGe9 cluster, a tetracapped trigonal prism with C3v symmetry is found to be the GS structure The GS structure may be visualized as Ge10 cluster being substituted by one Mn atom at the convex position At this point we would like to mention that Zhao et al using DFT [26] have reported structure with C1 symmetry as the ground state structure which is found as one of the isomer less stable by 0.19 eV in our calculation The 1–5–3 layer structure is found to be less stable by 0.02 eV The Ge–Mn 4614 N Kapila et al / Physica B 406 (2011) 4612–4619 Fig The calculated lowest-energy structures for Gen Co (n–1–13) clusters Pink circles represent germanium atoms, and blue circles represent cobalt atoms (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig The calculated lowest-energy structures for Gen Ni (n–1–13) clusters Pink circles represent germanium atoms, and grey circles represent nickel atoms (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Ge MnGe CoGe NiGe Sec.Diff of Energy and Ge–Ge bond-lengths lie in the range 2.34–2.66 A˚ and 2.68– 2.77 A˚ respectively For MnGe10 cluster, a multi-rhombic structure with Cs symmetry as shown in Fig is found to be the GS, which is in agreement to Wang et al [25] and the Ge–Mn and Ge–Ge bondlengths are 2.52–2.73 A˚ and 2.64–2.71 A˚ respectively For MnGe11 cluster, a structure with C5 point group symmetry is obtained as the ground state structure, in agreement with Wang et al [25] The Ge–Mn and Ge–Ge bond-lengths are found to be 2.57–2.96 A˚ and 2.49–2.53 A˚ respectively The structure with C1 symmetry which has been reported as the ground state structure in TMSi11 [27] is found to be less stable by 0.13 eV in our calculations For MnGe12 cluster, a perfect hexagonal prism geometry with Mn atom lying inside the cage is found to be the ground state structure, which is in agreement to the work done by Zhao et al [26] The Ge–Mn and Ge–Ge bond-lengths are 2.57–2.96 A˚ and 2.49–2.53 A˚ respectively The structure with Ih symmetry reported as GS by Wang et al is found to be less stable by 0.40 eV in our calculations For MnGe13 cluster, a cage like structure with C1 point group symmetry is found to be the GS structure, in agreement to Zhao et al [26] The Ge–Mn and Ge–Ge bond-lengths are in the range 2.66–2.95 A˚ and 2.55–2.72 A˚ respectively Wang et al [25] reported structure with Cs symmetry as the GS which is found to be one of the isomer less stable by 0.24 eV in our calculations B.E./atom -1 -2 Cluster Size 10 11 12 13 Fig Shows the size dependence of the binding energies per atom and second difference of energy for Gen TM clusters 3.1.2 CoGen GeCo dimer with bond-length 2.14 A˚ is found to be the ground state configuration For CoGe2, the planar triangular structure having C3v symmetry with bond length lying between 2.25 A˚ and N Kapila et al / Physica B 406 (2011) 4612–4619 2.45 A˚ is found to be the ground state structure as shown in Fig The linear structures of Co–Ge–Ge and Ge–Co–Ge are less stable by 1.36 eV and 2.37 eV respectively The larger Ge–Co bond length in Ge2 Co than GeCo dimer implies comparatively weaker interaction For CoGe3, a pyramidal structure similar to MnGe3 having C2v symmetry with Co–Ge and Ge–Ge bond-lengths ranging between 2.29 A˚ and 2.30 A˚ is found to be the most stable structure The rhombic structure which is reported as the GS structure by Jing et al [19] is found to be less stable by 0.61 eV In CoGe4 cluster, the distorted rhombus structure with Cs symmetry is found to be the GS structure which is in agreement with the reported GS structure [19] The Co–Ge and Ge–Ge bond-lengths are found to be 2.32– 2.79 A˚ and 2.63–2.83 A˚ respectively For CoGe5 cluster, the square bipyramidal geometry with C4v symmetry is found to be the GS structure The Co–Ge and Ge–Ge bond-lengths are found to vary in the range 2.36–2.38 A˚ and 2.58–2.70 A˚ respectively The results are in agreement with Jing et al [19] For CoGe6, the bicapped pentagonal structure having C5v symmetry and with bond-lengths 2.32–2.44 A˚ (Co–Ge) and 2.53–2.94 A˚ (Ge–Ge) is found to be the GS structure The capped tetragonal bipyramid structure is found to be less stable by 0.16 eV In CoGe7 cluster, the distorted cubic geometry with C3v symmetry and bond lengths in the range 2.29–2.60 A˚ (Ge–Co) and 2.49–3.77 A˚ (Ge–Ge) is found to be the GS structure In CoGe8 cluster, the tricapped-trigonal prism geometry with C2v symmetry with Co atom on the surface is found to be the ground state structure The Co–Ge and Ge–Ge bond-lengths are found to vary from 2.33 A˚ to 2.71 A˚ and 2.67 A˚ to 2.72 A˚ respectively For n Z9, there is a significant difference in the position of Co in Gen clusters In CoGe9 cluster, the GS structure can be described as 1–5–3 layer structure with Co atom lying at the center of cluster with Cs symmetry The tetracapped trigonal prism structure is found to be less stable by 0.02 eV For CoGe10, the bicapped square antiprism structure is found to be the ground state structure The GS is remarkably stable with Co–Ge and Ge–Ge bond-lengths varying in the range 2.38–2.76 A˚ and 2.53–2.84 A˚ respectively In CoGe11 cluster, the GS structure has C2v point group symmetry with 1–4–4–2 layer structure and bond-lengths 2.38–2.76 A˚ and 2.51–2.89 A˚ for Co–Ge and Ge–Ge respectively The structure with C5 point group symmetry is less stable by 0.22 eV For CoGe12 cluster, the cage like structure is found to be the lowest energy geometry The GS geometry can be described as multi-pentagonal structure with Cs symmetry The hexagonal prism structure with Co inside the cage structure is found to be less stable by 0.60 eV In CoGe13 cluster, a cage like structure with C1 symmetry similar to MnGe13 with bond-lengths (Co–Ge) 2.46– 2.79 A˚ and (Ge–Ge) 2.62–2.85 A˚ is found to be GS structure The structure reported as GS by Jing et al [19] is found to be one of the isomer which is less stable by 0.21 eV 3.1.3 NiGen ˚ For NiGe dimer is stable with a bond length equal to 2.14 A NiGe2, a planar structure with C2v symmetry and bond-length of 2.23–2.43 A˚ is found to be the ground state structure The obtained ground state structure is in agreement with structure reported by Bandyopadhyay et al [28] The linear structures of Ni–Ge–Ge and Ge–Ni–Ge are found to be less stable by energy difference of 1.38 eV and 1.23 eV respectively Interestingly, the Ge–Ni bond distance in NiGe2 is larger than NiGe dimer indicating weak nature of the bonds In NiGe3 cluster, the GS structure is found with planar geometry having C2v symmetry as shown in Fig The Ge–Ni and Ge–Ge bond lengths are found to be 2.24 A˚ and 2.37 A˚ respectively The obtained GS structure is in agreement with Ref [28] 4615 The GS structure for NiGe4 is found to be a distorted rhombus structure with Cs symmetry and having bond lengths in the range 2.30–2.31 A˚ (Ge–Ni) and 2.47–3.04 A˚ (Ge–Ge) in agreement with the reported results [28] For NiGe5 cluster, a square bipyramidal geometry with C4v symmetry is found to be the GS structure The obtained GS structure is similar to as obtained for MnGe5 and CoGe5 The Ge–Ni and Ge–Ge bond lengths lie in the range 2.31– 2.46 A˚ and 2.53–2.87 A˚ respectively For NiGe6 cluster, the GS structure is a tetragonal bipyramid geometry with Cs symmetry The Ge–Ni and Ge–Ge bond-lengths vary in the range 2.38–2.40 A˚ and 2.48–2.75 A˚ respectively The bicapped pentagonal structure is less stable by 0.11 eV For NiGe7 cluster, a distorted cubic geometry is nearly isoenergetic with structure having Cs symmetry The distorted cubic structure is favoured to be the GS structure which is similar to the GS of MnGe7 and CoGe7 In NiGe8 cluster, a cage like structure with Ni atom on the surface having C2v symmetry is the GS structure The obtained GS structure is consistent with Bandyopadhyay et al [28] The Ge–Ni and Ge–Ge bond lengths lie in the range 2.37–2.87 A˚ and 2.69–2.76 A˚ respectively For NiGe9 cluster, the obtained GS structure can be described as 1–5–3 layer structure with Ni atom lying at the center of cluster having symmetry Cs The bond lengths vary from 2.28 A˚ to 2.78 A˚ for Ge–Ni and 2.56 A˚ to 2.84 A˚ for Ge–Ge respectively However, Wang and Han [29] using DFT have reported a structure with C1 symmetry as the GS structure which is found to be less stable by 0.48 eV in our calculations The tetracapped trigonal structure is less stable by 0.01 eV For NiGe10 cluster, a multirhombic structure with Ni atom at the endohedral position with Cs symmetry is the ground state structure The Ge–Ni and Ge–Ge bond lengths vary from 2.42 A˚ to 2.50 A˚ and 2.61 A˚ to 2.67 A˚ respectively The obtained GS structure is in agreement to the work done by Bandyopadhyay et al [28] For NiGe11 cluster, structure with 1–4–4–2 layers having C2 point group symmetry is found to be the ground state structure The bond lengths for Ge–Ni and Ge–Ge vary in the range 2.45– 2.64 A˚ and 2.55–2.90 A˚ respectively The obtained GS structure is in agreement with the reported GS by Bandyopadhyay et al [28] However, the structure with C5 symmetry which is found as GS structure for MnGe11 is less stable by 0.15 eV For NiGe12 cluster, the GS structure is a perfect hexagonal prism with Ni atom lying inside the cage The bond lengths of Ge–Ni and Ge–Ge vary in the ˚ However, the GS structure range 2.50–3.05 A˚ and 2.53–2.55 A obtained for CoGe12 is found to be less stable by 0.76 eV In NiGe13 cluster, a cage like structure with C1 symmetry is found to be the ground state structure The optimized structure obtained by Bandyopadhyay et al [28] is found to be less stable by 0.41 eV From the above structural analysis of Gen TM clusters and its comparison with available theoretical results many interesting trends can be summarized If we compare with pure Gen clusters, the TM doping leads to substantial structure reconstructions The TM has shown tendency to move from convex, to surface and to the interior site as the size varies from n ¼2 to 13 The TM atoms for a critical size of Gen cluster completely fall into the center of Ge frame and form cage This critical size of the cluster can be understood on the basis of radius of the TM atoms, larger the atom size more number of Ge atoms are needed to encapsulate the bigger atom In the present work, we find critical size of n¼ 11, 10 and for Mn, Co and Ni dopants respectively This is consistent with the order of their covalent radii Mn Co 4Ni To understand the relative stability of Gen TM clusters, the binding energy per atom is calculated The binding energy per atom is defined as Eb ½Gen TM ¼ ½nE½Ge þE½TMÀE½Gen TM=n þ 1, ð1Þ where E[Ge], E[TM] and E[Gen TM] denote the total energies of Ge atom, TM atom and Gen TM cluster respectively where TM¼ Mn, 4616 N Kapila et al / Physica B 406 (2011) 4612–4619 Table The binding energy per atom (B.E./A), dissociation energy (DE) and second difference of energy D2 E for Gen TM (TM¼Mn, Co, Ni) The positive and negative signs represent energy gain and loss respectively TMGe TMGe2 TMGe3 TMGe4 TMGe5 TMGe6 TMGe7 TMGe8 TMGe9 TMGe10 TMGe11 TMGe12 TMGe13 Mn Co Ni B:E:=A D.E (D2 E) B:E:=A D.E (D2 E) B:E:=A D.E (D2 E) À 1.47 À 2.25 À 2.67 À 3.02 À 3.27 À 3.38 À 3.44 À 3.53 À 3.63 À 3.71 À 3.73 À 3.75 À 3.76 À 3.48 À 3.82 À 3.92 À 4.27 À 4.69 À 4.04 À 3.85 À 4.28 À 4.49 À 4.56 À 3.88 À 3.85 À 3.93 À 0.11 À 0.35 À 0.46 0.65 0.18 À 1.03 À 0.27 À 0.07 0.68 À 0.09 0.04 À 1.96 À 2.88 À 3.00 À 3.28 À 3.50 À 3.57 À 3.65 À 3.69 À 3.81 À 3.90 À 4.11 À 3.88 À 3.88 À 3.91 À 4.33 À 4.18 À 4.11 À 4.64 À 3.85 À 4.32 À 4.08 À 4.90 À 4.74 À 3.70 À 3.85 À 3.87 0.16 0.21 À 0.67 À 0.81 À 0.46 0.24 À 0.79 0.12 1.06 À 0.15 À 0.02 À 2.14 À 2.85 À 3.15 À 3.29 À 3.57 À 3.62 À 3.66 À 3.68 À 3.80 À 3.95 À 3.89 À 3.87 À 3.88 2.09 À 4.29 À 4.03 À 3.86 À 4.96 À 3.92 À 3.94 À 3.90 À 4.86 À 5.41 À 3.32 À 3.56 À 4.11 0.26 0.17 À 1.10 1.04 À 0.02 0.04 À 0.96 À 0.55 2.09 À 0.24 À 0.55 Co, Ni The binding energy per atom of TM doped Gen clusters increases linearly as a function of cluster size as shown in Fig The figure shows that the binding energy of the Gen clusters increases marginally on doping with Mn, Co and Ni Further, these TMGen clusters gain energy during their growth process which indicate possibility of their formation experimentally For n o 4, the binding energy per atom is found to be maximum for NiGen and minimum for MnGen clusters However, for n Z the binding energy per atom shows almost similar pattern for Co and Ni doped Ge clusters except for n ¼11 The relative stability is examined by calculating the second difference of energy D2 E and the energy needed to dissociate the TM from TMGen cluster The second order difference in cluster energy is a sensitive quantity that reflects the relative stability of a cluster and is defined as D2 E½Gen TM ¼ E½Gen þ TM þ E½GenÀ1 TMÀ2E½Gen TM: MnGe n CoGe n NiGe n ð2Þ The D2 E as a function of size is tabulated in Table and plotted in Fig 4, which shows oscillatory pattern and most stable structure for n ¼10 in all cases The dissociation energy (DE) which is defined as the energy required for dissociation of Gen TM into GenÀ1 TM and Ge and is calculated as DE ¼ DE½Gen TM ¼ E½Gen TMÀE½GenÀ1 TMÀE½Ge: Spin Up Spin Down HOMO-LUMO Gap TMGen ð3Þ The dissociation energy varies in the range of 3.48–4.56 eV for MnGen, 3.70–4.90 eV for CoGen and 2.09–5.41 eV for NiGen respectively The higher values of dissociation energy for n ¼5 and 10 for TM¼Mn, Co and Ni doped Gen clusters indicate their extra stability Electronic properties The electronic properties of TMGen clusters are investigated in terms of the variation in HOMO–LUMO gap as a function of clusters size as shown in Fig To investigate the change in the electronic density due to TM doping, the change in the electronic density of states (EDOS) near fermi level is also calculated and plotted in Fig The HOMO–LUMO gap of TM doped Gen clusters predicts their ability to undergo chemical reactions with small molecules A large HOMO–LUMO gap corresponds to a closed shell electronic configuration with high stability The HOMO–LUMO gap for spin up (m) and spin down (k) states for TM (TM¼ Mn, Co and Ni) doped Gen clusters with increasing atomic number is plotted in 10 12 14 Cluster Size Fig Shows the size dependence of the spin up and spin down HOMO–LUMO gaps for Gen TM clusters for lowest energy structures Red points indicate the spinup and green indicates the spin down gap (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig At this point we would like to mention that HOMO–LUMO gap for spin (m) and spin (k) is same for pure Gen clusters However, due to TM doping there is a significant variation in the spin up and spin down HOMO–LUMO gap as a function of cluster size In MnGen clusters, the spin up HOMO–LUMO gap is found to be maximum for MnGe dimer which shows sharp decrease to 0.2 eV in MnGe2 For n 3, the HOMO–LUMO gap for spin up electrons increases oscillatory with local maxima at n ¼5 and n¼12 The HOMO–LUMO gap of spin down electrons shows magnitude greater than gap for spin up electrons except for n¼1 and The HOMO–LUMO gap is maximum for n ¼6 and 12 for Mn in agreement with Wang et al [25] For both spin-up and spin-down electrons, the HOMO–LUMO gap is close to eV, indicating its metallic behavior In CoGen clusters, the HOMO–LUMO gap for spin up (m) electrons is maximum for n ¼9 For n 43, the HOMO–LUMO gap for spin up electrons increases oscillatory with local maxima at n¼9 and n ¼11 The HOMO–LUMO gap for spin down (k) electrons shows magnitude less than gap for spin up electrons except for n¼11 The HOMO–LUMO gap is maximum for n ¼10 The magnitude of the HOMO–LUMO gap for spin-up electrons is close to 1.0 eV and for spin-down electrons is less than 1.0 eV which is smaller as compared to MnGen N Kapila et al / Physica B 406 (2011) 4612–4619 30 20 4617 MnGe MnGe CoGe CoGe 10 NiGe NiGe 10 -10 -20 -30 40 Density of States 30 20 10 -10 -20 -30 -40 40 30 20 10 -10 -20 -30 -40 -7 -6 -5 -4 -3 -2 -1 -7 -6 -5 -4 -3 -2 -1 Energy Fig The electron density of states (EDOS) for MnGe, CoGe and NiGe Red line denotes the spin-up electronic charge density and black denotes the spin-down electronic charge density The dotted vertical line indicates the Fermi level in Kohn–Sham eigenvalues (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) In NiGen clusters, the HOMO–LUMO gap for spin (m) and spin (k) electrons exists only for n ¼2, and The HOMO–LUMO gap is maximum for n ¼2 which decreases sharply for n ¼1 and For n¼ 8, there is overlap of HOMO–LUMO gap of spin up and spin down electrons The HOMO–LUMO gap as a function of cluster size shows maximum value for n ¼2 and 10 which is in agreement with Bandyopadhyay et al [28] The HOMO–LUMO gap remains close to 1.0 eV for all the cases A spin arrangement in any magnetic cluster is magnetically stable only if both the spin gaps are positive [24] In our calculation of HOMO–LUMO gap for TM doped Gen, these gaps are positive for all the clusters In order to further elucidate the origin and change in the electronic properties due to TM doping, we calculated the spin electronic density of states (EDOS) of TMGen clusters The EDOS of few representative cases are shown in Fig Figure shows a significant change in EDOS of TMGen clusters w.r.t pure Gen clusters At this point we would like to mention that there is no polarization in EDOS of pure Gen In MnGe3 and MnGe6 clusters, the spin polarization results in change of EDOS near Fermi level as shown in Fig 6(a) and (b) For MnGe3, the EDOS shows finite value at Fermi level for spin down electrons In MnGe6 cluster, there is finite EDOS at Fermi level with unequal magnitude The EDOS profile of spin up and spin down electrons below Fermi level shows significant variation in EDOS profile For CoGe9 and CoGe10 clusters, the EDOS is plotted in Fig 6(c) and (d), both show finite value of EDOS at Fermi level However, there is a significant change in EDOS profile below Fermi level for spin up and down channels In case of NiGe7, the EDOS for spin up and down electrons is same suggesting no spin polarization is induced, both spin up and spin down EDOS are zero at Fermi level resulting into magnetic insulator For NiGe8, there is a finite value of EDOS at Fermi level and unequal EDOS for spin up and spin down electrons below Fermi level resulting into half metallic magnetic cluster Therefore, the Gen TM clusters which show half metallic behavior capable of retaining magnetism Magnetic properties The magnetic properties of Gen TM clusters are investigated in terms of total MM calculated for the GS structure and the local MM of TM atom The magnetic moment is calculated from the difference of spin up and spin down electrons Q(m À k) The total MM of TMGen clusters, local MM of TM atoms, MM contribution of s and d orbitals of TM and p orbital of Ge atoms, along with total charge on TM atom ðQTM Þ are summarized in Tables and For MnGen clusters, the magnitude of total MM oscillates between 1mB and 3mB The calculations are performed for all possible spin combinations (1mB , 3mB , mB ) for all GS structures of MnGen clusters For n ¼1, 2, 4, 5, and 11, the total MM is found to be 3mB whereas it is 1mB for other clusters However, MM of 3mB and 1mB have been reported [26] for n¼7 and 11 respectively The total MM is mainly located at the TM site and the main contribution is from d orbital The s and p orbital contribution is very small A small MM of the order of 0:00120:28mB is induced on the nearest Ge atoms which interacts AFM with Mn atom except for n ¼9 and 11 The origin of magnetism may be attributed to the presence of unpaired electrons of the 3d states 4618 N Kapila et al / Physica B 406 (2011) 4612–4619 Table The total magnetic moment mtotal , m3d , m4s and m4p are the magnetic moments of the 3d, 4s, 4p states of Mn atom respectively mMn and QMn are the local magnetic moment and charge of Mn atom (d1 ) and (d2 ) are the spin-up and spindown gaps MnGen mtotal m3d m4s m4p mMn QMn (d ) (d2 ) MnGe MnGe2 MnGe3 MnGe4 MnGe5 MnGe6 MnGe7 MnGe8 MnGe9 MnGe10 MnGe11 MnGe12 MnGe13 3 3 1 1 1 3.82 3.40 2.86 3.50 3.55 3.03 1.99 2.11 0.78 1.26 2.47 1.76 1.87 0.14 0.09 0.06 0.06 0.06 0.04 0.03 0.03 0.03 0.01 0.02 0.02 0.02 0.03 0.00 À 0.03 À 0.03 0.00 0.00 0.00 0.00 0.03 0.01 0.02 0.02 0.02 3.94 3.48 2.88 3.53 3.61 3.07 2.00 2.14 0.85 1.27 2.51 1.80 1.91 5.49 5.59 5.64 5.60 5.57 5.57 5.77 5.78 5.92 6.03 5.88 5.74 5.74 2.28 0.29 0.33 0.51 1.44 1.09 0.15 0.44 0.30 0.11 0.84 1.35 0.61 1.48 1.04 0.97 0.76 0.76 1.23 1.30 1.27 1.18 1.30 0.97 1.60 0.73 Table The total magnetic moment mtotal , m3d , m4s and m4p are the magnetic moments of the 3d, 4s, 4p states of Co atom respectively mCo and QCo are the local magnetic moment and charge of Co atom (d1 ) and (d2 ) are the spinup and spindown gaps CoGen mtotal m3d m4s m4p mCo QCo (d ) (d2 ) CoGe CoGe2 CoGe3 CoGe4 CoGe5 CoGe6 CoGe7 CoGe8 CoGe9 CoGe10 CoGe11 CoGe12 CoGe13 3 1 1 1 1 1.74 1.78 1.88 1.12 1.19 0.89 0.85 0.92 1.32 0.65 0.33 0.43 0.66 0.04 0.06 0.07 À 0.02 À 0.16 À 0.01 0.01 0.00 0.04 0.01 0.00 0.00 0.00 À 0.03 0.02 0.02 0.01 0.00 0.01 0.04 0.01 0.04 0.00 0.03 0.00 0.00 1.76 1.87 1.98 1.10 1.21 0.89 0.90 0.92 1.40 0.66 0.36 0.43 0.67 7.92 7.80 7.94 8.13 8.15 8.21 8.23 8.24 8.34 8.61 8.34 8.29 8.34 1.57 1.40 0.43 0.70 1.0 0.86 0.48 0.81 1.85 1.33 1.26 0.79 1.21 0.47 0.80 0.35 0.38 0.05 0.19 0.29 0.17 0.99 0.19 1.52 0.52 0.20 Co atom There is internal charge transfer from s orbital to d orbital of Co atom However, the MM is mainly contributed by d orbital of Co atom Interestingly, similar behavior has been reported for W doped Gen clusters, where the charge transfer takes place from Ge to W At this point we would like to mention that Co has shown magnetic quenching for Sin Co [13] but no quenching is observed in our calculation in agreement with other ab initio studies [19] For NiGen cluster, the magnetic properties are different as compared to Mn and Co The quenching of MM is observed for all n considered except for n ¼2, and This magnetic behavior is similar to as reported for NiSin [30] At this point we would like to mention that magnetic properties of NiGen clusters have not been reported in the literature The quenching of MM implies a nonmagnetic cluster which may be explained on the basis of charge transfer between Ni and Ge atoms and strong hybridization between 3d orbital of Ni and 4p orbital of Ge Here all the spin up states are occupied but spin down states are empty, therefore induced MM on Ge atoms is antiparallel w.r.t Ni resulting in zero MM However, for n ¼2, and there is FM coupling between Ni and neighbouring Ge atoms The magnetic behavior in Sin Ni has shown MM quenching for n¼3–8 [30] From the magnetic properties of Mn, Co and Ni doped Gen clusters, it can be concluded that the total MM is mainly contributed by TM atom and magnetic interaction with nearest Ge atoms The local MM decreases gradually in the following order Mn 4Co Ni, conforming the gradual reduction in their number of unpaired d-electrons For Gen TM clusters the Ge atoms are aligned anti-ferromagnetically except in CoGen for n ¼2,3, 6–8,10–13 which interacts ferromagnetically The total MM oscillates between 3mB and 1mB for both Mn and Co doped Gen clusters whereas for NiGen it oscillates between 0mB and 2mB The quenching of MM is observed only for Ni doped Gen clusters for all n except for n ¼2,4 and Summary and conclusion and p–d hybridization between Ge and TM atoms as it is clear from the PDOS plot shown in Fig The maximum value of 4mB local MM on Mn is less than 5mB of the Mn atom in small Mn clusters The valence shell configuration of Mn atom is 3d5, 4s2, therefore according to Hund’s rule the MM for Mn is 5mB However, the hybridization between 3d and 4p orbital induces the AFM interaction between the Ge atoms and Mn resulting in reduction of MM of the Mn atom The local MM of TM is delocalized and distributed over the surrounding Ge atoms For CoGen, the magnetic moments are tabulated in Table for n ¼1–13 We have considered all the possible spin combinations (1,3,5) for all the GS structures of CoGen clusters Table shows a total MM of 1mB for all size except for n ¼2, and However, the MM of 3mB , 1mB and 3mB have been reported for n¼ 1, and [19] respectively A small MM of the order 0:00420:17mB is induced on Ge atoms and is aligned ferromagnetically to Co atom for n¼ 2, 3, 6–8, and 10–13 However, induced MM of 0:04mB is aligned antiferromagnetically w.r.t Co for n¼ 1, and The valence shell electronic configuration for Co is 3d7, 4s2 and according to Hund’s rule the atomic MM of Co atom is 3mB however due to hybridization between Co 3d and 4p orbitals with Ge 4s, 4p orbitals, as shown in projected DOS plots, Fig 7, there is a reduction in local MM of Co atom in CoGen clusters The induced MM on Ge is aligned ferromagnetically w.r.t Co atom except for n ¼1, and which favours AFM alignment The local MM is less than the total MM implying the FM alignment which is opposite to magnetic behavior in MnGen clusters In CoGen clusters there is an electronic charge transfer from Ge atom to The structural growth behavior, electronic and magnetic properties have been calculated using first principle calculation of TM (Mn, Co, and Ni) doped Gen clusters The results are summarized as follows: (1) The ground state structures of TMGen for n o show preference to occupy surface positions whereas for n Z the TMs show tendency to move towards endohedral positions There is a critical size of the cluster above which TM tends to form endohedral complexes which is n ¼11, 10 and for Mn, Co and Ni respectively The TM–Ge bond length decreases in the order of Mn, Co and Ni in accordance to their size The binding energy per atom increases in the TMGen clusters as a function of cluster size, suggesting gain in their structural stability The binding energy does not vary significantly w.r.t pure Gen clusters (2) The TM doping alters the HOMO–LUMO gap of pure Gen clusters significantly The HOMO–LUMO gap for spin up electrons varies from 0.29 eV to 2.28 eV, 0.43 eV to 1.85 eV, 0.0 eV to 1.71 eV for Mn, Co and Ni respectively whereas for spin down electrons the HOMO–LUMO gap varies from 0.73 eV to 1.60 eV, 0.05 eV to 1.52 eV and 0.0 eV to 0.91 eV for Mn, Co and Ni respectively (3) The magnetic behavior of TMGen clusters is due to TM dopant The MM is mainly localized at the TM site and nearest Ge atoms The local MM at TM site decreases gradually in the order Mn, Co, Ni in accordance to their number of unpaired N Kapila et al / Physica B 406 (2011) 4612–4619 4619 1.5 1.0 0.5 0.0 -4 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 -4 -3 -2 -1 -0.5 PDOS -1.0 -1.5 -2 -4 -6 Fig The projected density of states (PDOS) for MnGe and CoGe The upper panel shows 2p-PDOS for Ge atoms and the lower panel shows 3d-PDOS for Mn and Co respectively The vertical line indicates the Fermi energy which is shifted to 0.0 eV d-electrons The MM is mainly localized on TM atom however a small MM is induced on nearest Ge atoms The magnetic properties of TM doped germanium clusters offer a direction for further improvements in group-IV semiconductor clusters Before their application can be realized other crucial issues such as low solubility of the TM impurities in semiconducting matrix must be resolved Therefore, the 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