Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 Contents lists available at SciVerse ScienceDirect Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm First principle investigation into structural growth and magnetic properties in GenCr clusters for n ¼ 1–13 Neha Kapila a, Isha Garg 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 144601, Punjab, India a r t i c l e i n f o abstract Article history: Received April 2010 Received in revised form April 2012 Available online May 2012 The ground state structures and their magnetic properties have been investigated for GenCr clusters ð1 r n r 13Þ using spin polarized density functional theory The growth behavior of GenCr clusters for n r 13 shows preference of Cr atom to stabilize at the exohedral position The binding energy increases with the increase in cluster size, but shows a small decrease w.r.t pure Gen clusters Interestingly, the magnetic moment in Cr doped Gen is found to be either 4mB or 6mB and shows no sign of magnetic quenching in any of the ground state structures and isomers investigated up to n ¼ 13 It is found that the magnetic moment is mainly localized at the Cr atom along with small induced magnetic moment on surrounding Ge atoms The results are consistent with the available theoretical results for n r & 2012 Elsevier B.V All rights reserved Keywords: Density functional theory Doped germanium cluster Magnetic semiconductor Introduction The dilute magnetic semiconductors (DMSs) continue to get immense attention [1–4] due to their novel functionalities beyond conventional semiconductors utilizing both the charge and spin of electrons [5–9] While the conventional semiconductor devices use s and p electrons and magnetic devices use d electrons to perform their functions The DMS based spintronic devices are supposed to use both s and p electrons of host semiconductors and d electrons of transition metal impurities to perform their semiconducting and magnetic functions In the recent past, the room temperature DMS have been prepared experimentally by incorporating magnetic ions Mn, Fe with host semiconductors based mainly on III–IV, III–V, II–IV and II–VI group compounds Since the origin of ferromagnetism in DMS is still debated The ferromagnetism have also been reported in IVgroup semiconductor Mnx Ge1Àx [10], Crx Ge1Àx [11] and Cr, Fe doped bulk Ge single crystals [12] The Cr doped Ge single bulk crystal using vertical gradient solidification method is found to show ferromagnetic ordering at 126 K [13] whereas Cr doped Ge film using molecular beam epitaxy (MBE) has shown weak paramagnetic behavior between 1.8 K and 300 K [13] Therefore, possibility of realizing IV DMS with room temperature Tc is yet to fully understood and requires further investigation Recent work on germanium clusters have shown doping of Gen clusters with halogens [14–19], Zn [20], Ni [21], Cu [22], Fe [23,24], W [25], Mn [6,26] and Co [5] However, the potential of transition metal (TM) n Corresponding author Tel.: þ91 9478098060 E-mail address: dr.hitesh.phys@gmail.com (H Sharma) 0304-8853/$ - see front matter & 2012 Elsevier B.V All rights reserved http://dx.doi.org/10.1016/j.jmmm.2012.04.042 doped Gen as a possible DMS has not been explored completely As among the TM doped Gen clusters, the magnetic properties have been reported only for Gen Mn, Gen Fe and Gen Co clusters Since Cr atoms possess highest atomic magnetic moment among 3d TM and when doped on Gen clusters have shown high magnetic moment in small GenCr clusters for n ¼1–5 [7] However, the magnetic behavior for n Z5 have not been investigated so far, although Nukermans et al [28] have reported synthesis of Gen Cr þ for n ¼14–16 Therefore, a systematic investigation of the structural growth, and evolution of magnetic properties of Cr doped GenCr for n is of immense importance in understanding ferromagnetism in GenCr clusters In this paper, we report the results of our systematic investigation of Cr doped GenCr clusters ð1 o n r 13Þ using spin dependent density functional theory (DFT) We report their ground state structures, size dependent binding energies and the evolution of magnetic properties The plan of this chapter is the computational details of the method are presented in Section 2, results and discussion in Section and conclusions in Section Computational details We have used the Spanish Initiative for Electronic Simulation with thousands of atoms (SIESTA) computational code which is based on numerical atomic orbital density functional theory [29–31] The spin polarized calculations are carried out using generalized gradient approximation (GGA) that implements Perdew, Zunger and Ernzerhof (PBE) exchange–correlation functional [32] Core electrons are replaced by non-local, norm-conserving pseudopotentials factorized in the Kleinman–Bylander form [33], 2886 N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 whereas valence electrons are described using DZP ðdouble-z þ polarizationÞ basis set We have used 3d 4s1 configuration for Cr 2 and 4s 4p for Ge The k grid integration has been carried using gamma point only The structures are obtained by the minimization of the total energy using Hellmann–Feynman forces, including Pulay like corrections Structural optimizations are performed using conjugate gradient algorithm until the residual forces in the ˚ In order to obtain the optimization are smaller than 0.001 eV/A global minimum structures of GenCr clusters, we considered large number of possible isomeric structures by (a) taking all structures reported in the previous papers [5–7,14–26]; (b) substituting one Ge atom by Cr atom from the ground state structures and isomers of Gen þ clusters; (c) adopting from those known structures for TM doped Gen and Sin clusters such as Gen Mn, Gen Co, Sin Fe, Sin Cr and Sin Co The spin unrestricted calculations are performed for all allowable spin multiplicities of GenCr clusters to reveal the possible magnetism of the clusters The on-site charges and magnetic moments are obtained from Mulliken charge analysis Test calculations were performed on Ge2 and GeCr clusters The structural parameters such as bond lengths are found to be 2.41 A˚ and 2.54 A˚ which are in agreement with the experimental values of 2.43 A˚ [34,35] and 2.50 A˚ [7] respectively The harmonic vibrational frequency analysis has been performed on the lowest energy state structures to verify their global minimum structures Fig The Ge–Ge and Ge–Cr bond lengths, as well as the point symmetries for all the lowest energy structures are tabulated in Table In order to study the relative stabilities of the clusters, binding energies per atom, the second difference in energies as well as the dissociation energies have been plotted in Figs 6–8 3.1 Structures Results and discussion 3.1.1 Gen clusters Firstly, we have obtained the ground state (GS) structures for pure Gen and Cr doped Gen clusters Pure Gen clusters for n¼ 1–4 adopt planar geometries as their ground state structures For Ge3, the triangle with C2v symmetry, for Ge4, the rhombus structure with D2h symmetry and Ge5, trigonal structure with D3h symmetry are found to be the global minimum structures When n Z5, Gen clusters have a tendency to form three dimensional (3D) configurations as minimum energy structures as Ge6 shows a bicapped quadrilateral with D4h symmetry, Ge7 forms a pentagonal bipyramid structure (D5h symmetry), Ge9 gives a bernal structure with C2v symmetry, Ge10 adopts a tetracapped trigonal prism having C3v symmetry, Ge8, Ge11 and Ge14 show Cs symmetry whereas Ge12 and Ge13 shows C5v and C2v symmetries respectively The obtained structures are in agreement with the existing theoretical results The equilibrium properties of Gen clusters such as binding energy/atom, ionization potentials and electron affinities are in agreement with the available experimental results [34,35] The spin polarized DFT calculations have been performed on Gen and GenCr clusters for n¼1–13 The global minimum structures as well as the isomers for GenCr clusters for n r5 are presented in Fig 1, n¼6–8 in Fig 2, n¼9–11 in Fig 3, n¼12 in Fig and n¼13 in 3.1.2 GenCr clusters GeCr dimer with a bond length of 2.54 A˚ having antiferromagnetic (AFM) interaction is found more stable than with ferromagnetic (FM) interaction by 0.03 eV The bond length of 2.54 A˚ for GeCr is in good Fig The ground state structures of GenCr for n¼ 1–5 The numbers under the structures are relative difference of energy w.r.t the ground state structure and total magnetic moment in Bohr magneton The light blue and magenta balls denote Cr and Ge atoms respectively (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 2887 Fig The ground state structures of GenCr for n¼ 6–8 The numbers under the structures are relative difference of energy w.r.t the ground state structure and total magnetic moment in Bohr magneton The light blue and magenta balls denote Cr and Ge atoms respectively (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) agreement with the theoretical value of 2.52 A˚ [7] For Ge2Cr, the planar structure with C2v symmetry (Fig 1(2)) is the lowest energy structure and the Cr atom have AFM interaction with two Ge atoms The Ge–Cr bond distance in Ge2Cr increases to 2.60 A˚ which is higher than in GeCr dimer, indicating its relative weak nature In Ge3Cr, the ground state (GS) structure shows a non-planar structure with C3v symmetry (Fig 1(3a)) having Ge–Cr and Ge–Ge bond distance of ˚ The obtained GS structure is similar to Ge3Mn 2.80 A˚ and 2.48 A cluster but different from the planar structure with C2v symmetry as shown in Fig 1(3b), which was predicted as GS by Hou et al [7], is found less stable by 0.55 eV The Ge4Cr cluster forms a 3D pyramidal GS structure with C2v symmetry as shown in Fig 1(4a) The Ge–Cr bond distance have increased to 2.76–2.90 A˚ and the Ge–Ge bond ˚ The obtained structure is in agreement distance is found to be 2.53 A with Hou et al [7] Interestingly, similar GS structures have been reported for Mn and Co doped Gen clusters For Ge5Cr cluster, the GS structure forms a square bipyramidal geometry having C4v symmetry as shown in Fig 1(5a) The Ge–Cr bond distances varies from 2.71 to ˚ The 5b 2.84 A˚ and Ge–Ge bond distance is found to be 2.55 A structure with Cs symmetry has been reported as GS by Hou et al [7], is found to exist as isomer less stable by 0.21 eV Interestingly the GS structures reported for Ge5Mn and Ge5Co is similar to as obtained for Ge5Cr At this stage, we would like to add that as per our knowledge the magnetic properties of GenCr clusters for n 45 are being reported for the first time For Ge6Cr, the structure having pentagonal bipyramid geometry (Fig 2(6a)) and structure with C5v symmetry (Fig 2(6b)) are nearly isoenergetic and differ by a small energy 0.01 eV However, the (6a) structure with magnetic moment B is slightly more stable The (6b) structure has also been predicted as GS for Ge6Mn The capped tetragonal bipyramid structure as shown in Fig 2(6c), predicted as the GS structure for Ge6Co, is less stable by 0.52 eV For Ge7Cr, the structure (Fig 2(7a)) with Cr bonded to pentagonal bipyramid (C2v) of Ge7 cluster is found to be the GS structure The distorted cube structure with C3v symmetry as shown in Fig 2(7b) has been predicted as ground state structure for Ge7Mn and Ge7Co, is found to less stable by 0.74 eV For Ge8Cr, we found a tricapped trigonal prism geometry with C2v symmetry Fig 2(8a) as the global minimum structure The structure Fig 2(8b) which has been reported as ground state structure for Ge8Co is less stable by 0.47 eV So far a trend has emerged in which the GS structure for a particular cluster size Cr prefers to occupy the surface position For n Z 9, 3d TMs such as Mn, Fe, Co and Cu when doped in Gen clusters have shown tendency to occupy internal encapsulated positions However, due to weak bonding of Cr–Ge, the Cr atom is expected to show different growth behavior For n ¼9, the structure with C2v symmetry as shown in Fig 3(9a) is found to be the GS structure This may be envisaged to have been formed by Cr adsorption on Ge9 structure The Ge–Cr bond distance varies in the range 2.73–2.81 A˚ and Ge–Ge bond ˚ We observe that structures with distance has increased to 2.70 A Cr atom at the surface position are lower in energy than Cr at encapsulated position The structure with Cr at central encapsulated site is found to be higher in energy by 2.2 eV showing its 2888 N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 Fig The ground state structures of GenCr for n¼ 9–11 The numbers under the structures are relative difference of energy w.r.t the ground state structure and total magnetic moment in Bohr magneton The light blue and magenta balls denote Cr and Ge atoms respectively (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) Fig The ground state structures of Ge12Cr The numbers under the structures are relative difference of energy w.r.t the ground state structure and total magnetic moment in Bohr magneton The light blue and magenta balls denote Cr and Ge atoms respectively (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 2889 Fig The ground state structures of Ge13Cr The numbers under the structures are relative difference of energy w.r.t the ground state structure and total magnetic moment is in mB The light blue and magenta balls denote Cr and Ge atoms respectively (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) Table The total energy (Etotal) and binding energy (BE) of the GenCr clusters The structural parameters are expressed in terms of mean bond lengths between Ge–Cr (RGe–Cr) and Ge–Ge (RGe–Ge) in GenCr for n¼ 1–13 clusters Symmetry ETotal (eV) BE in eV RGe–Cr RGe–Ge GeCr Ge2Cr Ge3Cr Ge4Cr Ge5Cr Ge6Cr Ge7Cr Ge8Cr Ge9Cr Ge10Cr Ge11Cr Ge12Cr Ge13Cr D1h C2v D2h D3h C4v C5v C3v C2v C3v Ci Ci C2v Ci À 363.409 À 470.439 À 577.141 À 683.921 À 792.183 À 899.219 À 1005.771 À 1112.809 À 1219.785 À 1327.151 À 1433.334 À 1539.744 À 1646.856 0.06 1.32 1.72 2.16 2.46 2.78 2.83 2.93 3.02 3.09 3.08 3.08 3.13 2.54 2.61 2.80 2.76–2.90 2.71–2.84 2.70–2.90 2.76–2.81 2.68–2.81 2.73–2.81 2.87–2.90 2.70–2.98 2.61–3.01 2.66–2.84 – 2.28 2.48 2.53 2.55 2.56 2.65 2.64 2.70 2.74 2.75 2.70 2.65 Binding Energy per atom (eV) Cluster Gen GenCr 30 20 10 4 10 12 14 1 less stability For Ge10Cr, the tricapped trigonal prism of Ge9 capped with one Cr and one Ge atom with Cs symmetry is the ground state structure Fig 3(10a) The structure Fig 3(10c) with Cr encapsulated in Ge structure with Cs symmetry which is predicted to be GS structure for Ge10Mn is less stable by 3.16 eV For Ge11Cr, the Cr atom tends to stabilize at the surface Fig 3(11a) rather than at the central encapsulated position Fig 3(11b and 11c) which are less stable by 0.79 eV and 0.91 eV respectively For Ge12Cr and Ge13Cr clusters, the GS structure and close isomers are shown in Figs and respectively The Cr atom has also shown a tendency to settle at peripheral position of Ge cluster with increased coordination number For Ge12Cr, the ground state may be understood as Ge13 structure with C2v symmetry with one Ge atom replaced by Cr The structure with Cr encapsulated at the center of Ge cage with Ih symmetry which is the GS structure for MnGe12 [6] is less favored by 0.84 eV For Ge13Cr, the structure with Cr absorbed on the Ge13 unit is more stable than other isomer structures by 0.29 eV, 0.61 eV, 0.63 eV, 1.63 eV and 1.86 eV respectively 40 10 11 12 13 14 Number of Ge atoms Fig The binding energy per atom of GenCr clusters for n ¼1–13 and Gen clusters for n ¼1–14 The inset shows the total binding energy as a function of cluster size for GenCr and Gen clusters The trend which has emerged from structural growth shows that GenCr cluster shows similarities in the configuration w.r.t pure Gen þ clusters except for n ¼8 and 12 The structural stability of GenCr clusters are investigated by calculating the total binding energy w.r.t pure Gen clusters which is plotted in Fig The binding energy of GenCr clusters increases with increase in cluster size which indicates that these clusters can continuously gain energy during the growth process This is consistent with the experimental observation of Ge14 Cr þ , Ge15Cr þ and Ge16Cr þ [28] Further, we observe Cr doped clusters show a small decrease in binding energy per atom w.r.t Gen clusters implying that Cr does not enhance cluster stability At this point we would like to draw attention to the interesting pattern shown by structural stability of various 3d TM doped Gen and Sin clusters reported in the literature [6,21–26] From the binding energy per atom variation N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -4.5 where E is the total energy of GenCr clusters which is plotted in Fig From the graph, it is observed that for n ¼5, and 10, D2 E show higher values as compared to pure Gen clusters which suggest their higher relative stability as compared to neighboring clusters The higher value of D2 E for n ¼5, and 10 is consistent with higher fragmentation energy The energy needed to dissociate Cr from GenCr clusters can be calculated as GenCr Gen DEn ¼ EðCrGem Þ þEðGenÀm ÞÀEðCrGen Þ, Number of Ge atoms 10 11 12 Fragmentation or Dissociation energy (eV) Fig The second difference of energy of GenCr for n¼ 1–13 and Gen clusters for n¼ 1–14 8.0 7.5 7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 ð2Þ where r m rnÀ1 When m¼0, it gives the energy needed to dissociate a single Cr atom from GenCr cluster When m¼n À1, the energy is required to dissociate a Ge atom from GenCr clusters Fig shows that GenCr clusters prefer to fragment as Cr and Gen units which is consistent with the weak interaction of Ge and Cr atoms Electronic and magnetic properties The size dependent electronic properties of GenCr clusters are investigated by calculating the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gap, vertical ionization potentials (IPs) and electron affinities (EAs) m=0, prob of Cr m=1 m=n-1, prob of Ge atom 3.2 Gen GenCr 3.0 2.8 2.6 10 11 12 13 14 Number of Ge atoms HOMO-LUMO in eV Second difference energy (eV) 2890 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 Fig The fragmentation or dissociation energy of GenCr for n¼ 1–13 and Gen clusters for n¼ 1–14 0.8 0.6 D2 E ¼ EðGen þ CrÞ þ EðGenÀ1 CrÞÀ2EðGen CrÞ, ð1Þ 10 11 12 13 14 Number of Ge atoms Fig The HOMO–LUMO gap of GenCr clusters for n¼ 1–13 and Gen clusters for n¼1–14 Energy (eV) of GenCr clusters as a function of cluster size for Mn, Fe, Ni, Co and Cu doped Ge clusters, we find that when the binding energy per atom tends to increase with TM doping and the TM atom prefers to stabilize at the endohedral positions for n Similar pattern is observed for SinTM clusters except for Ag doped Sin clusters for n ¼1–13 which have shown decrease in binding energy on Ag doping and Ag atom prefers to stabilize at the exohedral position [10] Similar behavior of decrease in binding energy with Cr doping has been reported for GenCr, n ¼3–5 by Hou et al [7] The binding energy curve as plotted in Fig shows a small reduction in binding energy and Cr atom has also shown a tendency to stabilize at the exohedral position Further, the decrease in the binding energy due to Cr doping is consistent with behavior of Ge–Ge and Ge–Cr bond distances which tend to increase with increase in cluster size In order to examine the relative stability of Cr doped Ge clusters, we calculated second difference of binding energies and the energy needed to dissociate Cr from GenCr clusters For the optimized GS structures the second difference of binding energy which reflects the relative stability of the clusters is calculated as EAs IPs 1 10 11 12 13 Number of Ge atoms (n) Fig 10 The electron affinities (EAs) and ionization potentials (IPs) of GenCr clusters for n ¼1–13 N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 2891 Fig 11 Electron density of states (EDOS) for Ge3 and Ge2Cr shows a significant change in the EDOS at the Fermi level due to Cr doping The dotted line corresponds to Fermi level; black and red lines denote spin up and spin down density of states The projected density of states (PDOS) of 3d, 4s and 4p orbitals at Cr site in Ge2Cr are also shown (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) (see Figs and 10) The HOMO–LUMO gap for pure Gen and GenCr clusters is plotted as function of cluster size in Fig Fig shows local peaks at n ¼1, 3, 6, 8, 10, and 13 for GenCr clusters, implying the stronger chemical stability of these structures relative to their counterparts The range of HOMO–LUMO gaps for GenCr clusters is lower than the corresponding pure Gen clusters which suggests the increase in the metallic nature of Cr doped Gen clusters The IP and EA variation as a function of cluster size of Ge is shown in Fig 10, which shows a gradual increase for EA, small decrease in IP up to n¼ and oscillatory behavior thereafter In order to understand the variation of HOMO–LUMO gap, we have performed a detailed analysis of molecular orbitals by examining the electronic density of states (EDOS) of Gen þ and GenCr clusters for n¼2 and as representative cases (see Figs 11 and 12) It can be seen that the EDOS in the vicinity of the Fermi level is changed significantly when Gen clusters are doped with Cr The difference in the spin up and spin down EDOS for Cr doped Gen cluster indicates the presence of strong electronic polarization The electronic polarization may be explained on the basis of electric field generated due to the charge transfer between Cr and Ge atoms From the contribution of different orbital components (s, p, d) it can be seen that electronic states in the vicinity of Fermi level mainly come from 4p and 3d states The spin down d states are unoccupied, which indicates that HOMO–LUMO states are mainly localized around the Cr atom and there is a small electronic distribution around the Ge atom Therefore, the p–d hybridization may be responsible for the size dependence of HOMO–LUMO gap In order to elucidate the bonding nature of the Ge–Cr and Ge–Ge bonds in GenCr clusters, the Mulliken charge analysis was performed at each atomic site In all the GenCr clusters, the charge transfer takes place from Cr atom to Ge atoms indicating that Cr atom acts as electron donor Such charge transfers may be explained on the basis of half filled 3d orbital of Cr This charge transfer behavior is similar to Fe, Mn and Co doped Ge clusters but different from W (another IVB group element) in which charge transfer takes place from Ge unit to W All the ground state structures of GenCr clusters for n¼1–13 exhibit high spin electronic states of S¼2 with quintet state (with multiplicity (2Sþ1¼5)) and S¼3 with septet state (2Sþ 1¼7) The electronic structure and bonding may be explained qualitatively from electronic configuration of Cr atom and Ge2 atoms In Cr atom, the electronic configuration is 3d 4s1 , where the entire valence orbitals are singly occupied and in Ge2, the ground state is triplet and unpaired electrons occupy the degenerate p MOs, which are Ge–Ge bonding MOs The Ge2 unit approaches toward Cr atom such that there is maximum orbital overlap and electron paring This leads to an electron pairing in the following two MOs: (i) the MO formed as a result of overlap between the Cr 4s1 orbital with one of the singly occupied p MO of Ge2 and (ii) the MO resulting from the overlap of dyz orbital of Cr with the degenerate p MO of Ge2 This leaves four unpaired electrons in the valence d orbitals of Cr, namely dz2 , dx2 Ày2 , dxz and dxy Note that singly occupied dxz and dxy MOs can overlap with antibonding p MOs of Ge2 unit resulting in a d2p back donation from Cr atom to Ge2 unit The Mulliken charge shows a net charge of þ0.19e on Cr atom and À 0.09e is derived for each of Ge atom consistent with Hou et al [7] The total magnetic moment along with local magnetic moment (LMM) at Cr site and the contribution of 3d, 4p and 4s orbital toward LMM as well as the induced magnetic moment at Ge site are 2892 N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 12 Ge 10 Ge Cr DOS (states/eV) 8 4 0 -2 -4 -4 -8 -6 -8 -12 3d -3.80 eV Ge Cr-4s and 3d 1.0 Ge Cr-4p 4p 4p 1.6 0.8 3d PDOS (states/eV) 1.2 3d 0.6 4p 4p 0.8 3dx -y 3d 0.4 4p 0.2 0.4 0.0 0.0 -0.2 -0.4 4p -0.4 4p -0.8 3d -1.2 4s -20 -15 -10 -0.6 3d 3dx -y 3d 3d -5 Energy (eV) -0.8 4p -20 -15 -10 -5 Energy (eV) Fig 12 Electron density of states (EDOS) for Ge8 and Ge7Cr shows a significant change in the EDOS at the Fermi level due to Cr doping The dotted line corresponds to Fermi level; black and red lines denote spin up and spin down density of states Projected density of states (PDOS) at Cr site in Ge7Cr shows significant contribution at the Fermi level due to d and p orbitals (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.) Table The total spin magnetic moment of the GenCr clusters, mCr is the local magnetic moment on Cr atom; and m3d , m4s and m4p are magnetic moments of the 3d, 4s, 4p states of Cr atom respectively mind is the maximum induced magnetic moment on nearest Ge atoms Clusters GeCr Ge2Cr Ge3Cr Ge4Cr Ge5Cr Ge6Cr Ge7Cr Ge8Cr Ge9Cr Ge10Cr Ge11Cr Ge12Cr Ge13Cr mTotal Cr in mB mCr m3d m4p m4s 4 4 6 6 5.20 5.13 5.12 4.90 4.92 5.17 4.98 5.02 5.03 5.44 4.98 5.01 4.88 4.65 4.62 4.57 4.62 4.64 4.69 4.61 4.65 4.73 4.79 4.67 4.66 4.64 0.06 0.09 0.01 0.02 0.07 0.01 0.09 0.10 0.10 0.09 0.17 0.21 0.10 0.58 0.33 0.41 0.26 0.21 0.20 0.18 0.17 0.20 0.55 0.14 0.13 0.22 1.21 0.55 0.44 0.38 0.36 0.29 0.35 0.27 0.36 0.22 0.24 0.27 0.25 Ge tabulated in Table The total magnetic moment of GenCr clusters for n¼ 1–13 is not a monotonic function of the cluster size and interestingly only two magnetic states with 4mB and 6mB are observed The high magnetic moments observed in all the GS structures are consistent with the empirical rule relating Cr–Ge distance with magnetic moment i.e the larger is the average distance between TM impurity and the atom of the host cluster the larger is the multiplicity [36] The high spin states of GenCr may be explained on the basis of the unpaired electrons in the system The total magnetic moment arises mainly due to localized magnetic moment at Cr site, small induced magnetic moment on Ge atoms and magnetic interaction with Ge atoms The charge transfer occurs in the same direction i.e from Cr atom to the Ge atoms The maximum induced magnetic moment of 1:21mB is developed on Ge atom in GeCr The induced magnetic moment on Ge atom varies from 0:55mB to 0:38mB for n¼2–5 For n 5, the small magnetic moment of 0:0220:36mB is induced on Ge atoms some of them which align antiferromagnetically w.r.t to Cr atom At Cr atom in GenCr clusters, the spin magnetic moment comes mainly from the unpaired electrons of the 3d state and very small contribution from 4s As in free Cr atom, the valence configuration is 3d 4s1 with 6mB magnetic moment and a careful investigation of magnetic moment in Table shows a charge transfer from Cr to Ge beside an internal charge transfer with in 3d, 4p and 4s orbitals of Cr atom Therefore, for the GenCr cluster, the charge transfer mainly happens between the 4s, 3d and 4p orbitals of Cr and the 4s, 4p orbitals of Ge Thus, there exits spd hybridization in Cr, s–p hybridization of Ge and p–d hybridization between the Cr and Ge atoms, whose combined effect may explain the observed FM in group IV DMSs Therefore, the present work has predicted the presence of high magnetic moment in Cr doped Gen clusters in intermediate size clusters (n¼1–13) However, their reduced stability is a major challenge which needs to be addressed for their possible application as DMS Conclusion We have presented the results of spin polarized DFT based investigation of GenCr and pure Gen clusters for n ¼1–13 N Kapila et al / Journal of Magnetism and Magnetic Materials 324 (2012) 2885–2893 2893 The growth behavior, electronic and magnetic properties of the GenCr clusters may be summarized as received from the Department of Science and Technology, New Delhi The Cr atom tends to stabilize at exohedral position and not show tendency to fall into center of Ge outer frame, which is different from the behavior of other 3d TMs such as Mn, Fe, Co, Ni, and Cu doped Germanium clusters The ground state geometries of Cr doped Ge clusters exhibits lower symmetry as compared to pure Gen clusters This may be explained on the basis of second Jahn Teller theorem i.e the geometries of the relaxed clusters are easy to distort when the filled and empty molecular orbitals are close in energy The binding energies per atom of Cr doped Gen increases with increase in cluster size suggesting that cluster may gain energy while formation which is in agreement with experimental observation of GenCr þ for n ¼14, 15 and 16 However the magnitude of the binding energy shows a decrease w.r.t pure Gen clusters thereby indicating its less stability though changing magnetic properties significantly The second difference in energies predict the extra relative stability for Ge5Cr and Ge10Cr than their neighboring clusters The analysis of possible fragmentation channels for GenCr clusters shows that the most probable channel for dissociation of GenCr clusters is to dissociate into Cr atom and Gen unit All the ground state structures of GenCr clusters exhibit high spin quintet and septet states For n¼ 1, 2, 4, 5, 6, 8, and 13 the GenCr clusters possess magnetic moment of 4mB and 6mB for n ¼3, 7, 9, 10, 11 and 12 The magnetic moment is localized mainly at Cr site in GenCr The Cr atoms interact AFM with some of the nearest Ge atoms The Mulliken charge analysis suggest donor nature of Cr atoms as there is uniform charge transfer from Cr to Ge atoms The majority of the induced magnetic moment is mainly developed on Ge atoms which are nearest to Cr atom The 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