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.. using DFT [26] have r
Trang 1Structural, electronic and magnetic properties of Mn, Co,
Neha Kapilaa, V.K Jindala, Hitesh Sharmab,n
a
Department of Physics, Center of Advanced Studies in Physics, Punjab University, Chandigarh 160014, India
b Department of Physics, Punjab Technical University, Jalandhar, Kapurthala 144601, Punjab, India
a r t i c l e i n f o
Article history:
Received 6 March 2011
Received in revised form
1 August 2011
Accepted 12 September 2011
Available online 17 September 2011
Keywords:
Density functional theory
Doped germanium clusters
Magnetic semiconductors
a b s t r a c t
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 no9 and endohedral positions for nZ9 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 TMGenclusters increases with increase in cluster size The Ni doped Genclusters have shown higher stability as compared to Mn and Co doped Genclusters The HOMO–LUMO gap for spin up and down electronic states of Genclusters is found to change significantly on TM doping The magnetic moment in TMGenis 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 NiGenclusters for all n except for n ¼ 2, 4 and 8
&2011 Elsevier B.V All rights reserved
1 Introduction
In recent years transition metal (TM) doped group IVA
semi-conductor 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– ]
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
clus-ters 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
In the recent past, room temperature ferromagnetism (FM) has been reported in Ge1xMnx 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 Tc¼285 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 Genclusters[19] Ferromagnetism has been reported in MnxGe1xand CrxGe1xsingle 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 theo-retical 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 Genclusters using DFT with plane wave basis sets to understand the origin of magnetism
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n
Corresponding author Tel.: þ91 9501109031; fax: þ 91 1822 662523.
E-mail address: dr.hitesh.phys@gmail.com (H Sharma).
Trang 22 Computational details
The calculations are performed using density functional theory
(DFT) within the pseudopotential plane wave method as
imple-mented in VASP (Vienna Ab initio Simulation Package)[22] The
projector augmented wave method with PW-91 exchange
corre-lation function is used for spin polarized generalized gradient
approximation (GGA) The valence shell electronic configuration
used for potential generation of Ge is 4s2, 4p2and for Mn, Co and
Ni it is 4s13d6, 4s13d8and 4s13d9respectively 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 forces are less than 0.01 eV/ ˚A The cubic supercell with
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 Ge2and Ge3the 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
agree-ment 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 1clusters; (c) adopting known structures for TM
doped Genand Sinclusters such as GenMn, GenCo, SinNi and SinCo;
(d) handmade geometries, taking into consideration basic
chemi-cal properties
3 Results and discussion
Using the computational procedure described above we
opti-mized a large number of low-lying isomers and determined the
ground state structures for TM doped Genclusters up to n ¼13 as
shown inFigs 1–3for 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 inFig 4
3.1 Structural growth of TMGenclusters
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
symme-try 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
Ge–Mn and Ge–Ge bond lengths lie in between 2.49–2.65 ˚A and 2.51–2.84 ˚A respectively For MnGe5cluster, 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 MnGe6cluster, a bicapped pentago-nal geometry with C5vsymmetry 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 struc-ture is less stable by 0.03 eV For MnGe7cluster, 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 MnGe8cluster, a cage structure having C2vsymmetry 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 Ge10cluster 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
Fig 1 The calculated lowest-energy structures for Ge n Mn (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.)
Trang 3and Ge–Ge bond-lengths lie in the range 2.34–2.66 ˚A and 2.68–
2.77 ˚A respectively
For MnGe10cluster, a multi-rhombic structure with Cs
sym-metry as shown in Fig 1 is found to be the GS, which is in
agreement to Wang et al.[25]and the Ge–Mn and Ge–Ge
bond-lengths are 2.52–2.73 ˚A and 2.64–2.71 ˚A respectively For MnGe11
cluster, a structure with C5point 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 MnGe12cluster, 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
symme-try as the GS which is found to be one of the isomer less stable by
0.24 eV in our calculations
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 C symmetry with bond length lying between 2.25 ˚A and
Fig 2 The calculated lowest-energy structures for Ge n 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 3 The calculated lowest-energy structures for Ge n 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.)
-2 -1 0 1 2 3 1 2 3 4 5
Cluster Size
Ge MnGe CoGe NiGe
Fig 4 Shows the size dependence of the binding energies per atom and second difference of energy for Ge n TM clusters.
Trang 42.45 ˚A is found to be the ground state structure as shown inFig 2.
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
Ge2Co 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 CoGe4cluster, the
distorted rhombus structure with Cssymmetry 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 CoGe5cluster, the square
bipyramidal geometry with C4vsymmetry 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 CoGe7cluster, 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
symme-try 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 Genclusters In CoGe9cluster, the GS structure can be described
as 1–5–3 layer structure with Co atom lying at the center of
cluster with Cssymmetry The tetracapped trigonal prism
struc-ture 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 CoGe12cluster, 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 CoGe13cluster, a cage like structure with
C1symmetry similar to MnGe13with 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
NiGe dimer is stable with a bond length equal to 2.14 ˚A For
NiGe2, a planar structure with C2vsymmetry 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 NiGe2is larger than NiGe dimer indicating
weak nature of the bonds In NiGe3 cluster, the GS structure is
found with planar geometry having C2vsymmetry as shown in
Fig 3 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
agree-ment with Ref.[28]
The GS structure for NiGe4is found to be a distorted rhombus structure with Cssymmetry 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 NiGe5cluster, a square bipyramidal geometry with C4vsymmetry 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 Cssymmetry 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 NiGe7cluster, 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 MnGe7and CoGe7 In NiGe8cluster, a cage like structure with Ni atom on the surface having C2vsymmetry 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 NiGe9cluster, 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 C1symmetry 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 multi-rhombic structure with Ni atom at the endohedral position with
Cssymmetry 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 C5symmetry which is found as GS structure for MnGe11is less stable by 0.15 eV For NiGe12cluster, 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 range 2.50–3.05 ˚A and 2.53–2.55 ˚A However, the GS structure obtained for CoGe12 is found to be less stable by 0.76 eV In NiGe13cluster, a cage like structure with C1symmetry 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 GenTM clusters and its comparison with available theoretical results many interesting trends can be summarized If we compare with pure Genclusters, 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 Gencluster 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 9 for Mn, Co and Ni dopants respectively This is consistent with the order of their covalent radii Mn 4 Co 4Ni
To understand the relative stability of GenTM clusters, the binding energy per atom is calculated The binding energy per atom is defined as
Eb½GenTM ¼ ½nE½Ge þE½TME½GenTM=n þ 1, ð1Þ where E[Ge], E[TM] and E[GenTM] denote the total energies of Ge atom, TM atom and Ge TM cluster respectively where TM¼ Mn,
Trang 5Co, Ni The binding energy per atom of TM doped Gen clusters
increases linearly as a function of cluster size as shown inFig 4
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 no4,
the binding energy per atom is found to be maximum for NiGen
and minimum for MnGenclusters However, for n Z 4 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 energyD2E 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
D2E½GenTM ¼ E½Gen þ 1TM þ E½Gen1TM2E½GenTM: ð2Þ
TheD2E as a function of size is tabulated inTable 1and 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 GenTM into Gen1TM and Ge and is
calculated as
DE ¼DE½GenTM ¼ E½GenTME½Gen1TME½Ge: 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 Genclusters indicate their
extra stability
4 Electronic properties
The electronic properties of TMGenclusters are investigated in
terms of the variation in HOMO–LUMO gap as a function of
clusters size as shown inFig 5 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 inFig 6
The HOMO–LUMO gap of TM doped Genclusters 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 (TM¼Mn, Co and Ni)
doped Ge clusters with increasing atomic number is plotted in
Fig 5 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 MnGenclusters, 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 4 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 5 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 1 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 MnGe
Table 1
The binding energy per atom (B.E./A), dissociation energy (DE) and second difference of energyD2 E for Ge n TM (TM¼Mn, Co, Ni) The positive and negative signs represent energy gain and loss respectively.
0
2 0 2
CoGe n
Cluster Size
NiGe n
0
MnGe n
Fig 5 Shows the size dependence of the spin up and spin down HOMO–LUMO gaps for Ge n TM clusters for lowest energy structures Red points indicate the
spin-up 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.)
Trang 6In NiGen clusters, the HOMO–LUMO gap for spin (m) and
spin (k) electrons exists only for n¼2, 4 and 8 The HOMO–LUMO
gap is maximum for n ¼2 which decreases sharply for n ¼1 and 3
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 TMGenclusters The EDOS of
few representative cases are shown in Fig 6 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 MnGe3and MnGe6clusters,
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 CoGe9and
CoGe10clusters, the EDOS is plotted inFig 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 GenTM clusters which show half metallic behavior capable of retaining magnetism
5 Magnetic properties
The magnetic properties of GenTM 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(mk) The total
MM of TMGenclusters, 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 ðQTMÞare summarized inTables 2 and 3 For MnGen clusters, the magnitude of total MM oscillates between 1mB and 3mB The calculations are performed for all possible spin combinations (1mB, 3mB, 5mB) for all GS structures of MnGenclusters For n ¼1, 2, 4, 5, 6 and 11, the total MM is found
to be 3mB whereas it is 1mB for other clusters However, MM of
3mBand 1mBhave 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 0:00120:28mBis 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
-30
-20
-10
0
10
20
30
-40
-30
-20
-10
0
10
20
30
40
-40
-30
-20
-10
0
10
20
30
40
Energy
NiGe7
NiGe8
Fig 6 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.)
Trang 7and p–d hybridization between Ge and TM atoms as it is clear
from the PDOS plot shown inFig 7 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 inTable 3for
n ¼1–13 We have considered all the possible spin combinations
(1,3,5) for all the GS structures of CoGenclusters.Table 3shows a
total MM of 1mBfor all size except for n ¼2, 3 and 9 However, the
MM of 3mB, 1mBand 3mBhave been reported for n¼ 1, 3 and 7[19]
respectively A small MM of the order 0:00420:17mBis induced on
Ge atoms and is aligned ferromagnetically to Co atom for n¼ 2, 3,
6–8, and 10–13 However, induced MM of 0:04mBis aligned
anti-ferromagnetically w.r.t Co for n¼ 1, 4 and 5
The valence shell electronic configuration for Co is 3d7, 4s2and
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 CoGenclusters The
induced MM on Ge is aligned ferromagnetically w.r.t Co atom
except for n ¼1, 4 and 5 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
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 SinCo [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, 4 and 8 This magnetic behavior is similar to as reported for NiSin[30] At this point we would like to mention that magnetic properties of NiGenclusters 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 hybridiza-tion 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, 4 and 8 there is FM coupling between Ni and neighbouring Ge atoms The magnetic behavior in SinNi 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 4 Ni, conforming the gradual reduction in their number of unpaired d-electrons For GenTM 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 NiGenit oscillates between 0mBand 2mB The quenching of MM is observed only for Ni doped Genclusters for all
n except for n ¼2,4 and 8
6 Summary and conclusion 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 no9 show pre-ference to occupy surface positions whereas for n Z 9 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 9 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 TMGenclusters 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 TMGenclusters 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
Table 2
The total magnetic momentmtotal,m3d,m4sandm4pare the magnetic moments of
the 3d, 4s, 4p states of Mn atom respectively.mMnand Q Mn are the local magnetic
moment and charge of Mn atom (d1 ) and (d2 ) are the up and
spin-down gaps.
MnGe 3 3.82 0.14 0.03 3.94 5.49 2.28 1.48
MnGe 2 3 3.40 0.09 0.00 3.48 5.59 0.29 1.04
MnGe 3 1 2.86 0.06 0.03 2.88 5.64 0.33 0.97
MnGe 4 3 3.50 0.06 0.03 3.53 5.60 0.51 0.76
MnGe 5 3 3.55 0.06 0.00 3.61 5.57 1.44 0.76
MnGe 6 3 3.03 0.04 0.00 3.07 5.57 1.09 1.23
MnGe 7 1 1.99 0.03 0.00 2.00 5.77 0.15 1.30
MnGe 8 1 2.11 0.03 0.00 2.14 5.78 0.44 1.27
MnGe 9 1 0.78 0.03 0.03 0.85 5.92 0.30 1.18
MnGe 10 1 1.26 0.01 0.01 1.27 6.03 0.11 1.30
MnGe 11 3 2.47 0.02 0.02 2.51 5.88 0.84 0.97
MnGe 12 1 1.76 0.02 0.02 1.80 5.74 1.35 1.60
MnGe 13 1 1.87 0.02 0.02 1.91 5.74 0.61 0.73
Table 3
The total magnetic momentmtotal,m3d,m4sandm4pare the magnetic moments of
the 3d, 4s, 4p states of Co atom respectively.mCoand Q Co are the local magnetic
moment and charge of Co atom (d1 ) and (d2 ) are the spinup and spindown gaps.
CoGe 1 1.74 0.04 0.03 1.76 7.92 1.57 0.47
CoGe 2 3 1.78 0.06 0.02 1.87 7.80 1.40 0.80
CoGe 3 3 1.88 0.07 0.02 1.98 7.94 0.43 0.35
CoGe 4 1 1.12 0.02 0.01 1.10 8.13 0.70 0.38
CoGe 5 1 1.19 0.16 0.00 1.21 8.15 1.0 0.05
CoGe 6 1 0.89 0.01 0.01 0.89 8.21 0.86 0.19
CoGe 7 1 0.85 0.01 0.04 0.90 8.23 0.48 0.29
CoGe 8 1 0.92 0.00 0.01 0.92 8.24 0.81 0.17
CoGe 9 3 1.32 0.04 0.04 1.40 8.34 1.85 0.99
CoGe 10 1 0.65 0.01 0.00 0.66 8.61 1.33 0.19
CoGe 11 1 0.33 0.00 0.03 0.36 8.34 1.26 1.52
CoGe 12 1 0.43 0.00 0.00 0.43 8.29 0.79 0.52
CoGe 13 1 0.66 0.00 0.00 0.67 8.34 1.21 0.20
Trang 8d-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
semicon-ductor 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 effect of
TM or nonmagnetic co-dopants on Ge system is required for its
complete understanding
Acknowledgments
Authors are thankful to VASP group for providing their
computational code Neha Kapila is thankful to Mukul Kabir for
helpful discussions HS acknowledges the financial support from
Department of Science and Technology, New Delhi
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-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-6
-4
-2
0
2
4
6
Fig 7 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.