Gen cr

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 6 April 2010
Received in revised form
5 April 2012
Available online 5 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 5.
& 2012 Elsevier B.V. All rights reserved.

Keywords:
Density functional theory
Doped germanium cluster
Magnetic semiconductor

1. 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: (H. Sharma).

0304-8853/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
/>
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 4 5 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 3 and
conclusions in Section 4.

2. 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
5
polarizationÞ basis set. We have used 3d 4s1 configuration for Cr
2
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 1 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. 5. The Ge–Ge and Ge–Cr bond lengths, as well as the point
symmetries for all the lowest energy structures are tabulated in
Table 1. 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

3. 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. 4 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. 1. 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. 2. 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 6 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. 3. 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. 4. 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. 5. 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 1
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

5
Binding Energy per atom (eV)

Cluster

Gen
GenCr

30
20
10

4

0
2

4

6

8

10 12 14

3

2

1

0
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. 4 and 5 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

2

3

4

5 6 7 8 9 10 11 12 13 14
Number of Ge atoms

Fig. 6. 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 1 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. 6.
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. 7. From the graph, it is observed that for n ¼5, 8 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, 8 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,

2

3

4

5
6
7
8
9
Number of Ge atoms

10

11

12

Fragmentation or Dissociation energy (eV)

Fig. 7. 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 0 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. 8 shows that GenCr clusters prefer to fragment as Cr and Gen
units which is consistent with the weak interaction of Ge and
Cr atoms.

4. 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

0

1

2

3

4

5 6 7 8 9 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. 8. 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 1 CrÞ þ EðGenÀ1 CrÞÀ2EðGen CrÞ,

ð1Þ

1

2

3

4

5 6 7 8 9 10 11 12 13 14
Number of Ge atoms

Fig. 9. 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 4 8. 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. 6 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

8
7

6
5
4
3
2
1
1

2

3

4

5
6
7
8
9 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. 9 and 10). The HOMO–LUMO gap for pure Gen and GenCr
clusters is plotted as function of cluster size in Fig. 9.
Fig. 9 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 7 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 1 and
GenCr clusters for n¼2 and 7 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
5
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
1
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
8

6

4

4
2

0

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
0
Energy (eV)

5

-0.8

4p

-20

-15

-10
-5
Energy (eV)

0

5

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 2
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

min

4
4
6
4
4
4
6
4
6
6
6
6
4

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 2. 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 4 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
5
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 2 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.

5. 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.

1. The Cr atom tends to stabilize at exohedral position and do 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. The majority of the induced magnetic moment is mainly
developed on Ge atoms which are nearest to Cr atom. The
induced magnetic moment on Ge atoms is found to decrease
with increase in cluster size.

References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]

[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[28]
[29]
[30]
[31]

Acknowledgments

[32]
[33]
[34]

Authors are thankful to SIESTA group for providing their
computational code. HS acknowledges the financial support

[35]
[36]

S. Maekawa (Ed.), Concepts in Spin Electronics, Oxford Press, 2006.
T. Dieti, et al., (Eds.), Spintronics, Academic Press, 2008.
D.D. Awschalom, M.E. Flatte, Nature Physics 3 (2007) 153.
C. Chappert, A. Fert, F.N. VanDau, Nature Materials 6 (2007) 813.
Q. Jing, F. Yang, Y.X. Wang, Journal of Chemical Physics 128 (2008) 124319.
J. Wang, L. Ma, J. Zhao, G. Wang, Journal of Physics: Condensed Matter 20
(2008) 335223.
X.J. Hou, G. Gopakumar, P. Lievens, M.T. Nguyen, Journal of Physical
Chemistry A 111 (2007) 13544.
L. Ma, J. Zhao, J. Wang, B. Wang, Q. Lu, G. Wang, Physical Review B 73 (2006)
125439.
J.R. Li, G.H. Wang, C.H. Yao, Y.W. Mu, J.G. Wan, M. Han, Journal of Chemical
Physics 130 (2009) 164514.
F.C. Chuang, Y.Y. Hsieh, C. Hsu, M.A. Albao, Journal of Chemical Physics 127
(2007) 144313.
S. Choi, et al., Applied Physics Letters 81 (2002) 3606.
S. Itaya, Y. Yamamoto, H. Hori, Journal of Superconductivity: Incorporating
Novel Magnetism 18 (2005) 83.
V. Koi, et al., Journal of Applied Physics 103 (2008) 053912.
S. Yoshida, K. Fuke, Journal of Chemical Physics 111 (1999) 880.
Y. Negishi, H. Kawamata, T. Hayase, T. Gomei, R. Kishi, F. Hayakawa,
A. Nakajima, K. Kaya, Chemical Physics Letters 269 (1997) 199.
K. Kaya, H. Kawamata, Y. Negishi, T. Hayase, R. Kishi, A. Nakajima, Zeitschrift
¨ Physik D 40 (1997).
fur
J.L. Wang, G.H. Wang, J.J. Zhao, Physical Review B 64 (2001) 205411.

J.G. Han, Z.Y. Ren, Y.W. Zhang, Chemical Physics 305 (2004) 253.
B.X. Li, P.L. Cao, Physical Review B 62 (2000) 15788.
J. Wang, J.G. Han, Chemical Physics 342 (2007) 253.
J. Wang, H.J. Han, Journal of Physical Chemistry B 110 (2006) 7820.
J. Wang, J.G. Han, Journal of Chemical Physics 123 (2005) 244303.
W.J. Zhao, Z. Yang, Y.L. Yan, X.L. Lei, G.X. Ge, Q.L. Wang, Y.H. Luo, Acta Physica
Sinica 56 (2007) 2596.
W.J. Zhao, Y.X. Wang, Chemical Physics 352 (2008) 291.
J. Wang, J.G. Han, Journal of Physical Chemistry A 110 (2006) 12670.
W.J. Zhao, X.Y. Wang, Journal of Molecular Structure: THEOCHEM 901 (2009) 18.
S. Nukermans, X. Wang, N. Veldeman, E. Janssens, R.E. Silverans, P. Lievens,
International Journal of Mass Spectrometry 252 (2006) 145.
P. Ordejon, E. Artacho, J.M. Soler, Physical Review B (Rapid Communications)
53 (1996) R10441-4.
J.M. Soler, E. Artacho, J.D. Gale, A. Garcia, J. Junquera, P.D. Ordejon, S. Portal,
Journal of Physics: Condensed Matter 14 (2002) 2745.
J. Junquera, O. Paz, D. Sanchez-Portal, E. Artacho, Physical Review B 64 (2001)
235111.
J.P. Perdew, K. Burke, M. Ernzerhof, Physical Review Letters 77 (1996) 3865.
L. Kleinman, D.M. Bylander, Physical Review Letters 48 (1982) 1425.
J.M. Hunter, J.L. Fye, M.F. Jarrold, J.E. Bower, Physical Review Letters 73
(1994) 2063.
S. Ogut, J.R. Chelikowsky, Physical Review B 55 (1997) R4914.
M.B. Torres, E.M. Fernandez, L.C. Balbas, Physical Review B 71 (2005) 155412.