Magnetic main-group element impurities in CdS
P. Bedolla Velazquez and P. Mohn
Center for Computational Materials Science,
Vienna University of Technology,
Gußhausstraße 25/134, A-1040 Vienna, Austria
(Dated: February 10, 2011)
On the basis of ab-initio supercell calculations employing density functional theory (DFT) we
investigate the behaviour of main-group element impurities (B,N,C,O,F,Al,Si,P,Ga,Ge) in wurtzite
(w) and zincblende (zb) CdS lattices. It is found that the impurities prefer the sulfur position
and most of them, depending on the concentration exhibit magnetic order. We find that for small
concentrations (64zb/72w and 32zb atom supercells) a half metallic ferromagnetic behaviour is
found. For a 16 atom supercell for both zb- and w-structure partly also unsaturated magnetic
moments occur. For Si, Ge and P impurities a metamagnetic behaviour appears, which is found
for the first time in p-electron systems. A field dependence of the magnetic moments in these
materials may lead to new technological applications in these magnetic semiconductors as tunable
spin injection materials.
I.
INTRODUCTION
Recently Pan et al.1 proposed carbon doped magnetic wurtzite CdS as a possible material for spintronics application.
Their proposal was motivated by the need for half metallic ferromagnets in spintronic devices2 , which are seen as
key ingredients. Magnetically ordered p-electron elements have been described by Sieberer et al.3 in stoichiometric
zinc-blende CaAs and other I/II-V compounds where magnetic order is carried by the anion p-electrons without any
direct involvement of d-electrons as in the magnetic transition metals and their compounds. These materials can be
regarded as parent compounds for the understanding of other systems, where the magnetic polarization again appears
at a main-group element, which however is an impurity replacing another p-electron element. Another type of pelectron polarization is defect triggered p-electron magnetism which occurs in irradiated pyrolytic graphite containing
defects4–6 or CaB6 doped with La7 . During the last decade an enormous amount of work has been invested to study
dilute magnetic semiconductors (DMS). The prospect to exploit both the charge and the electron spin as information
carriers would combine information processing and storage at the same time.8–10
In this paper we calculate the magnetic and electronic properties of main-group element impurities
(B,N,C,O,F,Al,Si,P,Ga,Ge) in CdS. Our calculations are performed for supercells of the wurtzite (w) and zinc-blende
(zb) modofication of CdS for cell sizes 72(w) and 64(zb), 32(zb) and 16(zb)(w) atoms. The main-group element
replaces a sulfur atom leading to nominal impurity concentrations of 2.7, 3.125, 6.25, and 12.5 atom-percent impurity.
For the large cell sizes it is found that errors due to the underlying periodicity are reasonably small, so that interactions between the impurity atoms can be ruled out. For the 16-atom cell however, the impurity atoms do interact
and the respective bands appear to be broadened leading not only to a non-fully polarized state but also to itinerant
electron meta-magnetism (IEM) of the p-electrons. IEM is characterised by
II.
COMPUTATIONAL METHOD
The calculations were performed within the framework of density-functional theory (DFT)12 in the generalized
gradient approximation (GGA)13 , using the VASP program.11 Projector augmented wave (PAW) pseudopotentials
are used to describe the potential between the ions. The system was modeled in the hexagonal wurtzite structure
(the ground state of CdS) as well as in the cubic zinc-blende structure. To simulate different impurity concentrations,
three supercells with the following dimensions were constructed in the zb-structure: 8.2505 × 8.2505 × 8.2505 Å3 (16
atoms), 8.2505 × 8.2505 × 11.6679 Å3 (32 atoms) and 11.6679 × 11.6679 × 11.6679 Å3 (64 atoms) and for wz two
supercells of 8.2897 × 8.2897 × 6.7220 Å3 (16 atoms) and 12.5747 × 12.5747 × 13.6026Å3 (72 atoms). The structures
were relaxed allowing movement of the ions as well as changes in the shape and volume of the cell. In order to
avoid the Pulay stress and related problems, plane waves up to a cutoff energy of 1050 eV were included in the basis
set for the supercells in the FCC and wurtzite structures containing 16 atoms, and up to 600 eV in the remaining
supercells. The tetrahedron method without Blöchl corrections has been used for the Brillouin zone integration.
The integration was performed over the following k-meshes generated based on a Γ centered Monkhorst-Pack grid
scheme: 6 × 6 × 6 for the FCC structure containing 16 atoms (16 irreducible k-points), 4 × 4 × 4 for the FCC
structure containing 32 atoms (18 irreducible k-points), 4 × 4 × 4 for the FCC structure containing 32 atoms (18
irreducible k-points), 4 × 4 × 4 for the FCC structure containing 64 atoms (10 irreducible k-points), 6 × 6 × 6 for the
2
FIG. 1: 16-atom supercell for Cd8 XS7 , large balls are Cd-atoms, smaller balls are S-atoms, the impurity is located at (0,0,0).
wurtzite structure containing 16 atoms (34 irreducible k-points) and 4 × 4 × 4 for the wurtzite structure containing
72 atoms (13 irreducible k-points). The total energy was converged to 1 × 10−6 eV for all the wurtzite structures,
to 1 × 10−5 eV for the FCC structure containing 16 atoms and to 1 × 10−4 eV for the FCC structures containing
32 and 64 atoms. It is known that GGA, as all bare LDA functionals, yields too small an energy gap. However,
for the present investigation, where we are mainly interested in the fomation of magnetic order, that actual size
of the gap does not influence the results since the calculated LDA gaps are in any case wider than the impurity p-bands.
III.
CRYSTAL STRUCTURE
Wurtzite CdS is a prototypical II/VI semiconductor with an experimental direct bandgap of 2.5 eV. At a pressure
of 3 GPa the wurzite structure becomes transformed into the rocksalt structure and the bandgap is reduced to about
1.5 eV. We perform our simulation for the 2 closely related structures; wurtzite and zinc-blende16 :
i) The hexagonal wurtzite
(WZ) structure (P 63 mc, Nr. 186) is the ground state modification of CdS. If one assumes
p
the ideal c/a ratio of 8/3 and an internal u-parameter of 3/8 for the anion site and 0 for the cation site at the (2b)
Wyckoff position one obtains the same coordination numbers as for the zinc-blende structure.
ii) The zinc-blende (ZB) structure (I 43m, Nr. 216) is the cubic analog of the wurtzite and consists of two inter
penetrating fcc lattices, one of them shifted by a vector [ 14 , 41 , 41 ], resulting in a two component analog of the diamond
structure. Each atom of one kind is situated in an ideal tetrahedron made up of atoms of the other kind. As most
semiconductors crystallize in this structure, it is of great technological importance.
IV.
ZINC-BLENDE SUPERCELL CALCULATIONS
To study the concentration dependence of the magnetic properties of the impurities we perfom calculations for 3
diferent supercells containing 16, 32, and 64 atoms. The 16-atom supercell is shown in Fig. 1. For this small supercell
the impurities are only separated from each other by a single S atom. Consequently the impurties are not decoupled
from each other and their interaction leads to a relatively large width of the impurity bands.
The summary of the results is given in Table I. In this system three major interactions exists: i) interaction between
the impurities, ii) interaction between the impurity and the NN Cd, and iii) interaction between the impurity and
the NNN S. All three can produce a broadening of the impurity bands which suppresses the formation of a magnetic
moment. A detailed analysis of the interactions in carrier-mediated magnetic systems has been given by Dalpian and
Wei.17 For the 2nd period substitutions all but C impurities are non magnetic. For these elements the interaction
between the impurity and NNN S dominates, leading to a band broadening. Only for C substitutions the Fermi energy
in the non-magnetic state lies in a peak of the density of states which is large enough to fulfill the Stoner criterion so
that the p-bands of C split magnetically and produce a magnetic moment of 1.9µB . For the third period impurities
we find magnetic ordering throughout. Due to the increasing energetic separation of the S-2p and the impurity-3p
states, the overlap and consequently the impurity bandwidth is reduced so that for all 3 elements magnetic order
occurs. For the fourth period substitution the interaction between the impurity and Cd becomes important again
leading to a broadening of the impurity band and a subsequent supression of magnetic order. For all cases we also
calculated the respective fixed-spin-moment18 (FSM) curves which show the expected behaviour. Only on the case of
3
-47,015
total energy (eV)
-47,020
-47,025
-47,030
-47,035
-47,040
-47,045
0,0
0,5
m
1,0
agnetic
mm
o
1,5
2,0
ent (µB)
FIG. 2: FSM calculation for Cd8 SiS7 . The two minima at M ≈ 0.5µB and 1.5 µB are clearly visible.
TABLE I: 16-atom zinc-blende cell. Magnetic moments are given in bohr magnetons.∆ X-Cd is the change in distance between
the impurity and the NN Cd atom after relaxation. ∆ X-S is the change in distance between the impurity and the NNN S atom
after relaxation. ∆ V volume change after relaxation. All structural changes due to relaxation are related to the theoretical
equilibrium CdS structure.
Cd8 BS7
M = 0.0000
∆ B-Cd = -6.6808%
∆ B-S = 0.6043%
∆ V =1.8156%
Cd8 AlS7
M = 0.4076
∆ Al-Cd = 6.3662%
∆ Al-S = 2.7752%
∆ V = 8.5566%
Cd8 GaS7
M = 0.0000
∆ Ga-Cd = 5.8970%
∆ Ga-S= 2.6469%
∆ V= 8.1512%
Cd8 CS7
M = 1.8925
∆ C-Cd = -8.8218%
∆ C-S =0.2251%
∆ V = 0.6648%
Cd8 SiS7
M = 1.2916
∆ Si-Cd = 2.6497%
∆ Si-S = 2.1777%
∆ V = 6.6756%
Cd8 GeS7
M = -0.0022
∆ Ge-Cd = 4.3503%
∆ Ge-S= 2.4573%
∆ V= 7.5544%
Cd8 NS7
M = 0.0000
∆ N-Cd =-12.0424%
∆ N-S = -0.2130%
∆ V = -0.6623%
Cd8 PS7
M = 0.1753
∆ P-Cd = 0.2427%
∆ P-S = 1.7865%
∆ V = 5.4543%
Cd8 OS7
M = 0.0000
∆ O-Cd = -8.5643%
∆ O-S = -0.0130%
∆ V = 0.0478%
Cd8 S8
Cd8 FS7
M = 0.0000
∆ F-Cd = -1.6677%
∆ F-S = 1.1452%
∆ V = 3.4750%
a Si impurity we find a double minimum in the magnetic free energy at T = 0K (Figure 2). Such a behaviour is called
itinerant electron metamagnetism19 which leads to a discontinuous change in the magentic moment upon application
of an external field. While meta-magentism is well known for compounds containing 3d elements like YCo2 , Cd8 SiS7
is the rather rare case where meta-magnetism occurs for magnetically polarized p electrons.
Increasing the supercell size to 32 atoms (Fig. 3) reduces the impurity-impurity interaction and thus the dispersion
of the impurity bands. However, for the 2nd period substitutions we observe a large inward relaxation of the NN Cd
atoms which results in an enhanced interaction. This effect is particularily strong for N so that the N p-band is too
broad to allow for magnetic order. It should be noted that without relaxation nitrogen indeed polarizes magnetically
with a moment of 1µB , after relaxation the moment vanishes. For C and B impurities, the Fermi energy falls in a
peak of the density of states, so that the Stoner criterium becomes fulfilled, despite of the relatively broad p-band.
In both cases we find a saturated integer moment and consequently a malf metallic ferromagnetic groundstate. All
other impurities are either non-magnetic or they show very weak ferromagnetic order with small unsaturated moments
between 0.4 and 0.7µB with a very small magnetic stabilization energy of below 20meV .
For the 64 atom supercell the magnetic moments are found according to 6 − N , where 6 is the number of the S
valence electrons and N is the number of the impurity valence electron so that 6 − N counts the number of holes
inserted by the impurity. The only exception is again N which remains non-magnetic due to the large lattice relaxation
of the NN Cd atoms.
4
FIG. 3: 32-atom supercell for Cd16 XS15 , large balls are Cd-atoms, smaller balls are S-atoms, the impurity is located at (0,0,0).
FIG. 4: 64-atom supercell for Cd32 XS31 , large balls are Cd-atoms, smaller balls are S-atoms, the impurity is located at (0,0,0).
TABLE II: 32-atom zinc-blende cell. Magnetic moments are given in bohr magnetons.∆ X-Cd is the change in distance between
the impurity and the NN Cd atom after relaxation. ∆ X-S is the change in distance between the impurity and the NNN S atom
after relaxation. ∆ V volume change after relaxation. All structural changes due to relaxation are related to the theoretical
equilibrium CdS structure.
Cd16 BS15
mag = 3.0000
∆B-Cd = -5.0698%
∆B-S = 1.3959%
∆V = 4.0089%
Cd16 AlS15
mag = 0.6864
∆Al-Cd = 6.6766%
∆Al-S = 2.0169%
∆V = 7.0760%
Cd16 GaS15
mag = 0.6901
∆Ga-Cd = 6.5699%
∆Ga-S= 2.0331%
∆V= 6.9816%
Cd16 CS15
mag = 2.0000
∆C-Cd = -9.5537%
∆C-S = 1.2622%
∆V = 3.0910%
Cd16 SiS15
mag = 0.6886
∆Si-Cd = 2.0587%
∆Si-S = 1.9052%
∆V = 5.9806%
Cd16 GeS15
mag = 0.4352
∆Ge-Cd = 4.8823%
∆Ge-S= 1.7668%
∆V= 6.3483%
Cd16 NS15
mag = 0.0849
∆N-Cd = -12.4715%
∆N-S = 0.2398%
∆V = 1.4894%
Cd16 PS15
mag = 0.0001
∆P-Cd = 0.1951%
∆P-S = 1.3800%
∆V = 5.2680%
Cd16 OS15
mag = 0.0000
∆O-Cd = -9.0582%
∆O-S = 1.0410%
∆V = 2.9853%
Cd16 S16
Cd16 FS15
mag = 0.0000
∆F-Cd = -0.4692%
∆F-S = 1.5541%
∆V = 4.7014%
5
TABLE III: 64-atom zinc-blende cell. Magnetic moments are given in bohr magnetons.∆ X-Cd is the change in distance
between the impurity and the NN Cd atom after relaxation. ∆ X-S is the change in distance between the impurity and the
NNN S atom after relaxation. ∆ V volume change after relaxation. All structural changes due to relaxation are related to the
theoretical equilibrium CdS structure.
Cd32 BS31
mag = 3.0000
∆B-Cd = -5.2328%
∆B-S = 1.0907%
∆V = 4.6340%
Cd32 AlS31
mag = 3.0000
∆Al-Cd = 6.2569%
∆Al-S = 2.5729%
∆V = 6.0643%
Cd32 GaS31
mag = 3.0000
∆B-Cd = 5.9031%
∆B-S = 2.4518%
∆V = 5.9699%
Cd32 CS31
mag = 2.0000
∆C-Cd = -10.092%
∆C-S = 0.1251%
∆V = 4.2324%
Cd32 SiS31
mag = 2.0000
∆Si-Cd = 2.1903%
∆Si-S = 2.0285%
∆V = 5.6123%
Cd32 GeS31
mag = 2.0000
∆B-Cd = 4.9326%
∆B-S = 2.4377%
∆V = 5.8138 %
Cd32 NS31
mag = 0.0000
∆N-Cd = -13.1493%
∆N-S = -0.6723%
∆V = 3.1810%
Cd32 PS31
mag = 1.0000
∆P-Cd = 0.3586%
∆P-S = 2.044%
∆V = 5.2680%
Cd32 OS31
mag = 0.0000
∆O-Cd = -9.5322%
∆O-S = -0.4718%
∆V = 3.9755%
Cd32 S32
Cd32 FS31
mag = 0.0000
∆F-Cd = 1.4574%
∆F-S = 0.9680%
∆V = 5.1143%
TABLE IV: 16-atom wurtzite cell. Magnetic moments are given in bohr magnetons.∆ X-Cd is the change in distance between
the impurity and the NN Cd atom after relaxation. ∆ X-S is the change in distance between the impurity and the NNN S atom
after relaxation. ∆ V volume change after relaxation. All structural changes due to relaxation are related to the theoretical
equilibrium CdS structure.
Cd8 BS7
mag = 0.0000
∆B-Cd =-1.5005%
∆B-S = -3.2660%
∆V =3.1849%
Cd8 AlS7
mag = -0.6222
∆Al-Cd = 2.6516%
∆Al-S =0.3560%
∆V =3.1849%
Cd8 GaS7
mag = 0.4408
∆Ga-Cd = 1.5197%
∆Ga-S= -0.5059%
∆V= 2.7713%
1
2
3
4
5
6
7
8
9
10
Cd8 CS7
mag = 1.8414
∆C-Cd = -11.5511%
∆C-S =-1.7079%
∆V = -4.3801%
Cd8 SiS7
mag = -0.0006
∆Si-Cd =-1.6303%
∆Si-S = 0.3115%
∆V = 1.1239%
Cd8 GeS7
mag = 0.0000
∆Ge-Cd = 0.5154%
∆Ge-S=0.1713%
∆V= 1.9440%
Cd8 NS7
mag = 0.0000
∆N-Cd =-14.3183%
∆N-S = -2.0450%
∆V = -5.4872%
Cd8 PS7
mag = 0.0000
∆P-Cd = -1.8137%
∆P-S = 0.3281%
∆V = 0.1699%
Cd8 OS7
mag = 0.0000
∆O-Cd = -12.2511%
∆O-S = -2.0833%
∆V =-5.18828%
Cd8 S8
Cd8 FS7
mag = 0.0000
∆F-Cd =-6.4109%
∆F-S = -2.0129%
∆V = -1.5994%
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6
TABLE V: 72-atom wurtzite cell. Magnetic moments are given in bohr magnetons.∆ X-Cd is the change in distance between
the impurity and the NN Cd atom after relaxation. ∆ X-S is the change in distance between the impurity and the NNN S atom
after relaxation. ∆ V volume change after relaxation. All structural changes due to relaxation are related to the theoretical
equilibrium CdS structure.
Cd8 CS7
mag = 2.0000
∆C-Cd = -7.3950%
∆C-S = -1.2035%
∆V = -0.9610%
Cd8 SiS7
mag = 2.0000
∆Si-Cd = 3.9039%
∆Si-S =0.8704 %
∆V = 0.3519%
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