PHYSICAL REVIEW B 76, 195209 共2007兲
Effects of vacancies and impurities on the relative stability of rocksalt and zincblende structures
for MnN
M. S. Miao* and Walter R. L. Lambrecht
Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079, USA
共Received 28 September 2007; published 30 November 2007兲
Using density functional calculations, it is shown that pure MnN is stable in zincblende rather than in the
experimentally reported distorted rocksalt structure. However, about 4% N vacancies are found to stabilize the
rocksalt structure. It is found that C and O substitutions on N and Ga on Mn also favor rocksalt but Ni, SN,
FeMn, and CoMn stabilize zincblende. This suggests that zincblende MnN can possibly be grown under N-rich
condition with controlled doping of S, Fe, and Co.
DOI: 10.1103/PhysRevB.76.195209
PACS number共s兲: 61.72.Ji, 61.72.Ww, 71.20.Ps
I. INTRODUCTION
Manganese nitrides have been studied for decades because of the richness of the Mn-N phase diagram and the
variety of their magnetic properties.1,2 A renewed interest in
MnN has occurred in recent studies of dilute magnetic semiconductors because MnN might occur as a secondary phase
during the epitaxial growth of Mn doped nitride semiconductors, such as GaN, AlN, and InN.3–5 From this point of view,
it is of interest to better understand the phase stability and
structural preference of MnN. MnN is found experimentally
to occur in a distorted rocksalt 共RS兲 structure which is antiferromagnetic 共AFM兲 and metallic.6,7 The structure is distorted in the 关001兴 direction by a c / a ratio of 0.98, which
was shown8 to be related to the AFM order.
Although several computational studies have been performed based on first principles density functional methods
for MnN,8–11 few of them compared the energy difference
between different structures. Shimizu et al.12 found all the 3d
transition metal 共TM兲 nitrides to prefer the RS structure,
which is in contrast to the results that FeN and CoN were
reported to have the zincblende 共ZB兲 structure as ground
state in both experimental13,14 and theoretical studies.15 Using the full-potential linearized muffin-tin orbital 共FPLMTO兲 method, Miao and co-workers16,17 studied the relative stability of ZB and RS throughout the 3d series as a
function of lattice constant. It was found that the early TM
nitrides prefer RS and the later ones ZB, and lattice expansion favors ZB. The transition from RS to ZB stable structures occurs for MnN; i.e., the ground state of MnN was
found to be ZB and the RS structure became the preferred
state only under 4% compression. Being right at the transition, the energy difference between the two structures is
quite small for MnN, only 0.2 eV/ f.u. The recent first principles pseudopotential calculations performed by Hong et
al.18 also confirmed that MnN is globally stable in the ZB
structure. Yet, there have been no experimental reports of ZB
MnN. In this paper, we address potential reasons for this and
possible pathways to stabilize this phase in MnN.
At present, it is not clear whether the origin of this discrepancy between theory and experiment is due to experimental or computational inaccuracies. First, the calculations
used the local spin density approximation, which is known to
contract the lattice and stiffen the bonds and may have prob1098-0121/2007/76共19兲/195209共5兲
lems for systems containing localized d electrons. On the
other hand, most MnN samples have sizable concentration of
nitrogen vacancies and a tendency to lose N at higher temperature. In fact, the ␪ phase of MnN is sometimes labeled as
Mn6N5+x rather than MnN. Thus, vacancies could be stabilizing the RS structure.
In this work, we first check the total energy calculations
for MnN in both ZB and RS structures using different
exchange-correlation functionals. Second, we calculate the
total energies of MnN in the ZB and RS structures with
various concentrations of N vacancies. Finally, we study
other impurities and interstitial N and their effects on the
relative stability of ZB and RS and attempt to explain these
results in terms of known theories on the relative stability of
ZB and RS in TM nitrides.
II. COMPUTATIONAL METHOD
The basic methodology followed in this work is density
functional theory.19 The Kohn-Sham equations are solved using the linearized muffin-tin orbital 共LMTO兲 method.20 For
most of the calculations, we used the FP-LMTO method,21
which does not make any shape approximations to the potential or charge density and allows for accurate calculation
of the forces and hence structural relaxation in an all-electron
approach. Several exchange-correlation functionals are used
to test the robustness of our earlier prediction that ZB would
be the ground state of MnN.16 We used the von Barth–Hedin
共vBH兲,22 the Ceperley-Alder 共CA兲,23 and the Perdew-Wang
91 generalized gradient approximated 共GGA兲 functionals.24
The latter is currently only available in the atomic-sphere
approximation 共ASA兲 of our LMTO codes, while localdensity approximation 共LDA兲 is available in both ASA and
FP-LMTO. Therefore, we also studied the differences between FP-LMTO and ASA in the LDA. For the highly symmetric structures 共zincblende and rocksalt兲, the ASA is actually quite accurate if empty spheres are introduced in the
usual manner.
The major part of the paper concerns the effects of vacancies and other point defects on the relative stability of the
two structures. To study these defects, calculations are performed for supercells that contain 32 Mn and 32 N atoms.
Using the same supercell, we performed calculations for
MnN in ZB and RS structures with 0, 1, 2, 4, or 8 nitrogen
195209-1
©2007 The American Physical Society
PHYSICAL REVIEW B 76, 195209 共2007兲
M. S. MIAO AND WALTER R. L. LAMBRECHT
FIG. 2. 共Color online兲 The total energies for MnN in the ZB,
RS, and AFM distorted RS 共R1兲 structures for various nitrogen
vacancy concentrations.
FIG. 1. 共Color online兲 Cohesive energies for MnN in the ZB and
RS structures calculated by FP-LMTO and ASA-LMTO and with
various exchange-correlation functionals.
vacancies. The vacancies are uniformly distributed over the
cell, such that their distance to each other are approximately
the same. The advantage of using a constant supercell size
for different concentrations is that it makes the comparisons
of the total energy for different vacancy concentrations more
accurate. With the same unit cell and k-point mesh, numerical errors caused by the integrals in momentum space are
expected to cancel out to a large degree. A 4 ⫻ 4 ⫻ 4 k mesh
is used to ensure adequate convergence. The vBH exchange
and correlation functionals are used for the supercell calculations.
III. RESULTS
Figure 1 shows the cohesive energies of MnN in the ZB
and RS structures calculated using different combinations of
the exchange-correlation functionals and the LMTO methods. Both within GGA and LDA ZB are found to be lower in
energy than RS by about 0.2– 0.3 eV. Although there are
small quantitative differences between the different
exchange-correlation treatments, and between ASA and FPLMTO for the same exchange-correlation function, the basic
conclusion on which structure is the equilibrium one stays
the same. The present calculations are done for the ferromagnetic states only. The antiferromagnetic coupling for neighboring layers along the 关001兴 direction for the RS structure
and the corresponding strain relaxation along the 关001兴 direction can lower the energy of the RS structure. However,
this energy caused by the magnetic coupling is significantly
smaller than 0.1 eV and will not change the conclusion that
ZB is more stable.8 LDA calculations, FP or ASA, obtain RS
lattice constants slightly smaller than 4.0 Å that is about 5%
smaller than the experimental value. The ASA GGA calculations give a lattice constant of about 4.1 Å, which is still 3%
smaller than the experimental values. For the ZB structure,
both GGA and LDA, gave an equilibrium lattice constant of
4.2 Å.
Figure 2 shows the total energies for MnN in the ZB and
RS structures with various concentrations of N vacancies.
Because the equilibrium volume changes with the vacancy
concentration, we optimized the volume for each case. We
performed calculations for both the FM and distorted AFM
states of the RS structure, but only the FM state for the ZB
because the energy difference between the two, in this case,
is almost negligible. Figure 2 shows that the RS structure is
higher in energy for pure MnN but becomes lower in energy
than ZB in the presence of a sufficient concentration of nitrogen vacancies. The crossing point is at about 4%.
The existence of the nitrogen vacancies at the level of a
few percent cannot be excluded in the RS MnN samples
synthesized by Suzuki et al.6 by a reactive sputtering method
in N2 gas, a method which lacks N activation. The 共unstated兲
error bar in their chemical analysis method is likely to be of
the order of a few percent. Yang et al.,7 using molecular
beam epitaxy with a nitrogen plasma source, provided evidence of a closer to ideal Mn:N ratio of 1:1 but grew their
samples as very thin films on a MgO substrate, which may
have assisted in stabilizing the rocksalt structure.
It is interesting to note that the AFM distorted RS structure is predicted to be slightly higher in energy than the FM
RS for pure MnN near the calculated equilibrium volume.
However, when adding about 4% vacancies, the AFM state
becomes lower than the FM one, in agreement with experiment.
The energy of formation of the nitrogen vacancy for phase
␣ 共RS or ZB兲 is defined as
⌬E f 共␣兲 = E关D, ␣兴 − E关C, ␣兴 + ␮N ,
共1兲
with ␮N the chemical potential of N and E关D , ␣兴 and E关C , ␣兴
are the binding energies of the defect containing cell and
perfect crystal cell, respectively, relative to the energy of the
free atoms. In the N-rich limit, the chemical potential of N is
taken to be half the 共experimental兲 binding energy of a N2
molecule, or −4.9 eV,25 while in the Mn-rich limit, ␮Mn is
taken to be the binding energy in bulk fcc Mn, calculated to
be −2.7 eV and in good agreement with experimental data
共−2.94 eV兲.26 With our calculated cohesive energy of
−15.9 eV for MnN, this gives as energy for formation from
195209-2
PHYSICAL REVIEW B 76, 195209 共2007兲
EFFECTS OF VACANCIES AND IMPURITIES ON THE…
FIG. 3. 共Color online兲 N vacancy formation energies with different N chemical potentials.
bulk Mn and N2, ⌬H f 共MnN兲 = −8.3 eV. The excess chemical
˜ i = ␮i − ␮ref
potentials ␮
i are defined with respect to these reference states. To form MnN, the excess chemical potentials
of the Mn and N atoms should satisfy the condition,
˜ Mn + ␮
˜ N = ⌬H f 共MnN兲, and the allowed ranges of Mn and N
␮
˜ Mn 艋 0 and
excess chemical potentials are ⌬H f 共MnN兲 艋 ␮
˜ N 艋 0. The variation of the formation energy
⌬H f 共MnN兲 艋 ␮
with the N chemical potential is shown in Fig. 3. It reveals
that under nitrogen-rich condition, the nitrogen vacancy formation energy is 5 eV for RS structure and 9 eV for ZB
structure. However, under relative N-poor condition, the formation energy becomes negative for RS structure, indicating
that the system prefers to accommodate vacancies. For ZB
structure, the formation energy stays positive even under extreme N-poor condition, although it can be as low as 0.5 eV.
The above calculated formation energies are obtained
from 64 atom supercells with one vacancy, corresponding to
a concentration of about 3%. However, it is worth noting that
the calculated formation energy changes vary only slightly
with the concentration and thus correspond essentially to the
dilute limit. This can be clearly seen from Fig. 2. The total
energy for ZB, RS, and AFM RS almost fall on straight lines,
respectively. This indicates that the energy cost is proportional to the concentration and justifies the identification of
the energy per vacancy in these cells with the dilute limit of
the energy of formation. This also indicates that the interactions between the vacancies are small and very short range
even though the system is metallic. We can then, in principle,
obtain the minimum concentration of vacancies to stabilize
the RS structure from
xmin关⌬E f 共RS兲 − ⌬E f 共ZB兲兴 = EZB − ERS ,
共2兲
where the EZB and ERS are the binding energies of MnN
taken at zero concentration of vacancies. This gives
xmin = 0.043, close to the direct observation shown earlier and
independent of the choice of chemical potential.
In Fig. 4, we show the partial density of states 共PDOS兲 of
the Mn atom next to the vacancy in comparison with the Mn
atom far away from the vacancy, in the energy range of
mostly Mn d – N p antibonding states. One can see that the
changes in PDOS caused by the vacancy are more profound
in the ZB than in the RS structure. This is essentially because
in RS, the eg orbitals, which form ␴ bonds with the N, and
FIG. 4. 共Color online兲 Partial density of states for MnN in the
ZB and RS structures with N vacancies. The black solid lines show
the total density of states 共DOS兲 for Mn atoms around the vacancy.
The area shaded by pink pattern lines descending from left to right
shows the partial DOS of Mn d states with e symmetry, and the area
shaded by green pattern lines rising from left to right show the
states of t2 symmetry. The dashed lines show the total DOS of Mn
far from the vacancy.
are therefore most directly affected, occur far away from the
Fermi level as bonding or antibonding states, while in ZB, eand t2-like states are more mixed up near EF. It is not
straightforward to interpret the change in total energy in
terms of these PDOS changes because other terms than the
band structure come into play. Nevertheless, one may note
that in ZB, there is as strong depression of occupied PDOS
in the minority spin channel in the range of −2 eV to the
Fermi level and an increase in e-like states above EF which
would raise the sum of occupied one-electron energies. Thus,
this can at least partially be held responsible for the energy
cost of forming nitrogen vacancies in the ZB. In the RS, no
such effect is discernible, which would partially explain why
vacancies form more easily in RS and hence favor the RS
over the ZB structure.
We can also see in Fig. 4 that in ZB, there is a much
smaller splitting between up and down spin states, consistent
with the small magnetic moment in MnN.16 Examining the
magnetic moments in ZB in more detail, we also observe an
increase in magnetic moment for the Mn near the vacancy in
ZB, consistent with the PDOS changes. We can see in Fig. 4
that there is a gap just above EF for majority spin states,
making the system close to a half-metal. This only occurs
when we add vacancies in ZB-MnN. Thus, ZB-MnN containing vacancies or other magnetic impurities might be interesting as a magnetic material, but we have not yet investigated whether the system prefers ferromagnetic or
antiferromagntic alignment. This is rather difficult to ascertain if the moments are so small and taking into account the
disorder aspects. Furthermore, the desire to make ZB-MnN
ferromagnetic and stabilizing ZB-MnN in the first place appear to be in conflict with each other, since the latter requires
suppressing the vacancies.
Because most of the commonly used semiconductors have
tetrahedrally bonded structures, ZB MnN could give a better
interface matching, which could be useful for metal semicon-
195209-3
PHYSICAL REVIEW B 76, 195209 共2007兲
M. S. MIAO AND WALTER R. L. LAMBRECHT
TABLE I. Formation energies for various defects in MnN. The
chemical potential of N is taken as −8.7 eV which is neither at
N-rich nor at N-poor condition.
VN
CN
ON
SN
Ni
GaMn
FeMn
CoMn
RS 共FM兲
RS 共AFM兲
ZB 共tetra兲
ZB 共octa兲
2.45
−0.29
−2.89
1.11
6.32
5.65
6.48
5.60
2.18
−0.24
−2.54
2.34
5.69
5.88
6.17
5.42
6.26
0.27
−1.54
0.36
3.94
6.72
5.52
4.78
¯
¯
¯
¯
3.85
¯
¯
¯
ductor contacts. It thus appears interesting to search for a
way to stabilize ZB MnN. Our calculations suggest that one
might achieve this goal by controlling the growth condition
to avoid the formation of N vacancies in the sample. On the
other hand, other impurities might assist in stabilizing the ZB
structure. Our search includes anion impurities, such as C, S,
and O substitutions at N sites, N interstitials, and cation impurities, such as Ga, Fe, and Co substitutions at the Mn site.
Table I shows that the C and O substitutions have lower
formation energies for RS MnN and will stabilize it. The N
interstitial, however, does show a lower formation energy for
ZB structure. However, the formation energy of Ni is high.
Only under extreme N-rich condition, the formation energy
of N interstitials can be lowered to 0.13 eV for ZB structure
and 1.88 eV for RS structure. There are actually two different interstitial sites in ZB structure, the tetrahedral and the
octahedral sites, but as shown in Table I, their formation
energies differ only slightly.
For cation impurities, we notice that the nitrides of Ga,
Fe, and Co are stable in either wurtzite or ZB structures. The
energy difference between the wurtzite and the RS structures
for GaN can be as large as 0.7 eV/ f.u. However, as shown in
Table I, the formation energy of GaMn is significantly lower
for RS structure, which is in contrast to the bonding nature of
Ga atom which tends to be tetrahedrally bonded with the
surrounding N atoms. On the other hand, Fe and Co substitutions do have lower formation energies in ZB MnN.
An interesting discussion of the relative stability of the
ZB vs RS structure in the TM nitrides was given by Eck et
al.27 using the concept of crystal orbital Hamilton population
共COHP兲. This analysis is based on a partitioning of the band
structure energy into contributions from different bonds. It
allows one to discern bonding and antibonding regions for
different atomic orbital pairs. They found that the relative
stability of RS vs ZB is decided not so much by the N-TM
bonds but by the TM d-d interactions. In a rigid band structure view, only the bonding states are filled for early TMs,
and therefore, the RS structure is more stable. In contrast, for
late TMs, the antibonding states are also filled, therefore
weakening the d-d interactions in RS structure and destabilizing it. Based on the COHP analysis, they predicted that
MnN would be stable in the ZB structure.
We found that the behavior of most of the impurities in
Table I can be understood from this point of view. Because
the electrons have started to fill in the antibonding states in
MnN, an electron density increase will destabilize the RS
structure, and conversely, any electron decrease will stabilize
RS. Among the impurities shown in Table I, SN, Ni, FeMn,
and CoMn act like electron donors as they are rich in electrons. Therefore, they should favor the ZB structure. On the
other hand, CN and GaMn remove electrons and stabilize the
RS structure. We emphasize that the word donor here is used
in a chemical sense not in the sense of inducing shallow
impurity levels in the gap of a semiconductor. MnN is, in
fact, found to be metallic both in the ZB and RS phases. Mn
in MnN can be considered to be trivalent and thus isovalent
with Ga in terms of sp bonding, but Ga would lack the
d-valence electrons and thus reduce the effective number of
electrons in the d bands, so that the band filling is more as in
the early transition metals which favor RS. However, the
behavior of VN and ON cannot be understood from this point
of view. Both impurities are donors, yet favor the RS structure. Considering the strength of the Mn-N and Mn-O bonding that are involved in these two impurities, the relative
stability of RS and ZB structures in these cases appears to be
caused by the cation-anion bonding. Due to the strong
changes of such bonding states, the rigid band view might
not hold.
IV. CONCLUSIONS
In conclusion, our first principles calculations show that
MnN is thermodynamically stable in the ZB structure, provided the system has less than 4% nitrogen vacancies. Comparison of several LDA and GGA exchange-correlation functionals confirms this earlier finding.16 Impurities, such as C
and O substitutions at anion or Ga at cation sites, can also
stabilize the RS structure. On the other hand, N interstitials,
S 共on N兲, and Fe or Co 共on Mn兲 substitutions can significantly stabilize the ZB structure. The effects of most of these
various impurities can be understood in a rigid band picture
in terms of electron donation or removal from the d bands,
which strengthens 共weakens兲 the d-d bonding preferentially
in RS. However, ON and VN affect the Mn-N bonding too
strongly and are also found to favor rocksalt. Therefore, we
suggest that the growth of ZB MnN would be facilitated
under N-rich conditions and with controlled doping of S, Fe,
or Co.
ACKNOWLEDGMENTS
This work was supported by the Office of Naval Research
under Grant No. N00014-02-0880. The calculations were
performed at the Ohio Supercomputing Center.
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PHYSICAL REVIEW B 76, 195209 共2007兲
EFFECTS OF VACANCIES AND IMPURITIES ON THE…
*Present address: Institute for Shock Physics, Washington State
University, Pullman, WA 99164-2816.
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