PHYSICAL REVIEW B 72, 033204 共2005兲
Electronic structure and magnetic properties of Mn3GaN precipitates in Ga1−xMnxN
M. S. Miao, Aditi Herwadkar, and Walter R. L. Lambrecht
Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079 USA
共Received 6 March 2005; published 15 July 2005兲
The electronic structure and the magnetic properties of Mn3GaN are studied as a function of lattice constant
and are compared with those of Mn4N. The local moments on the Mn atom in Mn3GaN and the face centered
Mn atoms in Mn4N show very similar values and behavior as a function of lattice constant. Mn3GaN is found
to be ferromagnetic near its equilibrium volume. Under volume expansion, the spins become antiparallel in the
关001兴 direction. However, the total spins in successive planes are different, leading to a net nonzero magnetic
moment. The density of states at the Fermi level is very different for majority and minority spins for both
Mn3GaN and Mn4N, indicating they can be used for spin injection.
DOI: 10.1103/PhysRevB.72.033204
PACS number共s兲: 75.50.Pp, 75.10.Lp, 75.90⫹w
Among the many different dilute magnetic semiconductors, Ga1−xMnxN is one of the most interesting, as the mean
field theory predicts it to be a good candidate for room temperature ferromagnetic semiconductor behavior. However, it
is a technically challenging problem to dope Mn in GaN to a
high concentration. Currently, many heavily doped samples
have been found to contain precipitates of secondary phases
with high Mn concentration, such as Mn3GaN,1–3 Mn4N,4–6
Mn3Ga,3 and even Mn metal.3 The mixing of the magnetism
of these precipitates with the intrinsic GaN:Mn dilute magnetic semiconductor behavior also raises uncertainties about
the results for low concentration Mn doped GaN samples
that are nominally homogeneous but may contain precipitates of sizes below the detection limit. On the other hand,
these precipitates, especially Mn3GaN, may form ohmic contacts with the sample and offer a high concentration of carriers to the Ga1−xMnxN solid solution region1 of the sample.
These properties are of considerable practical interest for applications to magnetotransport and maybe also to spin injection. Finally, the observed room temperature ferromagnetism
in GaN:Mn has so far not been assigned to the Mn3GaN
phase because it is believed to be paramagnetic at room temperature. However, in a Ga1−xMnxN sample, the precipitates
region might suffer a large volume expansion due to the
lattice mismatch. Therefore, it is important to understand
how its magnetic properties change with volume.
Mn3GaN has not been thoroughly studied. However,
many theoretical and experimental studies have been devoted
to Mn4N.7–16 Several band structure calculations and experimental measurements found that Mn4N is ferrimagnetic. Pop
et al. showed evidence that Mn4N is an itinerant magnetic
system.13 Uhl et al. found that in addition to the dominant
ferrimagnetic ordering, a small noncollinear component exists in the magnetic moments of Mn4N.15
In this paper, we study the electronic structure and the
magnetic properties of Mn3GaN by means of the full potential linear muffin tin orbital 共FP-LMTO兲 method and the von
Barth and Hedin spin polarized local density approximated
exchange correlation functional.17 For comparison, we also
discuss computational results for cubic Mn4N and a model
Mn3N system.
Mn3GaN has antiperovskite structure. One Ga atom occupies the corner of the simple cubic unit cell and one N atom
1098-0121/2005/72共3兲/033204共4兲/$23.00
the center of the cube. Three Mn atoms occupy the face
centers of the cube. If the Ga atom is replaced by another Mn
atom, it becomes Mn4N. Therefore, in Mn4N, the Mn atoms
are in two classes. The Mn atoms at the face centers 共labeled
MnI兲 are connected with one nitrogen atom, whereas the Mn
at the corner 共MnII兲 is isolated from nitrogen bonding. For
comparison, we also studied a model system Mn3N that can
be derived from Mn3GaN by taking off the Ga atom at the
cube corner.
Figure 1 presents the total energy of Mn4N, Mn3N, and
Mn3GaN in several different magnetic states, including ferromagnetic 共FM兲, antiferromagnetic 共FR-关001兴1兲, and cubic
ferrimagnetic 共c-FR兲 states. The FR-关001兴1 ordering corresponds to an antiferromagnetic 共AFM兲 ordering of ferromagnetically aligned spins in 共001兲 planes but allowing the magnetic moments to be different on successive planes and with
the spin flipping every layer. The alternate c-FR ordering
studied only for Mn4N corresponds to opposite spin orientations for the MnI and MnII sublattices. Whereas the
FR-关001兴1 configuration has effectively tetragonal symmetry, c-FR maintains cubic symmetry.
The calculated equilibrium lattice constants are very close
for the three different systems. They are all around 3.65 Å.
FIG. 1. 共Color online兲 The total energy for Mn4N, Mn3GaN, and
Mn3N in different magnetic ordering configurations.
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©2005 The American Physical Society
PHYSICAL REVIEW B 72, 033204 共2005兲
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FIG. 2. 共Color online兲 The energy differences between c-FR and
FR-关001兴1 states and FM state. The vertical line shows the experimental lattice constant for Mn4N.
FIG. 3. 共Color online兲 Magnetic moments for Mn4N, Mn3GaN,
and Mn3N under different lattice constants. The experimental lattice
constant for Mn4N is shown by a vertical line.
This value is about 5% smaller than the experimental value
for Mn4N.11,18 This reduction of the volume is a typical
discrepancy of the local density approximation 共LDA兲. We
also note that this lattice constant is much smaller than the
cubic GaN lattice constant of 4.50 Å. Therefore, the hypotehtical Mn3GaN precipitates in GaN:Mn would be stretched
due to the lattice mismatch.
Figure 2 shows that Mn3GaN is FM near its equilibrium
volume. But under large volume expansion it can become
FR-关001兴1. In the cubic cell, there are two Mn atoms in one
sublattice but only one in the other. Therefore the total magnetic moment is still not zero and the system is in fact ferrimagnetic. Another important feature is that under large volume expansion, the energy difference between the FM
and the FR-关001兴1 state becomes larger, which indicates a
stronger magnetic interaction between the neighboring Mn
atoms. Therefore the critical temperature might be expected
to increase with volume expansion.
Mn4N is c-FR around the equilibrium and becomes
FR-关001兴1 under volume expansion. Their energy differences
from the FM state are much larger than those of Mn3GaN.
This is because the magnetic moment on the isolated Mn is
usually significantly larger than that of the other Mn. Therefore it possesses larger magnetic interactions. Although most
of the experimental and theoretical works agree that Mn4N
has the c-FR ordering, some early works propose the tetragonal FR-关001兴1 ordering, showing that the two are not so
easy to distinguish. Mn3N clearly has a much stronger tendency to FR-关001兴1 ordering. Its energy difference between
the FM and FR-关001兴1 configurations is in between those of
the Mn3GaN and Mn4N systems.
Figure 3 presents the magnetic moments of MnI and MnII
in Mn4N in the c-FR state and the magnetic moments of Mn
in Mn3GaN and in Mn3N in FM state as function of lattice
constant. It shows that the isolated Mn in Mn4N has the
largest magnetic moments. Near the experimental volume, its
value is ⬃3, whereas, the face centered MnII has a magnetic
moment close to 1. The net magnetic moment is very small,
only 0.6. The net spin direction is parallel to that of the
isolated Mn. The moment of Mn3GaN is very close to that of
MnII in Mn4N. Under large volume expansion, both Mn in
Mn3GaN and MnII in Mn4N have much larger moments than
at the equilibrium volume.
Under compression, the Mn changes from a high spin
configuration to a low spin configuration. As the lattice constant is reduced from the highest value considered in Fig. 3
the magnetic moment of the isolated MnI in Mn4N initially
decreases slowly, but at a compression factor of about 0.93,
the magnetic moment drops suddenly to a value very close to
0. Interestingly, the curve of the magnetic moment as a function of lattice constant of Mn in Mn3GaN is very similar to
that of the face centered MnII in Mn4N, except for the jump
at 7% lattice constant compression for the latter. This jump is
caused by the jump of the magnetic moment of MnI. The
overall reduction of the magnetism during volume compression can be understood by noticing that the d electrons are
more delocalized with smaller volume and the spin polarization is smaller. The drastic changes of the MnII in Mn4N and
Mn in Mn3GaN around lattice constants of about 4.0 Å is
due to the competition between the spin splitting and the
crystal field splitting. The curve for Mn3N is different from
the other two systems. At large lattice constant the Mn is in
a high spin configuration. The magnetic moment decreases
increasingly faster until it disappears at a ⬇ 3.6 Å. This behavior is similar to that of the isolated Mn in Mn4N.
Figure 4 presents the total and partial density of states
共DOS兲 of Mn4N, Mn3GaN, and Mn3N calculated at a lattice
constant of 3.852 Å, the experimental value for Mn4N.18 It
shows that the DOS near the Fermi level is mainly contributed by Mn d orbitals. The lower group of the valence bands
consist mostly of the nitrogen p states. Comparing the partial
density of states 共PDOS兲 of Mn in Mn3GaN and MnII in
Mn4N, we find that the two are very similar to each other,
including important features such as the spin splitting. We
note that the MnII spin is in the opposite direction to the MnI
and the total spin. Therefore its majority spin channel is spin
down and shown as negative values in Fig. 4. In other words,
we need to compare MnII-d↓ in Mn4N with Mn-d↑ in
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FIG. 5. 共Color online兲 Spin polarization at Fermi level for
Mn3GaN and Mn4N as a function of lattice constant. The vertical
line shows the experimental lattice constant for Mn4N.
FIG. 4. 共Color online兲 Density of states for Mn4N, Mn3GaN,
and Mn3N systems. The black solid lines are for total DOS. The
green dashed lines are for MnI partial DOS in Mn4N and for Ga
partial DOS in Mn3GaN. The filled red areas are for MnII in Mn4N
and Mn in Mn3GaN and Mn3N.
Mn3GaN. Figure 4 also shows that the isolated MnI in Mn4N
has much stronger spin polarization.
Figure 4 also shows another important feature of
Mn3GaN. Its Fermi level is located in a dip of its majority
spin channel. Therefore its DOS at the Fermi level is very
different for the two spin channels. This indicates that the
carrier concentrations are different for the different spin
channels. Mn3GaN should thus be potentially useful as spin
injection material into the Ga1−xMnxN system. However, in
real samples, Mn3GaN may have large lattice expansion due
to the lattice mismatch to the substrate that it is grown on.
For example, GaN is a potential substrate to grow Mn3GaN
and its lattice constant is 4.5 Å in cubic structure. Under
such volume expansion, Mn3GaN is almost 100% spin polarized. As shown by Fig. 3, the spin polarization increases
with increasing lattice constant. The effectiveness of the spin
injection should generally become better. However, the spin
injection rate depends on the spin polarization of the DOS at
the Fermi level rather than on the total spin polarization integrated over all occupied states. The former does not necessarily increase monotonically with volume expansion.
To gain further insight into the spin injection efficiency,
we calculated the spin polarization of the DOS at the Fermi
level, which is defined as
PF =
N↑共EF兲 − N↓共EF兲
,
N↑共EF兲 + N↓共EF兲
共1兲
for Mn3GaN and Mn4N for different lattice constants. The
results are presented in Fig. 5. For Mn4N, the spin polarizations are calculated from both the total DOS as well as the
partial DOS of the face centered Mn 关MnII兴. From Fig. 4 one
can see that MnI states are strongly spin split and do not
contribute strongly to the DOS at the Fermi level. The calculation using only MnII atoms takes this idea to an extreme
limit by omitting its contribution to the DOS entirely. As one
can see, this does not change the behavior of PF very much.
It reinforces the idea that the MnII atoms provide the localized moments responsible for the magnetism while the MnI
atoms provide the itinerant electrons at the Fermi level responsible for the metallic transport behavior.
Figure 5 shows that at the equilibrium lattice constant, PF
is around 0.6 to 0.7 for both compounds. However, with a
slight increase of lattice constant, PF drops quickly for
Mn4N. It drops to a value close to zero and even becomes
negative for a small range of lattice constants around 4.0 Å,
meaning that it behaves opposite to the total integrated spinpolarization or magnetic moment. However, at lattice
constants larger than 4.0 Å, the PF increases quickly with
increasing lattice constant and regains a value of about 0.6 at
lattice constants close to that of GaN. The PF for Mn3GaN
shows a similar trend as that of Mn4N. However, it keeps a
value around 0.6 until 4.0 Å and shows a wiggled structure
around 4.1 to 4.2 Å. It increases with lattice constant larger
than 4.2 Å and restores its large value of 0.6 at lattice constants larger than 4.4 Å. This more complex behavior simply
reflects the behavior of the peaks in the density of states
which move apart for spin up and spin down as the lattic
constant increases.
In conclusion, we have calculated the electronic structure
of Mn3GaN, Mn4N, and Mn3N as a function of lattice constant. Our results show that Mn3GaN is ferromagnetic near
its equilibrium volume and becomes ferrimagnetic
FR-关001兴1 under large volume expansion. The magnetic moment and its behavior as a function of lattice constant are
very similar to those of the face centered MnII in Mn4N. The
PDOS for Mn4N and Mn3GaN reveals that the electronic
structure of their face centered Mn are very close to each
other. These results indicate that Mn4N can be be viewed as
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consisting of local spins 共on the corner sites of the simple
cubic cell兲 embedded in a weaker itinerant ferromagnetic
system formed by the face centered Mn atoms. The DOS at
the Fermi level is very different for the two spin channels,
indicating that Mn3GaN should be useful for spin injection
into magnetic semiconducting nitrides. Our calculations
show that Mn3GaN does have a large polarization ratio both
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This work was supported by the Office of Naval Research
under Grant No. N00014-02-0880 and the National Science
Foundation under Grant No. ECS-0223634. Most of the calculations were performed at the Ohio Supercomputing Center under Project No. PDS0145.
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