Physics Letters A 372 (2008) 1512–1515
www.elsevier.com/locate/pla
A first-principles study of half-metallic ferromagnetism
in binary alkaline-earth nitrides with rock-salt structure
G.Y. Gao a , K.L. Yao b,a,∗ , Z.L. Liu a , J. Zhang a , Y. Min a , S.W. Fan a
a Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
b International Center of Materials Physics, Chinese Academy of Science, Shenyang 110015, China
Received 12 June 2007; received in revised form 28 August 2007; accepted 25 September 2007
Available online 5 October 2007
Communicated by R. Wu
Abstract
In this Letter, using the first-principles full-potential linearized augmented plane-wave (FP-LAPW) method, we extend the electronic structure and magnetism studies on zinc-blende structure of II–V compounds MX (M = Ca, Sr, Ba; X = N, P, As) [M. Sieberer, J. Redinger,
S. Khmelevskyi, P. Mohn, Phys. Rev. B 73 (2006) 024404] to the rock-salt structure. It is found that, in the nine rock-salt compounds, only
alkaline-earth nitrides CaN, SrN and BaN exhibit ferromagnetic half-metallic character with a magnetic moment of 1.00 μB per formula unit.
Furthermore, compared with the zinc-blende structure of CaN, SrN and BaN, the rock-salt structure has lower energy, which makes them more
promising candidates of possible growth of half-metallic films on suitable substrates.
© 2007 Elsevier B.V. All rights reserved.
PACS: 75.90.+w; 71.20.Dg; 71.15.Mb
Keywords: Half-metallic ferromagnetism; Alkaline-earth metals; First-principles calculations
In recent years, half-metallic (HM) ferromagnets, where one
of the two spin channels is metallic and the other is semiconducting or insulating, leading to complete (100%) spin polarization at the Fermi level, have attracted more and more research
interest because of their promising application in spintronic
devices, in particular as a source of spin-polarized carriers injected into semiconductors. The original introduction of HM
ferromagnet was in 1983 by de Groot et al. [1], who calculated the band structure of half-Heusler compound NiMnSb.
Since then more HM ferromagnets were also found and extensively studied, e.g., half-Heusler alloys such as CoMnSb and
CoVSb [2], full-Heusler alloys such as Co2 FeSi [3], Co2 MnSi
and Co2 MnGe [4], metallic oxides such as CrO2 [5] and
Fe3 O4 [6], diluted magnetic semiconductors such as Co-doped
* Corresponding author at: Department of Physics, Huazhong University of
Science and Technology, Wuhan 430074, China. Tel.: +86 27 87556264; fax:
+86 27 87556264.
E-mail addresses: [email protected] (G.Y. Gao),
[email protected] (K.L. Yao).
0375-9601/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.physleta.2007.09.064
ZnO [7] and Mn-doped GaN [8], and perovskite compounds
such as Sr2 FeMoO6 [9] and La0.7 Sr0.3 MnO3 [10]. Recently,
Akinaga et al. [11] predicted CrAs in the metastable zincblende (ZB) structure to be a half-metal, then they grew it
in thin films and found that it has a high Curie temperature
(> 480 K). This work inspired extensive studies on magnetism
and electronic structure of ZB transition-metal pnictides and
chalcogenides [12–15] as well as Mn-IV compounds [16]. Most
of them were found to be HM ferromagnets.
However, these HM ferromagnets mentioned above are all
based on transition metals. Remarkably, HM ferromagnets excluding transition metals were first reported in 2004 by Geshi
et al. [17]. Their first-principles calculations indicated that Ca
pnictides CaP, CaAs and CaSb with ZB structure are all HM
ferromagnets with a magnetic moment of 1.000 μB per formula
unit. These compounds do not contain any transition-metal
atoms and therefore the mechanism of ferromagnetism is different from both the double exchange and the p–d exchange
that are important in magnetic 3d compounds. Here the crucial
role is played by the spin polarization of the p states of pnic-
G.Y. Gao et al. / Physics Letters A 372 (2008) 1512–1515
1513
Table 1
The calculated equilibrium lattice constants of rock-salt MX (M = Ca, Sr, Ba;
X = N, P, As) in ferromagnetic state and the total magnetic moments per formula unit
Ca
Sr
Ba
Equilibrium lattice constant (Å)
N
P
As
Total magnetic moment (μB )
N
P
As
5.03
5.40
5.69
1.00
1.00
1.00
5.86
6.21
6.58
6.02
6.36
6.72
0.27
0.50
0.88
0.02
0.09
0.04
tides. Later, several research groups [18,19] completely investigated the electronic structure and magnetism of all ZB II–V
compounds. It was found that MgN and MZ (M = Ca, Sr, Ba;
Z = N, P, As, Sb, Bi) with ZB structure are all HM ferromagnets. Recently, Volnianska et al. [20] further extended the analysis of ZB structure of Ca pnictides to the NiAs structure. Their
results indicated that in the NiAs structure only CaN is a ferromagnetic half-metal.
To the best of our knowledge, the previous studies on HM
ferromagnets excluding transition metals based on II–V compounds were almost focused on the ZB structure. There have
been few reports on HM ferromagnetism in rock-salt structure.
In Ref. [18], Sieberer et al. calculated the total energy versus volume for CaAs, as a prototype of II–V compounds, in
various structures of ZB, wurtzite, rock-salt and NaO. Their
calculations indicated the rock-salt structure is energetically
more stable than the ZB structure, but their studies on the magnetic properties of II–V compounds were only focused on the
ZB structure. In this Letter, therefore, we extend the magnetic
study on ZB structure of II–V compounds MX (M = Ca, Sr, Ba;
X = N, P, As) to the more stable rock-salt structure. Our firstprinciples calculations indicate that only CaN, SrN and BaN
exhibit HM character in these nine rock-salt alkaline-earth pnictides MX.
The present calculations of the geometry optimization and
the electronic structure of rock-salt MX are performed by
employing the first-principles full-potential linearized augmented plane-wave (FP-LAPW) method implemented in the
Wien2k code [21]. The radii Rmt of the muffin tins are
chosen to be as large as possible, but not overlapped. We
use the generalized gradient approximation in the scheme of
Perdew–Bueke–Ernzerhof (GGA-PBE) [22] for the exchange–
correlation functional, and the relativistic effects are taken into
account in the scalar approximation. The Rmt Kmax is set as 8.0,
and 3000 k-points are used in the first Brillouin zones. The selfconsistency is considered to be achieved when the total-energy
difference between consequent iterations is less than 10−5 Ry
per formula unit.
In order to search for HM ferromagnetism in rock-salt MX,
we must firstly determine their equilibrium lattice constants,
thus we perform geometry optimization of rock-salt MX by ferromagnetic (FM) calculations of total energy versus volume.
The equilibrium lattice constants in the FM state and the total
magnetic moments per formula unit of rock-slat MX are obtained, which are presented in Table 1. From Table 1 we can
see that the magnetic moments of rock-salt MAs are very small,
Fig. 1. Total energy versus volume per formula unit for rock-salt CaN with
ferromagnetic (FM), antiferromagnetic (AFM) and paramagnetic (PM) states.
and only the magnetic moments of three rock-salt nitrides CaN,
SrN and BaN are an integer value of 1.00 μB , which is the typical character of HM ferromagnets. Therefore, only rock-salt
CaN, SrN and BaN may be half-metals. This is different from
the ZB cases: all the ZB MX compounds are half-metals [18].
We further perform geometry optimization for rock-salt CaN,
SrN and BaN with antiferromagnetic (AFM) and paramagnetic
(PM) configurations. For the AFM calculations, we refer to
Ref. [18], i.e., a cell of eight atoms is considered, where the
spins between the two anions in the z = 0 plane and the two anions in the z = a/2 plane are antiparallel. The obtained results
indicate that the FM state is most stable in the FM, AFM and
PM states for all the three nitrides. The PM state is the most unstable one. As an example, the total energy versus volume per
formula unit for rock-salt CaN with FM, AFM and PM states
is shown in Fig. 1. The total energy differences between the
AFM and FM states are about 53, 28 and 3 meV per formula
unit for CaN, SrN and BaN, respectively. The value of BaN
is very small. In the following, we concentrate the discussion
on the FM properties of the three rock-salt alkaline-earth nitrides.
Indeed, the calculated spin-dependent total density of states
(DOS) of nine rock-salt alkaline-earth pnictides MX at their
equilibrium lattice constants also show that only CaN, SrN and
BaN exhibit HM character, which is consistent with the calculated total magnetic moment (Table 1). For simplicity, we here
give the spin-dependent total DOS only for CaN, SrN and BaN
(Fig. 2). It is found that for all the three rock-salt nitrides the
minority-spin (spin-down) electrons are metallic whereas in the
majority-spin (spin-up) channel there is an energy gap of about
3.09, 2.86 and 1.87 eV for CaN, SrN and BaN, respectively,
i.e., the rock-salt CaN, SrN and BaN are HM ferromagnets. We
note that the HM gap [13], which is determined as the minimum
between the lowest energy of majority- (minority-)spin conduction bands with respect to the Fermi level and the absolute
values of the highest energy of the majority- (minority-)spin
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G.Y. Gao et al. / Physics Letters A 372 (2008) 1512–1515
Fig. 2. Spin-dependent total DOS of rock-salt CaN, SrN and BaN at their equilibrium lattice constants. The dashed line indicates the Fermi level at 0 eV.
Fig. 3. Spin-dependent band structure of rock-salt SrN at its equilibrium lattice
constant.
valence bands, is 0.03, 0.26 and 0.38 eV, respectively, for CaN,
SrN and BaN. So the HM gap increases from CaN to SrN and
BaN.
Now, let us further investigate the electronic structure and
the ferromagnetism of rock-salt CaN, SrN and BaN. We show
the spin-dependent band structure and main partial DOS of SrN
in Figs. 3 and 4, respectively. The corresponding properties of
CaN and BaN are similar to that of SrN. Note that, in Fig. 4,
only the partial DOS of Sr d states and N p states are given, because the other ones are very small in the energy range from
−3 to 4 eV. From Figs. 3, 4 and 2(b), we can see, for the majority spin channel, that there are three fully filled bands, which
are mainly formed by the N p states with a small contribution
from the hybridized Sr d states. However, for the minority spin
channel, the corresponding three bands are partly filled. This
can be explained from the electronic arrangements: in rock-salt
SrN, seven valence electrons (Sr : 5s2 and N : 2s2 2p3 ) con-
Fig. 4. Spin-dependent main partial DOS of Sr d states and N p states in
rock-salt SrN.
tribute to bond formation and magnetism; two of them occupy
the N s states in the lowest energy (below −10 eV, not shown
in Fig. 4), and the remaining five electrons occupy mainly
the N p states. The three isolated majority spin bands of predominantly N p character are fully filled (Figs. 3 and 4). The
remaining two electrons lead to the partial occupation of the
corresponding three minority spin bands, resulting in the total
magnetic moment of 1.00 μB per formula unit in rock-salt SrN
(Table 1). The total magnetic moment consists of three parts:
the N atom (0.93 μB ), the Sr atom (0.02 μB ) and the interstitial
area (0.05 μB ). So the main contribution to the total magnetic
moment of SrN comes from the spin polarization of N p states
(there is a large exchange splitting around the Fermi level in
Fig. 4), and the contribution of Sr atom to the total moment is
very small, this results from the hybridization between the N p
states and the Sr d states.
We note that the calculations of Sieberer et al. [18] has indicated the rock-salt structure is energetically more stable than
the ZB structure for CaAs, but rock-salt CaAs is not a halfmetal. They pointed out the highly interesting magnetic properties might warrant experimental efforts to stabilize these II–V
compounds in ZB structure on suitable substrates. Here, one
naturally considers that the rock-salt CaN, SrN and BaN are
more possibly stabilized if their rock-salt structure is energetically more stable than the ZB structure. Therefore, we further
optimize the ZB structure of CaN, SrN and BaN with FM state
by calculating the total energy versus volume. The total energies as a function of volume per formula unit for FM CaN, SrN
and BaN with ZB and rock-salt structures are plotted in Fig. 5.
We indeed find, for all the three alkaline-earth nitrides, that the
rock-salt structure has lower energy than that of the ZB structure. Therefore, compared with the ZB structure of CaN, SrN
and BaN, the rock-salt structure is more possibly stabilized on
suitable semiconductor substrates.
Finally, we estimate the cohesive energies of rock-salt CaN,
SrN and BaN in the FM state. The cohesive energy is defined
G.Y. Gao et al. / Physics Letters A 372 (2008) 1512–1515
1515
Acknowledgements
This work was supported by the China 973 plan under the
Grant Nos. 2006CB921605 and 2006CB921606, and by the
National Natural Science Foundation of China under the Grant
Nos. 20490210, 10574047 and 10574048.
References
Fig. 5. Total energy versus volume per formula unit for CaN, SrN and BaN in
rock-salt and ZB structures with ferromagnetic state.
as
1
Ecoh = Etot − Ecat + EN2 .
2
(1)
Here, Etot is the FM total energy of rock-salt CaN (SrN, BaN)
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