JOURNAL OF APPLIED PHYSICS 103, 083908 共2008兲
Half-metallic properties for the Mn2FeZ „Z = Al, Ga, Si, Ge, Sb… Heusler
alloys: A first-principles study
H. Z. Luo,1,a兲 H. W. Zhang,1 Z. Y. Zhu,1 L. Ma,1 S. F. Xu,1 G. H. Wu,1 X. X. Zhu,2
C. B. Jiang,2 and H. B. Xu2
1
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,
Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
2
Beijing University of Aeronautics and Astronautics, Beijing 100083, People’s Republic of China
共Received 18 November 2007; accepted 24 January 2008; published online 21 April 2008兲
The electronic structure and magnetism of the Mn2FeZ 共Z = Al, Ga, Si, Ge, Sb兲 Heusler alloys have
been studied by density functional calculations. Two half-metallic ferromagnets, namely, Mn2FeAl
and Mn2FeSb, are predicted. It is found that a small expansion of the crystal lattice can restore the
half-metallicity in Mn2FeSi. The calculated total magnetic moments M tot are 1␮B / f.u. for Mn2FeAl
and Mn2FeGa, 2␮B / f.u. for Mn2FeSi and Mn2FeGe, and 3␮B / f.u. for Mn2FeSb, which agree with
the Slater–Pauling curve quite well. The moments of Mn 共A兲 and Mn 共B兲 are large and antiparallel
to each other, which is indicative of ferrimagnetism in Mn2FeZ alloys. Fe shows only a small
moment and its moment is parallel to that of Mn 共B兲. By investigating the effect of lattice distortion
on the half-metallicity and magnetic moments of Mn2FeZ, it is found that the half-metallic
properties of Mn2FeSb are insensitive to the lattice distortion and a 100% spin polarization can be
obtained within the wide range of 5.4–6.05 Å. This is preferable in practical applications. © 2008
American Institute of Physics. 关DOI: 10.1063/1.2903057兴
I. INTRODUCTION
The rapid development of spintronics1,2 has been receiving much attention in recent years and offers opportunities
for a new generation of devices combining standard microelectronics with spin-dependent effects. Widely possible applications such as single spin electron sources and spin injectors have been thoroughly investigated.3,4 For the source
of the spin-polarized charge carriers, an ideal choice is the
half-metallic materials. The half-metallic materials have an
energy gap in one spin direction at the Fermi level EF,
whereas the other spin band is strongly metallic. As a result,
a complete spin polarization of the conduction electrons can
be obtained. Therefore, the half-metals have a 100% spinpolarized current and can be used as spin injectors for magnetic random access memories and other spin-dependent
devices.4
NiMnSb, a half-Heusler alloy, was first predicted to be a
half-metal by de Groot et al.4 Since then, much attention has
been paid to the Heusler alloy family for new candidates.
Some Heusler alloys have been theoretically predicted to be
half-metals in quick succession and since then, many experiments have been carried out to establish their magnetic and
transport properties.5–12 Usually, the Heusler alloy crystallizes in the L21 structure and has a stoichiometric composition of X2YZ, where X and Y are transition metal elements
and Z is a main group element. Most of the predicted halfmetallic Heusler alloys belong to the Co2YZ and Mn2YZ
families. In Mn2YZ, the half-metallic properties can be retained regardless of whether the Y atoms are low-valent elements, such as V and Cr, or high-valent elements, such as
Co. Furthermore, the half-metallic properties are found even
a兲
Electronic mail: [email protected].
0021-8979/2008/103共8兲/083908/7/$23.00
in the Mn3Ga alloy.13–16 In contrast, the half-metallicity in
Co2YZ is established only when the Y atom has less valence
electrons than Co. So, the Mn atom in Mn2YZ plays an important role in the formation of the half-metallicity.
In the Mn2YZ Heusler alloys, Mn2VAl was the first one
proposed to be a half-metallic ferromagnet and was studied
both experimentally and theoretically in detail.13,17 Then,
Mn2CrZ 共Z = Al, Sb兲,14 Mn2CoSb,15 and Mn3Ga 共Ref. 16兲
have also been thoroughly studied. However, up until now,
no reports on the half-metallicity in Mn2FeZ alloys have
been found. In this paper, we investigated the electronic
structure and magnetism of the Mn2FeZ 共Z = Al, Ga, Si, Ge,
and Sb兲 alloys by density functional calculations. Two halfmetals, namely, Mn2FeAl and Mn2FeSb, are predicted. An
antiparallel alignment between the large local moments of
the Mn atoms is observed. Finally, the effect of lattice distortion on the magnetic properties and half-metallicity of
Mn2FeZ is discussed.
II. COMPUTATIONAL METHOD
The electronic structure is calculated by using the
pseudopotential method with a plane-wave basis set based on
density functional theory.18,19 The interactions between the
atomic core and the valence electrons were described by the
ultrasoft pseudopotential.20 The electronic exchangecorrelation energy was treated under the generalized-gradient
approximation.21 The plane-wave basis set cutoff used was
500 eV for all the cases and 182 k points were employed in
the irreducible Brillouin zone. These parameters ensured
good convergences for the total energy. The convergence tolerance for the calculations selected was 1 ⫻ 10−6 eV/ atom.
The calculations were performed based on the theoretical
equilibrium lattice parameters.
103, 083908-1
© 2008 American Institute of Physics
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083908-2
J. Appl. Phys. 103, 083908 共2008兲
Luo et al.
TABLE I. The equilibrium lattice constants, band gaps of the minority spin states, total and partial magnetic
moments, and spin polarization ratios of the Mn2FeZ 共Z = Al, Ga, Si, Ge, Sb兲 alloys.
Compound
Lattice constant
共Å兲
Gap width
共eV兲
M tot
共␮B / f.u.兲
M Mn共A兲
共 ␮ B兲
M Fe
共 ␮ B兲
M Mn共B兲
共 ␮ B兲
MZ
共 ␮ B兲
P
共%兲
5.725
5.800
5.600
5.675
5.925
0.44
0.05
0.60
0.47
0.53
1.01
1.05
2.01
2.01
3.00
−2.54
−2.94
−1.30
−1.60
−1.52
0.06
0.28
0.28
0.40
1.00
3.42
3.62
3.00
3.16
3.46
0.08
0.06
0.04
0.04
0.06
100
95
84
92
100
Mn2FeAl
Mn2FeGa
Mn2FeSi
Mn2FeGe
Mn2FeSb
Generally, the Heusler structure can be taken as four
interpenetrating face-centered-cubic lattices, which has four
unique crystal sites, namely, A共0 , 0 , 0兲, B共 41 , 41 , 41 兲, C共 21 , 21 , 21 兲,
and D共 43 , 43 , 43 兲 in Wyckoff coordinates. In the Heusler alloys,
the X and Y atoms usually occupy the 共A , C兲 and B sites, and
the Z atom occupies the D site. The site preference of the
different 3d elements in Heusler alloys is determined by the
number of their valence electrons.22 For example, in Fe2YSi,
the 3d elements Y with fewer d electrons than Fe tend to
occupy the B sites, whereas elements with more electrons
prefer the 共A , C兲 sites; Si occupies the D site.23 In Mn2FeZ,
the Fe atom and a Mn atom equally occupy the 共A , C兲 sites
and the other Mn and Z atoms enter the B and D sites, respectively. Similar results have also been observed in
Mn2CoSb 共Ref. 15兲 and Mn2NiGa.24
III. RESULTS AND DISCUSSION
To determine the equilibrium lattice constant and find
how the total energy varies with the lattice constant, we perform structural optimizations on Mn2FeZ alloys for both the
paramagnetic 共PM兲 and ferromagnetic 共FM兲 states. The equilibrium lattice constants and the calculated spin moments are
listed in Table I. Figure 1 shows the total energy as a func-
tion of lattice parameters for both the PM and FM states for
Mn2FeZ 共Z = Al, Ga, Si, Ge, Sb兲 compounds. It is clear that
in all the alloys studied, the FM state shows the lower energy. The relative energy difference between the FM and PM
states at their corresponding equilibrium lattice increases
with increasing atomic number of the Z atoms in the same
column of the Periodic Table. This means that a large Z atom
is beneficial in stabilizing the FM state.
The electronic structures of the Mn2FeZ alloys have
been studied by density functional calculations. The calculated total and partial densities of states 共DOSs兲 of Mn2FeZ
are shown in Fig. 2. It can be seen that the total DOSs of
Mn2FeZ for Z = Al, Ga, Si, Ge, and Sb are similar in shape.
The low energy states are mainly contributed by the s electrons of the Z atoms, which are below −6 eV for Z = Al and
Ga, below −7 eV for Z = Si and Ge, and below −10 eV for
Z = Sb. The s states are relatively small and are separated
from the d states by a dip in the DOSs in both spin directions. Thus, they are unaffected by the d-d interaction and
are not presented in Fig. 2. The states around −5 eV are
mainly the p states of the Z atoms in the occupied valence
states, which hybridize with the p and d electrons of the Mn
and Fe atoms and determine the occupation degree of the p-d
FIG. 1. Calculated total energy for
Mn2FeZ 共Z = Al, Ga, Si, Ge, Sb兲 compounds as a function of lattice parameters for both the PM and FM states.
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083908-3
Luo et al.
J. Appl. Phys. 103, 083908 共2008兲
FIG. 2. The calculated spin-projected total and partial DOS plots for 共a兲 Mn2FeAl, 共b兲 Mn2FeGa, 共c兲 Mn2FeSi, 共d兲 Mn2FeGe, and 共e兲 Mn2FeSb.
orbital. The d states of the transition metal atoms extend
from −4 to +2 eV and hybridize with each other. The widely
spread d states are mainly due to the strong hybridization of
the 3d metals. The bonding and antibonding bands have been
caused by the strong covalent hybridization between the
lower-energy d states of the high-valent transition metal
atom such as Fe and the higher-energy d states of the lowvalent transition metal such as Mn.25 Meanwhile, there are
also contributions from the p electrons of the Z atoms.
In the majority spin states, the total DOS shows a threepeak structure. The peak above EF is mainly composed of the
antibonding peaks of the Fe and Mn 共B兲 atoms, and the two
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083908-4
Luo et al.
peaks below EF result from the hybridization of the d states
of Mn 共A兲, Mn 共B兲, and Fe. In the minority spin states, a
two-peak structure is observed. It is composed of the bonding and antibonding states of the 3d atoms and are separated
by an energy gap at EF.
It is clear that in the total DOSs of Mn2FeZ, there is a
gap in the minority spin states at EF, while in the majority
spin states, the DOSs are quite high. This results in a high
spin polarization at the Fermi level. For Mn2FeAl and
Mn2FeSb, there are no DOSs at the Fermi level in the minority gap and the spin polarization ratio is 100%. So,
Mn2FeAl and Mn2FeSb are “true” half-metals. For
Mn2FeGa, Mn2FeSi, and Mn2FeGe, the minority spin valence band maximum overlaps with the Fermi level and there
are still small DOSs at EF in the minority gap, so they are not
half-metals at equilibrium lattice constants. This difference
may have two possible causes. One is the lattice constants:
the larger lattice constant seems to shift the Fermi level high
above the top of the minority spin valence band, as will be
presented at the end of this paper. It is also found that the
expansion of the lattice can decrease the minority gap
width,6,17 which is quite obvious in the comparison between
Mn2FeAl and Mn2FeGa. The other possible cause is the p-d
hybridization. As can be seen from the partial DOSs patterns,
the energy of p electrons is strongly dependent on the Z atom
in Mn2FeZ alloys. The Z atom plays an important part in the
half-metallicity of the Heusler alloys, although it does not
directly form the minority gap, which provides s-p states to
hybridize with d electrons and determines the degree of occupation of the p-d orbital. Thus, the hybridization between
p electrons affects the formation of the energy gap. All these
lead to loss of half-metallicity in Mn2FeZ 共Z = Ga, Si, Ge兲.
Meanwhile, the two factors also obviously influence the gap
width. The calculated gaps for minority carriers are listed in
Table I. It is clear that the gap width decreases as Z varies
from Al to Ga or from Si to Ge. Similar results have also
been found in Co2MnX 共X = Si, Ge, Sn兲6 and Mn2CrZ
共Z = Al, Ga, Si, Ge兲.14
The calculated partial DOSs for the Mn2FeZ alloys are
also shown in Fig. 2. Both Mn 共A兲 and Fe have four Mn 共B兲
and four main group atoms as nearest neighbors, so they
have extra states between the bonding and antibonding
peaks. Mn 共B兲 has four Mn 共A兲 and four Fe in the nearest
shell. The d states of Mn 共B兲 are split into a doublet with eg
symmetry and a triplet with t2g symmetry in the cubic crystal
field. As shown in Fig. 2, the Mn 共B兲 d states show a twopeak structure 共a bonding and an antibonding peak兲, which is
separated by a dip in DOSs. In the majority DOSs of Mn 共B兲,
both peaks are basically below the Fermi level and occupied,
while in the minority DOSs, the exchange splitting moves
the antibonding peak high above the Fermi level, which results in a large local moment of Mn 共B兲. Large Mn moments
have also been observed in other Heusler alloys, such as
Mn2NiGa 共Ref. 24兲 and Cu2MnAl.26 On the contrary, the
partial DOSs of Mn 共A兲 lies mainly below EF in the minority
spin states and partly above EF in the majority spin states.
Thus, the contributions to the total DOSs from the Mn 共A兲
and Mn 共B兲 are opposite to each other, indicating the antiparallel configuration of their spin moments.
J. Appl. Phys. 103, 083908 共2008兲
It is known that in covalent hybridization between highvalent and low-valent atoms, the bonding hybrids are mainly
localized at the high-valent transition metal atom, such as Fe,
while the unoccupied antibonding states are mainly at the
low-valent transition metal, such as Mn.25 The atomic energy
level E共A,C兲 ⬍ E共B兲 has been reported by Bansil et al.27 The
spin-down bonding states preferentially reside at Fe 共C兲 sites
and produce a negative spin density in occupied states,
which results in strong bonding states in the minority spin
states of Fe and causes a small exchange splitting. As a result, Fe shows only a small magnetic moment.
Because the gap in the minority DOS of Mn 共B兲 is much
wider than those of Mn 共A兲 and Fe, as shown in Fig. 2, the
shape of the minority gap is mainly determined by the states
of the atoms at the 共A , C兲 sites in Mn2FeZ. Galanakis et al.28
studied the origin of the gap in Co2MnSi in detail. According
to their studies, in Mn2FeZ, hybridization occurs not only
between the nearest neighbors of the Mn–Mn 3d orbital but
also between the next nearest neighbor Fe–Mn 3d orbital.
Thus, nonbonding states 共eu and t1u兲 in the minority states are
caused and a gap occurs between them.
The calculated total spin moments M tot are listed in
Table I. It can be seen that they are all integral values, which
are 1␮B for Mn2FeAl and Mn2FeGa, 2␮B for Mn2FeSi and
Mn2FeGe, and 3␮B for Mn2FeSb. It is known that the total
spin moment for a stoichiometric half-metallic Heusler alloy
is an integral value and follows the Slater–Pauling curve,
that is, M t = Zt − 24, where M t is the total magnetic moment
per f.u. and Zt is the total number of valence electrons. In
half-metals, the Fermi energy is usually pinned in the minority gap, which makes the number of occupied minority states
an integer and the spin moment an integral. In full-Heusler
alloys, the minority band contains 12 electrons per unit cell.
So, the 24 valence electrons are equally distributed into each
spin direction and the alloy is nonmagnetic. If the alloy has
more than 24 valence electrons, spin polarization will occur
and the exchange interaction will shift the majority states to
lower energies. The extra electrons will fill in only majority
spins, which results in an integral spin moment.28 For the
Mn2FeZ alloy, they have 25–27 valence electrons, so their
total spin moment varies from 1␮B to 3␮B. This increase in
the total magnetic moment mainly results from the increase
in the Mn 共A兲 and Fe moments, as will be presented below.
The calculated partial spin moments for the Mn2FeZ 共Z
= Al, Ga, Si, Ge, Sb兲 alloys are listed in Table I. It is clear
that in these alloys, the spin moments are in ferrimagnetic
alignments. The Mn 共B兲 has a large magnetic moment that is
antiparallel to that of Mn 共A兲. Fe has only a small contribution to the total spin moment. The antiparallel alignment between the Mn spin moments has also been observed in
Mn2NiGa and other Heusler alloys with high Mn
content.24,29 This can be attributed to the small distance between the Mn 共A兲 and Mn 共B兲 atoms, which are the nearest
neighbors in Mn2FeZ or Mn2NiGa. The small distance between the Mn 共A兲 and Mn 共B兲 atoms gives rise to the antiferromagnetic coupling between their moments.24
The Z atoms play an important part in the physical properties of the half-metallic Heusler alloys although they are
not directly responsible for the appearance of the minority
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083908-5
Luo et al.
FIG. 3. 共Color online兲 Total and partial spin-projected DOSs for Mn2FeAl
共solid line兲 and Mn2FeSi 共dashed line兲.
gap.25 Here, we make a comparison between Mn2FeAl and
Mn2FeSi, in which the Z atoms have different numbers of
valence electrons, as presented in Fig. 3.
The substitution of Si for Al in Mn2FeZ does not lead to
a change in the general structure of the total DOSs. However,
since Si has one more valence electron than Al, both the
spin-up and spin-down states are shifted with respect to the
Fermi level to account for the extra electron. The majority
spin states move to a lower energy as Z varies from Al to Si.
The high majority DOS peak of the occupied d states locates
at −2.5 eV in Mn2FeAl and at −3 eV in Mn2FeSi. Meanwhile, the Fermi level locates at a large DOS peak in Al
alloy, while it moves to a deep DOS valley in Si alloy, which
leads to a drastic decrease in the spin polarization ratio in
Mn2FeSi. The change in the minority DOSs is not so obvious
because the extra charge mainly fills in the majority bands.
The spin-down states are slightly shifted to a lower energy
with respect to the Fermi level. Similar results have also
been observed for Co2FeAlxSi1−x, in which the Fermi level
moves through the gap in the minority states.30
For Z varying from Al to Si, the change in the partial
DOSs of Mn and Fe atoms can also be observed in Fig. 3.
The extra charge pushes the DOSs lower on the energy scale,
which leads to a change in their spin moments.
A small change in the lattice parameter may shift the EF
with respect to the minority gap, which obviously affects the
half-metallic character.31 In experimental studies, such as
melt spinning or ball milling, the strain may be quite large
and will make the lattice constant deviate from the ideal one.
Furthermore, the growth of thin film materials becomes possible by modern techniques. The lattice constant of the thin
films is strongly influenced by the lattice of the substrate.
Thus, it is meaningful to study the relationship between the
half-metallic character and the lattice constant for a given
material from both theoretical and technical aspects. Therefore, we study the dependence of the magnetic properties and
spin polarization on the lattice constants for Mn2FeAl,
Mn2FeSi, and Mn2FeSb.
Generally, in Heusler alloys, the change in the electronic
J. Appl. Phys. 103, 083908 共2008兲
structure with the lattice constant is for two reasons.32 One is
a change in the band gradients as expected from a freeelectronlike band structure, as well as a mere shift in EF due
to the accompanying changes in the DOSs. The other is the
higher overlap of the wave function, which results in a stronger delocalization of the electrons. In particular, they will be
larger for smaller values of the lattice constant a. With a
decrease in a, the interaction between the atoms becomes
stronger, so electrons will transfer from the majority to the
minority spin states and form broader d bands. Expanding
the lattice has the opposite effect. When the lattice distortion
transforms from negative to positive, the center and width of
the gap change and the electrons become more localized,31
so the majority and minority bands will be moved with respect to the EF, which will affect both the half-metallic and
magnetic properties.
Figure 4 gives the variation in the total DOSs of Mn2FeZ
with lattice constant a. It is clear that the lattice distortion
does not change the general shape of the DOSs. However,
the Fermi level shifted with the variation in the lattice constant. The change is more obviously seen in the minority spin
states, in which EF shifted from the gap to the edge of the
antibonding peak. This leads to the change in both spin polarization and magnetic moments.
The spin polarization ratio P trend of the three alloys are
shown in Fig. 5. P is calculated as the value of
共N↑ − N↓兲 / 共N↑ + N↓兲, where N↑ and N↓ are the majority and
minority DOSs at EF, respectively. It can be seen that for the
studied alloys, a 100% spin polarization can be obtained
within a wide range of lattice constants. Especially for
Mn2FeSi, which is not a half-metal at theoretical equilibrium
lattice constant, a small expansion of the lattice can induce
the half-metallicity.
In the three alloys studied, the case of Mn2FeSb is practically interesting. It is half-metallic from 5.4 to 6.05 Ǻ,
which indicates that the half-metallic properties of Mn2FeSb
are not sensitive to the lattice distortion. This is preferable in
technical applications. The formation of the Mn2FeSb is still
unclear. However, it has been reported that Mn2CoSb can
form a fine Heusler structure and is predicted to be a
half-metal.15 So, it may be expected that a single phase Heusler alloy can be formed in Mn2FeSb. The stable high spin
polarization ratio can be explained from its electronic structure. For Mn2FeSb and also Mn2FeAl, there is a large DOS
peak at the Fermi level in the majority spin states, whereas in
the minority DOSs, there is an energy gap, which cannot be
compared to the states of the majority one. Thus, it may be
expected that the high N↑ retains a high P value when EF
shifts because of some effects such as lattice distortion. For
Mn2FeSi, the majority DOS at EF is rather low, so a small
minority DOS may drastically decrease the spin polarization.
The total and partial magnetic moments as functions of
the lattice constant are shown in Fig. 5 for Mn2FeZ. A moderate variation in the lattice constant does not significantly
change the total magnetic moments in these alloys. This is
due to the movement of the Fermi level usually within the
minority gap. However, the partial spin moments of Mn and
Fe are quite sensitive to the lattice distortion. For the
Mn2FeZ 共Z = Al, Si, Sb兲 alloys, both absolute values of the
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083908-6
J. Appl. Phys. 103, 083908 共2008兲
Luo et al.
FIG. 4. The calculated total DOSs for
the Mn2FeZ 共Z = Al, Si, Sb兲 Heusler alloys at different lattice constants. Results are shown for 5.5 Å, for 6.0 Å,
and for the case of the equilibrium lattice constant.
moments of Mn 共B兲 and Mn 共A兲 increase with increasing
lattice constants. In Co2MnX 共X = Si, Ge, Sn兲, it is also found
that the moment of Mn 共B兲 increases with increasing lattice
constant a. This can be explained by the fact that the 3d
localization is strengthened and then the Mn moment is enlarged with increasing a.6 Simultaneously, the partial moment of Fe also increases with the expansion of the lattice
constant. Finally, in Mn2FeZ, the variation in the moment of
Mn 共A兲 is counterbalanced by the change in the moments of
both Mn 共B兲 and Fe, which retains the nearly fixed total
moment when the lattice constant is changed.
IV. CONCLUSION
The electronic structure and magnetism of the Mn2FeZ
共Z = Al, Ga, Si, Ge, and Sb兲 Heusler alloys were studied by
density functional calculations. A 100% spin polarization has
been found in Mn2FeAl and Mn2FeSb. The half-metallicity
FIG. 5. Total and partial magnetic moments and spin polarization ratio P as
functions of the lattice constant for the
Mn2FeZ 共Z = Al, Si, Sb兲 Heusler alloys. The calculation was performed
within the range of 5.5–6.1 Å.
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083908-7
in Mn2FeSi can be induced by lattice expansion. The calculated total magnetic moments M tot are 1␮B / f.u. for Mn2FeAl
and Mn2FeGa, 2␮B / f.u. for Mn2FeSi and Mn2FeGe, and
3␮B / f.u. for Mn2FeSb, which agree with the Slater–Pauling
curve quite well. The spin moments of Mn 共A兲 and Mn 共B兲
are large and antiparallel to each other. Fe has only a small
moment, which is parallel to the moment of Mn 共B兲. The
absence of an obvious variation in M tot with lattice constant
is mainly ascribed to the counterbalance of the change in
moments of Mn 共A兲 and Mn 共B兲. The spin polarization of
Mn2FeSb is found to be 100% for the lattice variation in the
range of 5.4–6.05 Ǻ, which is attractive in practical applications.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China through Grant No. 50531010 and
the Natural Science Foundation of Hebei through Grant No.
E2006000063.
M. Julliere, Phys. Lett. 54A, 225 共1975兲.
B. Dieny, V. S. Speriosu, S. S. P. Parkin, B. A. Gurney, D. R. Wilhoit, and
D. Mauri, Phys. Rev. B 43, 1297 共1991兲.
3
S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von
Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science
294, 1488 共2001兲.
4
R. A. de Groot, F. M. Mueller, P. G. van Engen, and K. H. J. Buschow,
Phys. Rev. Lett. 50, 2024 共1983兲.
5
S. Ishida, T. Masaki, S. Fujii, and S. Asano, Physica B 共Amsterdam兲 245,
1 共1998兲.
6
S. Picozzi, A. Continenza, and A. J. Freeman, Phys. Rev. B 66, 094421
共2002兲.
7
A. Kellou, N. E. Fenineche, T. Grosdidier, H. Aourag, and C. Coddet, J.
Appl. Phys. 94, 3292 共2003兲.
8
S. Ishida, S. Kawakami, and S. Asano, Mater. Trans., JIM 45, 1065
共2004兲.
9
Y. Miura, K. Nagano, and M. Shirai, Phys. Rev. B 69, 144413 共2004兲.
10
S. Ishida, S. Sugimura, S. Fujii, and S. Asano, J. Phys.: Condens. Matter 3,
1
2
J. Appl. Phys. 103, 083908 共2008兲
Luo et al.
5793 共1991兲.
R. Y. Umetsu, K. Kobayashi, R. Kainuma, A. Fujita, K. Fukamichi, K.
Ishida, and A. Sakuma, Appl. Phys. Lett. 85, 2011 共2004兲.
12
S. Wurmehl, G. H. Fecher, H. C. Kandpal, V. Ksenofontov, and C. Felser,
Appl. Phys. Lett. 88, 032503 共2006兲.
13
R. Weht and W. E. Pickett, Phys. Rev. B 60, 13006 共1999兲.
14
H. Z. Luo, Z. Y. Zhu, G. D. Liu, S. F. Xu, G. H. Wu, H. Y. Liu, J. P. Qu,
and Y. X. Li, “Prediction of half-metallic properties for the Heusler alloys
Mn2CrZ 共Z=Al, Ga, Si, Ge, Sb兲: A first principles study,” J. Magn. Magn.
Mater. 320, 421 共2008兲.
15
X. F. Dai, G. D. Liu, J. L. Chen, and G. H. Wu, Solid State Commun. 140,
533 共2006兲.
16
S. Wurmehl, H. C. Kandpal, G. H. Fecher, and C. Felser, J. Phys.: Condens. Matter 18, 6171 共2006兲.
17
K. Ozdogan, I. Galanakis, E. Sasioglu, and B. Aktas, J. Phys.: Condens.
Matter 18, 2905 共2006兲.
18
M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoolous, Rev. Mod. Phys. 64, 1065 共1992兲.
19
M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S.
J. Clark, and M. C. Payne, J. Phys. Condens. Matter 14, 2717 共2002兲.
20
D. Vanderbilt, Phys. Rev. B 41, 7892 共1990兲.
21
J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865
共1996兲.
22
H. C. Kandpal, G. H. Fecher, and C. Felser, J. Phys. D 40, 1507 共2007兲.
23
T. J. Burch, T. Litrenta, and J. I. Budnick, Phys. Rev. Lett. 33, 421 共1974兲.
24
G. D. Liu, X. F. Dai, S. Y. Yu, Z. Y. Zhu, J. L. Chen, G. H. Wu, H. Zhu,
and J. Q. Xiao, Phys. Rev. B 74, 054435 共2006兲.
25
I. Galanakis, P. H. Dederichs, and N. Papanikolaou, Phys. Rev. B 66,
134428 共2002兲.
26
J. Kübler, A. R. Williams, and C. B. Sommers, Phys. Rev. B 28, 1745
共1983兲.
27
A. Bansil, S. Kaprzyk, E. P. Mijnarends, and J. Tobola, Phys. Rev. B 60,
13396 共1999兲.
28
I. Galanakis, P. H. Dederichs, and N. Papanikolaou, Phys. Rev. B 66,
174429 共2002兲.
29
J. Enkovaara, O. Heczko, A. Ayuela, and R. M. Nieminen, Phys. Rev. B
67, 212405 共2003兲.
30
G. H. Fecher and C. Felser, J. Phys. D 40, 1582 共2007兲.
31
T. Block, M. J. Carey, B. A. Gurney, and O. Jepsen, Phys. Rev. B 70,
205114 共2004兲.
32
H. C. Kandpal, G. H. Fecher, C. Felesr, and G. Schonhense, Phys. Rev. B
73, 094422 共2006兲.
11
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