Effect of doping and disorder on the half-metallicity of full Heusler alloy

Abstract

Heusler alloys containing Co and Mn are amongst the most heavily studied half-metallic ferromagnets for future applications in spintronics. Using state-of-the-art electronic structure calculations, we investigate the effect of doping and disorder on their electronic and magnetic properties. Small degrees of doping by substituting Fe or Cr for Mn scarcely affect the half-metallicity. A similar effect is also achieved by mixing the sublattices occupied by the Mn and sp atoms. Thus the half-metallicity is a robust property of these alloys.

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arXiv:cond-mat/0603811v1 [cond-mat.mtrl-sci] 30 Mar 2006
Effect of doping and disorder on the half-metallicity of full Heusler alloys
I. Galanakis1, K.¨Ozdo˜ gan2, E. S ¸a¸ sıo˜ glu3,4, and B. Akta¸ s2∗
1Department of Materials Science, School of Natural Sciences, University of Patras, GR-26504 Patra, Greece
2Department of Physics, Gebze Institute of Technology, Gebze, 41400, Kocaeli, Turkey
3Max-Planck Institut f¨ ur Mikrostrukturphysik, D-06120 Halle, Germany
4Fatih University, Physics Department, 34500, B¨ uy¨ uk¸ cekmece,˙Istanbul, Turkey
(Dated: February 6, 2008)
Heusler alloys containing Co and Mn are amongst the most heavily studied half-metallic ferromag-
nets for future applications in spintronics. Using state-of-the-art electronic structure calculations,
we investigate the effect of doping and disorder on their electronic and magnetic properties. Small
degrees of doping by substituting Fe or Cr for Mn scarcely affect the half-metallicity. A similar
effect is also achieved by mixing the sublattices occupied by the Mn and sp atoms.
half-metallicity is a robust property of these alloys.
Thus the
PACS numbers:75.47.Np, 75.50.Cc, 75.30.Et
The intensive development of electronics based on the
combination of magnetic and semiconducting materials
has brought in the center of scientific research new exotic
materials. Half-metallic ferromagnets, which were first
predicted by de Groot and collaborators in 1983,1have
the peculiarity that the band-structure of the minority-
spin electrons is semiconducting while of the majority-
spin electrons is a normal metallic one. Such materials
could maximize the efficiency of spintronic devices.2Sev-
eral Heusler compounds like NiMnSb and Co2MnSi have
been predicted to be half-metals.3
Ishida and collaborators were, to the best of our knowl-
edge, the first to study by means of ab-initio calcula-
tions the full-Heusler compounds of the type Co2MnZ,
where Z stands for Si and Ge, and have shown that
they are half-metals.4Later the origin of half-metallicity
in these compounds has been largely explained.3Many
experimental groups during the last years have worked
on these compounds and have tried to synthesize them
mainly in the form of thin films and incorporate them
in spintronic devices. The group of Westerholt has ex-
tensively studied the properties of Co2MnGe films and
they have incorporated this alloy in the case of spin-
valves and multilayer structures.5The group of Reiss
managed to create magnetic tunnel junctions based on
Co2MnSi.6A similar study of Sakuraba and collabora-
tors resulted in the fabrication of magnetic tunnel junc-
tions using Co2MnSi as one magnetic electrode and Al-
O as the barrier (Co75Fe25 is the other magnetic elec-
trode) and their results are consistent with the presence
of half-metallicity for Co2MnSi.7Dong and collaborators
recently managed to inject spin-polarized current from
Co2MnGe into a semiconducting structure.8Finally Kall-
mayer et al. studied the effect of substituting Fe for Mn
in Co2MnSi films and have shown that the experimental
extracted magnetic spin moments are compatible with
the half-metallicity for small degrees of doping.9
It is obvious from the experimental results that the
full-Heusler compounds containing Co and Mn are of
particular interest for spintronics. Not only they com-
bine high Curie temperatures and coherent growth on
TABLE I: Total and atom-resolved spin magnetic moments
for the case of Fe and Cr doping of the Mn site in µB. The
total moment in the cell is the sum of the atomic ones multi-
plied by the concentration of this chemical element.
Total Co Mn Cr spTotal Co Mn Fesp
x
0.00 5.00 1.96 3.13
0.05 4.95 1.97 3.12 2.06 -0.09 5.05 2.02 3.13 2.87 -0.09
0.10 4.90 1.97 3.12 2.07 -0.09 5.09 2.06 3.17 2.85 -0.08
0.20 4.80 1.97 3.12 2.09 -0.08 5.14 2.13 3.16 2.82 -0.08
x
Co2Mn1−xCrxGe
0.00 5.00 1.87 3.20
-0.06 5.00 1.87 3.20
0.05 4.95 1.86 3.21 2.05 -0.06 5.05 1.91 3.22 2.88 -0.06
0.10 4.90 1.86 3.22 2.07 -0.06 5.10 1.96 3.23 2.88 -0.06
0.20 4.80 1.86 3.22 2.10 -0.06 5.19 2.06 3.26 2.89 -0.05
x
Co2Mn1−xCrxSn
0.00 5.02 1.78 3.32
-0.08 5.02 1.78 3.32
0.05 4.98 1.77 3.34 2.24 -0.08 5.06 1.82 3.35 2.89 -0.08
0.10 4.92 1.77 3.34 2.24 -0.08 5.11 1.87 3.36 2.90 -0.07
0.20 4.82 1.76 3.35 2.27 -0.08 5.20 1.98 3.38 2.91 -0.07
Co2Mn1−xCrxSiCo2Mn1−xFexSi
-0.09 5.00 1.96 3.13-0.09
Co2Mn1−xFexGe
-0.06
Co2Mn1−xFexSn
-0.08
top of semiconductors (they consist of four fcc sublattice
with each one occupied by a single chemical element)
but in real experimental situations they can preserve a
high degree of spin-polarization at the Fermi level. In
order to accurately control their properties it is impera-
tive to investigate the effect of defects, doping and dis-
order on their properties. Recently Picozzi et al. pub-
lished a study on the effect of defects in Co2MnSi and
Co2MnGe.10Our work aims to further study the effect
of doping and disorder on the electronic and magnetic
properties of such compounds. Doping is simulated by
substituting Fe or Cr for Mn while disorder occurs be-
tween the Mn and the sp atom. The electronic struc-
ture calculations are performed using the full–potential
nonorthogonal local–orbital minimum–basis band struc-
ture scheme (FPLO).11Details of similar type of calcu-
lations have been published elsewhere.12
The first part of our investigation concerns the dop-
ing of Co2MnSi, Co2MnGe and Co2MnSn. To simulate

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-5
0
5
Co2MnSi
Co2Mn1-xCrxSi
Co2Mn1-xFexSi
-6
-4-2 0
E(eV)
-5
0
5
-6
-4 -20
E(eV)
x=0.05
x=0.1 x=0.2
DOS(states/eV)
FIG. 1: (Color online)Spin-resolved total density of states
(DOS) for the case of Co2Mn1−xCrxSi and Co2Mn1−xFexSi
for three difference values of the doping concentration x.
DOS’s are compared to the one of the undoped Co2MnSi al-
loy. In the onsets we have blown up the region around the
Fermi level (which we have set as the zero of the Energy axis).
Note that positive values of DOS refer to the majority-spin
electrons and negative values to the minority-spin electrons.
the doping by electrons we substitute Fe for Mn while to
simulate the doping of the alloys with holes we substitute
Cr for Mn. We study the cases of moderate doping sub-
stituting 5%, 10% and 20% of the Mn atoms. The use
of coherent potential approximation in our calculations
ensures that the doping is performed in a random way.
In Table I we have gathered the total and atom-resolved
spin moments for all cases under study and in Fig. 1 the
total density of states (DOS) for the Co2Mn1−xFexSi and
Co2Mn1−xCrxSi compounds blowing up in the onsets the
region around the Fermi level where the gap exists.
We will start our discussion from the DOS presented
in Fig. 1. As discussed in Ref. 3 the gap is created
between states located exclusively at the Co sites. The
states low in energy (around -6 eV) originate from the
low-lying p-states of the sp atoms (there is also an s-type
state very low in energy which is not shown in the figure).
The majority-spin occupied states form a common Mn-
Co band while the occupied minority states are mainly
located at the Co sites and minority unoccupied at the
Mn sites. Doping the perfect ordered alloy with either
Fe or Cr first smoothens the valleys and picks along the
energy axis. This is a clear sign of the chemical disorder;
Fe and Cr induce picks at slightly different places than
the Mn atoms resulting to this smoothening and as the
doping increases this phenomenon becomes more intense.
The important detail is what happens around the Fermi
level and in what extent is the gap in the minority band
affected by the doping. So now we will concentrate only
at the enlarged regions around the Fermi level. The blue
dashed lines represent the Cr-doping while the red dash-
dotted lines are the Fe-doped alloys. Cr-doping has only
-3
0
3
-2
0
2
DOS(states/eV)
x=0.0
x=0.05
x=0.1
x=0.2
-6
-4-20
E(eV)
-1.4
-0.7
0
0.7
-6
-4-20
E(eV)
Co Co
Mn Mn
Si Si
Co2Mn1-xSi1+x Co2Mn1+xSi1-x
FIG. 2: (Color online) Atom resolved DOS for the cases of
Si (left panel) and Mn (right panel) excess in Co2MnSi alloy
with respect to the perfect one (x=0). In the onsets we have
blown up the region around the Fermi level.
marginal effects to the gap. Its width is narrower with
respect to the perfect compounds but overall the com-
pounds retain their half-metallicity. In the case of Fe-
doping the situation is more complex. Adding electrons
to the system means that, in order to retain the per-
fect half-metallicity, these electrons should occupy high-
energy lying antibonding majority states. This is ener-
getically not very favorable and for these moderate de-
grees of doping a new shoulder appears in the unoccupied
states which is close to the right-edge of the gap; a sign of
a large change in the competition between the exchange
splitting of the Mn majority and minority states and of
the Coulomb repulsion. In the case of the 20% Fe doping
this new peak crosses the Fermi level and the Fermi level
is no more exactly in the gap but slightly above it. Fur-
ther substitution should lead to the complete destruction
of the half-metallicity as in the Quaternary Heusler alloys
with a Mn-Fe disordered site.13
In Table I we have gathered the spin magnetic mo-
ments for all cases under study. The total spin moment
Mtof the perfect compounds follows the Slater Pauling
behavior being the number of the valence electrons in the
unit cell minus 24.3In the case of the chemically disor-
dered compounds, doping by 5%, 10% or 20% of Cr (or
Fe) atoms, means that the mean value of the total num-
ber of valence electrons in the unit cell is decreased (or
increased respectively) by 0.05, 0.10 and 0.20 electrons,

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TABLE II: Total and atom-resolved spin magnetic moments for the case of Mn-sp atom disorder in µB. The total moment in
the cell is the sum of the atomic ones multiplied by the concentration of this chemical element.
Co2Mn1+xSi1−x
Co
1.92
1.95
1.96
1.96
1.99
2.00
2.03
Co2Mn1+xGe1−x
Co
1.83
1.84
1.85
1.87
1.88
1.90
1.95
Co2Mn1+xSn1−x
Co
1.78
1.75
1.76
1.78
1.80
1.81
1.82
x
Total
4.40
4.70
4.85
5.00
5.15
5.30
5.60
Mn
3.19
3.15
3.14
3.13
3.10
3.09
3.05
SiTotal
4.40
4.70
4.85
5.00
5.15
5.30
5.60
Mn
3.29
3.25
3.23
3.20
3.19
3.16
3.11
Ge
-0.05
-0.06
-0.06
-0.06
-0.07
-0.08
-0.10
Total
4.41
4.73
4.88
5.02
5.17
5.32
5.62
Mn
3.41
3.41
3.37
3.32
3.28
3.26
3.24
Sn
-0.08
-0.08
-0.08
-0.08
-0.08
-0.09
-0.10
-0.20
-0.10
-0.05
0.00
0.05
0.10
0.20
-0.06
-0.08
-0.08
-0.09
-0.10
-0.10
-0.11
respectively. In most of the cases the total spin moments
follow this behavior a clear sign of the preservation of the
half-metallicity, but in the case of Co2Mn0.8Fe0.2Si com-
pound the total moment is 5.14 µB instead of the ideal
value of 5.20 µB. In the case of the corresponding Ge
and Sn compounds the Fermi level is more deep in the
gap and for the Sn compound it does not cross any more
the minority states. The atom-resolved moments present
no peculiarity and are little sensitive to the doping. Our
findings agree with the conclusions drawn by Kallmayer
et al. for the Fe-doped Co2MnSi films.9
In the second part of our study we study the effect of
disorder between the Mn and the sp atoms. In Fig. 2 we
present the atom-resolved DOS for both excess of the sp
atom on the left column and excess of the Mn atoms on
the right column. In Table II we have gathered the total
and atomic spin moments for all cases. Firstly note that
the gap is much wider for the Mn and sp atoms than
for the Co atoms since the states around the gap are
of Co-character only. Mixing Mn and sp atoms changes
the symmetry of the Co sites and in this way can induce
new states in the gap and affect the half-metallicity. As
shown in Fig. 2, substituting Si for Mn induces states
just at the right edge of the gap while substituting Mn
for Si pushes the unoccupied minority states even higher
in energy and the gap becomes wider. Overall the DOS
is smoothened by the disorder between the Mn and Si
atoms but the main picks do not change energy position.
In Table II we have gathered the total spin moments
for all cases under study. Substituting 5%, 10% or 20%
of the Mn atoms by the Si, Ge or Sn ones (which are
all isoelectronic, e.g. same number of valence electrons)
corresponding to the negative values of x in the table,
results in a decrease of 0.15, 0.30 and 0.60 of the total
number of valence electrons in the cell, while the inverse
procedure results to a similar increase of the mean value
of the number of valence electrons. The compounds con-
taining Si and Ge show perfect Slater-Pauling behavior
while the Co2Mn1+xSn1−xdeviate from the ideal values
of the total spin moment although in this case the Fermi
level is nearer the center of the gap. Sn is a much heavier
element than both Si and Ge and its mixing with Mn al-
ters considerably the Coulomb repulsions in the system
having a more profound effect on the half-metallicity of
the corresponding alloy. Thus disorder is more important
for the heavy sp elements.
It is interesting also to look at the Mn spin moments.
In the case of doping presented in the first part of our
study doping scarcely changed the Mn spin moments.
Mn atoms remained at the same sublattice with no im-
mediate change to their close environment. In the case
of disorder excess of Mn means that Mn atoms occupy
also sites in the sublattice of the sp atoms while excess of
the sp atoms means that sp atoms are found also in the
sublattice occupied by Mn having a much larger effect on
the Mn magnetic properties than in the case of doping
where Cr and Fe atoms were found in the Mn-occupied
sublattice. As a result the Mn spin moment can change
by as much as ∼0.2 µB between the disordered and the
perfect compound.
We have studied the effect of doping and disorder
on the magnetic properties of the Co2MnSi, Co2MnGe,
Co2MnSn full-Heusler alloys. Doping simulated by the
substitution of Cr and Fe for Mn overall keeps the half-
metallicity. Its effect depends clearly on the position of
the Fermi level, having the largest one in the case of
Co2MnSi where the Fermi level is near the edge of the
minority-spin gap. On the other hand disorder between
the Mn and the sp atom is more important for the heavy
sp atoms like Sn. Both disorder and doping have little
effect on the half-metallic properties of the compounds
which we study and they keep a high degree of spin-
polarization. It seems that Co2MnGe should be the most
robust compound with respect to its half-metallic char-
acter for experimentalists and realistic applications.
∗Electronic address: galanakis@upatras.gr,kozdogan@gyte.edu.tr,ersoy@mpi-halle.de
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