Experimental and computational investigation of structure and magnetism in pyrite Co1-xFexS2: Chemical bonding and half-metallicity

Article abstract of DOI:10.1103/PhysRevB.70.214409

Bulk samples of the pyrite chalcogenide solid solutions Co _1-xFe_xS₂ (0≤x≤0.5), have been prepared and their crystal structures and magnetic properties studied by x-ray diffraction and SQUID magnetization measurements. Across the solution series, the distance between sulfur atoms in the persulfide (S₂^2-) unit remains nearly constant. First principles electronic structure calculations using experimental crystal structures as inputs point to the importance of this constant S-S distance, in helping antibonding S-S levels pin the Fermi energy. In contrast hypothetical rock-salt CoS is not a good half metal, despite being nearly isostructural and isoelectronic. We use our understanding of the Co_1-xFe_xS₂ system to make some prescriptions for new half-metallic ferromagnetic.

Full text of DOI:10.1103/PhysRevB.70.214409

PHYSICAL REVIEW B 70, 214409 (2004)
Experimental and computational investigation of structure and magnetism in pyrite
Co1−xFexS2: Chemical bonding and half-metallicity
K. Ramesha and Ram Seshadri†
*
Materials Department and Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
Claude Ederer‡
Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA
Tao He§ and M. A. Subramanianʈ
DuPont Central Research and Development Experimental Station, E328/219 Wilmington, Delaware 19880-0328, USA
(Received 3 May 2004; revised manuscript received 7 September 2004; published 8 December 2004)
Bulk samples of the pyrite chalcogenide solid solutions Co1−xFexS2 ͑0ഛxഛ0.5͒, have been prepared and
their crystal structures and magnetic properties studied by x-ray diffraction and SQUID magnetization mea-
surements. Across the solution series, the distance between sulfur atoms in the persulfide ͑S22−͒ unit remains
nearly constant. First principles electronic structure calculations using experimental crystal structures as inputs
point to the importance of this constant S-S distance, in helping antibonding S-S levels pin the Fermi energy.
In contrast hypothetical rock-salt CoS is not a good half metal, despite being nearly isostructural and isoelec-
tronic. We use our understanding of the Co1−xFexS2 system to make some prescriptions for new half-metallic
ferromagnetic.
DOI: 10.1103/PhysRevB.70.214409
PACS number(s): 75.47.Ϫm, 71.20.Ϫb, 72.25.Ϫb, 85.75.Ϫd
I. INTRODUCTION
netic, and almost a half-metal, closely but not precisely re-
sembling the prototypic half-metallic ferromagnet
NiMnSb.12 Yamada et al.13 have optimized the structure and
Kwon et al.14 have performed LSDA=U (LSDA=local spin
density approximation) calculations on CoS2. Shishidou et
al.15 have performed first principles calculations on CoS2
with gradient corrections (GGA=generalized gradient ap-
proximation).
The rapid development of spin valve-based magnetic read
heads and the emergence of spintronics1 has thrown up a
need for new half-metallic ferromagnets for spin injection, as
well as the need for a better understanding of the underlying
materials issues in half-metallic ferromagnets.2,3 The recog-
nition that pyrite CoS2 is close to being a half-metallic
ferromagnet,4,5 and that half-metallicity is robust across the
solid solution Co1−xFexS2 (Ref. 6) has led to considerable
renewed efforts to understand this material.7 However, there
is as yet no report on why the solid solution Co1−xFexS2 is
special: What are the unusual features in the crystal and elec-
tronic structure of the pyrites that result in its properties?
Benoit and Néel first showed that cobalt pyrite CoS2 is a
ferromagnet.10 No other MX2 compound ͑X=chalcogenide͒,
or even MXY ͑Y=pnictide͒ is ferromagnetic.8,9 Jarrett et al.4
made magnetic and transport measurements on Co1−xFexS2
which indicated itinerant electron ferromagnetism. FeS2 ͑x
=1͒ is a d band semiconductor with filled octahedral t62g lev-
els of Fe2+ level separated from empty eg levels. As electrons
are added ͑0ഛxഛ1͒ the compounds become conducting and
ferromagnetic, even for x values as large as 0.97 (or electron
concentrations as small as 0.03 in the eg band). Over a wide
range of x, the magnetic moment (in Bohr magnetons) ob-
tained from saturation magnetization is precisely equal to the
number of eg electrons. DiTusa et al.11 have recently argued
that the dilute (x approaching 1) regions of the solid solution
are worthy of closer examination and that near x=0.99, an
insulator-metal transition is already observed. They report a
quantum critical point in the ferromagnetic-paramagnetic
transition between x=0.972 and x=0.964.
In a seminal paper, Mazin6 has shown from first-
principles calculations that half-metallic ferromagnetism is
“robust” in the system Co1−xFexS2, in the sense that in the
region 0.85ഛxഛ0.25 the compounds are perfect half metals,
with moments precisely equal to the spin only values
͓M͑␮ ͒/Co=1͔ in agreement with the experiments of Jarrett
B
et al.4 He ascribes the singular magnetic behavior of this
system to the fact that the Fermi lies on a steep slope in the
densities of states, and predicts that the onset of the ferro-
magnetic to paramagnetic transition in Co1−xFexS2 should
occur near x=0.84 in remarkable qualitative agreement with
experiment. From point-contact Andreev reflection measure-
ments, Cheng, Mazin, and co-workers16 determine the maxi-
mum transport half-metallicity to not exceed 61%. The
maximum occurs near x=0.5. The reduced half-metallicity is
ascribed to sulfur deficiency in the samples, which interest-
ingly, does not seem to affect bulk magnetism.
In this contribution, we focus on the cobalt rich side of the
pyrite Co1−xFexS2 phase diagram. We obtain a detailed struc-
tural description of the compounds 0ഛxഛ0.5 from
Rietveld17 refinement of powder x-ray diffraction patterns.
We also confirm from magnetic measurements that the
samples behave in the manner described by Jarrett et al.4 We
use the crystal structures as inputs for first principles elec-
tronic structure calculations based on the linear muffin-tin
orbital method,21 both for pristine CoS2 as well as the super-
Spin-polarized electronic structure calculations by Zhao,
Callaway, and Hayashibara5 found that CoS2 is ferromag-
1098-0121/2004/70(21)/214409(8)/$22.50
214409-1
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RAMESHA et al.
PHYSICAL REVIEW B 70, 214409 (2004)
cells Co0.75Fe0.25S2 and Co0.05Fe0.5S2. We use the crystal or-
bital hamiltonian population (COHP) (Ref. 19) to examine
details of spin-polarized chemical bonding across the solid
solution series, and examine the relation between chemical
bonding and half-metallicity. A comparison with rock-salt
CoS (whose spin polarized crystal and electronic structure
have been calculated from first-principles) confirms the spe-
cial features of the electronic structure of the pyrites.
II. EXPERIMENT
Samples of Co1−xFexS2 ͑0ഛxഛ0.5͒ were prepared start-
ing from the elements taken according to stoichiometry, by
heating well-ground powders in evacuated, sealed silica am-
poules for 1 week at 673 K. The powders were then re-
ground, pelletized, resealed in evacuated silica ampoules,
and heated for 873 K for 4 d. A final heating was performed
at 973 K for one week, of samples that had been ground up
and pelletized again. Powder x-ray diffraction patterns were
collected on powders using overnight runs on a Scintag X2
diffractometer operating in the Bragg-Brentano ␪-2␪ geom-
etry. Data were recorded using Cu K␣ radiation and a step
size of 0.02° in 2␪. The data were subject to Rietveld
FIG. 1. MX2 pyrite crystal structure showing MX6 octahedra
corner connected through X atoms which, in addition, are bonded
(shown by sticks) to X atoms on neighboring octahedra. The coor-
dination of X is 3͑M͒+1͑X͒. X2 sticks and M atoms (at the centers
of the octahedra) form two interpenetrating fcc lattices and a struc-
ture related to NaCl.
refinement17 using the pyrite (space group Pa3, No. 205)
¯
free structural parameter) was optimized using full-potential
linearized augmented plane wave (LAPW) calculations using
the WIEN2K code.26 Exchange correlation was considered fol-
lowing the Perdew-Burke-Ernzerhof27 parametrization.
structural model with the transition metal (Co or Fe) at
(0,0,0) and S at ͑xS,xS,xS͒ with xSϷ0.39. The XND (Ref. 20)
Rietveld program was employed for the refinements.
Magnetic measurements were performed using a Quan-
tum Design MPMS 5XL Magnetometer. Sample holders
(gelatin capsules inserted in plastic drinking straws) held
small solid pellets of the Co1−xFexS2 phases. We have not
corrected the measured magnetizations for any core or
sample-holder diamagnetism. Demagnetization corrections
have not been performed.
IV. RESULTS
A. Crystal structure
Powder x-ray diffraction revealed all compounds in the
series to be single phase, and well-fitted by Rietveld profile
refinement to the pyrite crystal structure described in Fig. 1.
Results of the x-ray refinement are summarized in Fig. 2(a),
which shows data for the two extreme compositions (x=0.0
and x=0.5) in the series studied here. The cubic a cell pa-
rameter varies linearly with x, as shown in Fig. 2(b) indicat-
ing the formation of a homogeneous solid-solution. Careful
analysis does however suggest a broadening in peak profiles
as x increases in Co1−xFexS2. The decrease in the a lattice
parameter as a function of increasing x (substitution of Co by
Fe) arises from the different sizes of these ions; six-
coordinate, low spin Co2+ has an ionic radius of 0.65 Å,
whereas the corresponding radius for Fe2+ is 0.61 Å.28 The
single internal parameter in the pyrite crystal structure is the
position ͑xS,xS,xS͒ of S. We have used refined values of xS
and a to calculate S-S distances across the solid solution
series. Within experimental error, we find nearly no change
in the S-S distance as a function of x as seen in Fig. 2(b).
This is an important experimental observation, which we dis-
cuss at length at a later stage. In Fig. 2(b) we also show for
comparison, structural data for the end-members CoS2 (Ref.
29) and FeS2.30
III. COMPUTATIONAL METHODS
Linear muffin-tin orbital (LMTO) calculations21 within
the atomic sphere approximation (ASA) were performed us-
ing the STUTTGART TB-LMTO-ASA program.18 Experimental
crystal structures used as inputs for the calculations were
obtained from x-ray Rietveld refinements from this study,
unless otherwise mentioned. Typically, more than 300 irre-
ducible k points within the primitive wedge of Brillouin zone
were employed in the calculations. The generalized gradient
approximation (GGA) for calculation of exchange correla-
tion was employed following the Perdew-Wang
prescription.22 This results in slightly larger moments over
the von Barth-Hedin23 LSDA, although not to the extent that
CoS2 is a perfect half metal as determined by Shishidou et
al.15 Calculations including the effect of the spin-orbit inter-
action were also performed using a modified version of the
LMTO code.24 The implementation of the spin-orbit coupling
into the otherwise scalar-relativistic LMTO formalism is
analogous to the implementation described in Ref. 25 for the
APW method. It was found that neither the states near the
Fermi energy, not the magnetic moment were in any way
affected by the inclusion of spin-orbit coupling. For ferro-
magnetic, rock-salt CoS, the cell volume (which is the sole
B. Magnetism
Zero field cooled (ZFC) and field-cooled (FC) magnetiza-
tion M as a function of temperature recorded on Co1−xFexS2
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PHYSICAL REVIEW B 70, 214409 (2004)
FIG. 2. (a) Powder x-ray Rietveld refinement of CoS2 ͑x=0͒ and
Co0.5Fe0.5S2 ͑x=0.5͒. Data (circles), the Rietveld fit (fit reliability
R
BraggϽ8% for all samples) and the difference profiles are shown
FIG. 3. (a) Zero-field cooled (dashed lines) and field-cooled
magnetization as a function of temperature of the Co1−xFexS2
samples. (b) Field-cooled MT vs T. (c) Tc onset (circles) and mid-
point, corresponding to the maximum value (squares) obtained from
the MT vs T plot, as a function of x. The lines are guides to the eye.
for each compound. Vertical lines at the top of the plot indicate
expected peak positions. (b) Filled circles: Evolution of the a cell
parameter (in Å) with x of the solid solution Co1−xFexS2. Error bars
are smaller than the circles. The dashed lines connects published
crystal structure (Refs. 29 and 30) data on the end members
(squares). Open circles: S-S distances as function of x. The dashed
line connects published (Ref. 29) data (squares).
Co1−xFexS2 is a soft ferromagnet. Therefore only the positive
M vs H quadrant is displayed. All the samples display satu-
ration at fields well below 1 T. The saturation magnetization
are indicated in Fig. 3(a). ZFC data were recorded in a field
of 1000 Oe upon warming from 5 K after cooling from room
temperature under zero field. FC data were also collected
upon warming from 5 K, after the samples were cooled un-
der a 1000 Oe field. All samples show evidence for ferro-
magnetism, with Tcs below 155 K. There is almost no
ZFC/FC separation in any of the samples, suggesting the
samples are homogeneous, and also that they combine high
permeability with low saturation fields. Clear ferromagnetic
Tc onsets as well as widths of the transition are best seen
from plots of MT vs T displayed in Fig. 3(b). The Tc onset
does not seem to depend very much on x, and after an ini-
tially increasing with x, almost remains constant as seen in
Fig. 3(c). Data were acquired under relatively high field
͑1000 Oe͒ so even small clusters of spins are sufficient for
the magnetization to rise. The midpoints of the MT vs T
traces are therefore better indication of ferromagnetic Tc.
These are also shown in Fig. 3(c), and are seen to initially
increase with x and then decrease. The constant width of the
transition [difference between Tc (onset) and Tc (midpoint)]
for the different values of x reflects that all the samples are
homogeneous, and the transition is not due to small ferro-
magnetic clusters.
in Bohr magnetons ͑␮ ͒ is plotted as a function of x in Fig.
B
4(b). The dashed line is the expected spin-only value assum-
ing each eg electron contributes 1 ␮ per formula unit to the
B
magnetization. Only the parent CoS2 phase is seen to have a
saturation magnetization less than the spin-only value. Start-
ing from x=0.1 through x=0.5, all samples display spin-only
behavior. This is an indication that all the samples except x
=0.0 are within experimental error, perfect half-metals in
terms of their being no “leak” in the magnetization from
majority to minority spin states. Such leaking is prevented by
the complete absence of there are no minority spin states at
the Fermi energy. Our results, for both ferromagnetic Tc
(midpoint) as well as saturation magnetization are nearly
identical with those obtained by Jarrett et al.4
C. Electronic structure
A number of authors have provided detailed electronic
structure descriptions of CoS2.5,13–15 Mazin6 has examined
magnetism across the series Co1−xFexS2. The purpose of this
section is to use structure refinements as inputs to obtain first
principles electronic structures, and in particular, to calculate
COHPs so that trends in spin-polarized bonding across the
solid solution series can be obtained.
Magnetization at 5 K is displayed in Fig. 4(a). None of
the samples showed any significant hysteresis implying
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RAMESHA et al.
PHYSICAL REVIEW B 70, 214409 (2004)
FIG. 4. (a) Magnetization at 5 K as a function of field. Since
none of the samples show appreciable hysteresis, only the positive
quadrant is displayed. Data were acquired from 5 T through 0 T.
(b) Closed circles are measured saturation magnetization (5 K, 5 T)
as a function of x. The open squares are the calculated LMTO
magnetic moments. The dashed line is the expected spin only value
assuming every eg electron contributes 1 ␮B.
FIG. 5. (a) LMTO densities of state of hcp Co metal. (b) Den-
sities of state of CoS2. The origin on the energy axis in (a) and (b),
indicated by a vertical line, are the respective Fermi energies. (c)
Densities of state of nonmagnetic FeS2 split into two spin direc-
tions. The energy axis in (c) has been shifted as described in the
text. The upper and lower parts of each panel indicate respectively,
majority and minority spin states.
Figure 5 shows total LMTO densities of state (DOS) in
the two spin states for (a) hcp Co metal, for (b) CoS2 (using
¯
the Pa3 crystal structure obtained from x-ray refinements
general trend amongst the first row transition metals that as
one goes to the right (from Sc through Cu), metal d levels are
stabilized. To some extent, this trend is reflected in the Paul-
ing electronegativities which are 1.83 for Fe and 1.88 for Co.
It is the same trend which shifts MX2 crystal structures from
being layered (with M4+) to being three-dimensional (with
M2+) in a process referred to as redox competition.32 In oxide
materials, the descent of cation d levels as one traverses first
row transition metals results in the famous Zaanen-
Sawatzky-Allen phase diagram.33 In making solid solutions
of CoS2 and FeS2, we believe the distinctly shifted d levels
of FeS2 have a role to play. While substitution of Co by Fe in
the series Co1−xFexS2 results in electrons being removed
from the eg manifold, the d levels themselves are pushed to
higher energies; the species (Fe) which “removes” electrons
actually creates donor states. This is one of the factors which
affects the electronic structure across the solid solution. A
more electronegative substituent might remove electrons
from p states of S, and this would be disastrous for the mag-
netism as demonstrated presently.
performed here) and (c) FeS2 using the crystal structure re-
ported by Finklea et al.;30 SG. Pa3, a=5.4281 Å, xS
¯
=0.38504. Fermi energies are taken as 0 on the energy axis
in panels (a) and (b). On going from Co metal to CoS2, we
observe a narrowing of d states as well as the effects of the
octahedral crystal generated by the S22− moieties. In Co
metal, the Fermi energy lies in the minority spin states, in a
region where majority ͓s͑↑͔͒ states are also found. Removal
of these s states by ionization (forming Co2+ from Co) is an
essential ingredient in rendering the system half metallic.
Panel (c) of this figure is the total DOS of nonmagnetic
semiconducting FeS2 distributed equally between the two
spin states. We have aligned s states of S (in the region
−20 eV to −10 eV with respect to the Fermi energy, not
shown) by shifting the origin on the energy axis for the DOS
of FeS2, in order to compare it with the DOS of CoS2 on an
“absolute” energy scale. The assumption is that S s is a core
state which should not be affected by compound formation,
and therefore can be used as a reference state in the different
compounds. FeS2 is a semiconductor with a calculated band
gap of about 0.8 eV.31 In both FeS2 and CoS2, p states of S
below EF extend from about −8 eV to −2.5 eV. In CoS2,
Co d states (the t2g manifold) start at −2.5 eV, where S p
states terminate. In FeS2, there is a gap between occupied S
p states and the metal t2g manifold. Comparing the DOS of
FeS2 with CoS2, we observe that the d manifold in the
former is shifted to higher energies. This is indicative of the
We have performed LMTO calculations on ordered super-
cells of pyrite CoS2 after systematically replacing some of
the Co by Fe. Lattice a and internal structural parameters xS
for the calculations were taken from structure refinements of
the nearest compositions as summarized in Fig. 2(b). Figure
6 shows densities of state for Co1−xFexS2, for (a) x=0.00, (b)
x=0.25, and (c) x=0.50. In all three compounds, the shape of
unfilled states just above EF is “boxlike” rising sharply with
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FIG. 6. Evolution of total LMTO densities of state as a function
in x in Co1−xFexS2: (a) CoS2 ͑x=0.00͒, (b) Co0.75Fe0.25S2 ͑x
=0.25͒, and (c) Co0.50Fe0.50S2 ͑x=0.50͒.
FIG. 7. (a) LMTO COHPs of nonmagnetic CoS2 showing Co-
S and S-S interactions. The nonmagnetic COHP has been scaled
by a factor of 0.5. ͑b͒ LMTO COHPs of the Co-S interactions in
CoS2 in the two spin directions. ͑c͒ LMTO COHPs of the S-S
interactions in CoS2 in the two spin directions. In the definition
we employ here, positive COHPs correspond to bonding interac-
tions and negative COHPs to antibonding interactions. This is
the opposite to the convention used in the original paper ͑Ref.
19͒.
energy. The evolution of t2g states with Fe substitution (in
both spin directions) seems to result from a weighted super-
position of the t2g states of spin-polarized CoS2 and nonmag-
netic FeS2 [shown in Figs. 5(b) and 5(c)]. Filled t2g levels
below EF seem pinned firmly in place. Partially filled eg
levels are shifted up in energy, to near (the respective) Fermi
energies.34 A feature of note is that at EF (the few) states in
the minority states are progressively removed as x increases
in Co1−xFexS2. This result, as previously reported in the cal-
culations of Mazin,6 explains the less-than-perfect
The COHP (Ref. 19) is a very useful tool for mapping the
energy dependence of pairwise bonding and antibonding in-
teractions between atoms from first-principles electronic
structure calculations, including in systems which are
spin-polarized.36,37 Figure 7(a) shows pairwise Co-S and S-
S COHPs of parent nonmagnetic CoS2, scaled by 0.5. We
have verified that the spin-orbit coupling is negligible.
Interactions are therefore confined to separate spin chan-
nels. Nonmagnetic CoS2 has sharply antibonding states at
the EF. Switching on spin-polarization decreases these an-
tibonding states, in keeping with the suggestion of Lan-
drum and Dronskowski36 that sharply peaked antibonding
COHPs in nonmagnetic calculations can be an indicator
͑the equivalent of a Stoner criterion͒ of the electronic in-
stability associated with spin polarization and ferromag-
netism.
From Fig. 7(b), we observe bonding Co-S COHPs in the
region of t2g states and antibonding COHPs corresponding to
the region of eg states. EF in spin-polarized CoS2 falls in a
gap flanked by antibonding Co-S͑↑͒ and antibonding Co-
S͑↓͒. The S-S COHP in Fig. 7͑c͒ shows the strongly
bonding region where the p states of S are found. The
effect of spin-polarization on S-S COHPs is small but
͓͑M/␮ ͒/CoϽ1͔ saturation magnetization of pure CoS2 ͑x
B
=0͒, and the increased ͓͑M/␮ ͒/Co=1͔ magnetization as x
B
increases, seen in our magnetic measurements, and in the
measurements of Jarrett et al.4 From a magnetism viewpoint,
the extent of half-metallicity in this system can be obtained
as the ratio of the saturation magnetic moment in Bohr mag-
netons to the number of unpaired eg electrons. Computation-
ally, the magnetic moment, or more precisely, the polariza-
tion index P given by35
N ͑EF͒ − N ͑EF͒
↑
↓
P =
ͯ ͯ
N ͑EF͒ + N ͑EF͒
↑
↓
provides an indication of the half-metallicity, though this
cannot easily be applied directly to Andreev reflection
studies.16 We calculate P=1 for both the x=0.25 and the x
=0.5 compounds. Correspondingly, magnetic moments per
formula units were, respectively, obtained to be 0.75 ␮ and
B
0.50 ␮B; whereas for CoS2 ͑x=0͒ it was 0.90 ␮B. These have
been plotted in Fig. 4(b) in comparison with experiment, and
are seen to correspond precisely to what is measured.
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RAMESHA et al.
PHYSICAL REVIEW B 70, 214409 (2004)
FIG. 9. (a) Summary of the nonmagnetic electronic structure of
Co1−xFexS2 for large x values (low eg filling). As x becomes slightly
less than 1, the eg levels are filled and descend below EF. The p
states remain above EF however. The boxlike shape of the unfilled
d states ensures the Stoner criterion is satisfied even for small fill-
ing. (b) Even at larger eg filling (smaller x), only d states descend
below EF, and EF is pinned to the bottom of the unfilled p states. (c)
Schematic nonmagnetic states in a more usual material such as
CoS, where unfilled states grow gradually, and the Stoner criterion
is satisfied only for large filling.
FIG. 8. (a) Total energy and magnetic moment per Co atom in
rock-salt CoS as a function of the cubic cell parameter, as obtained
from spin-polarized LAPW calculations. (b) Total densities of state
in the two spin directions of ferromagnetic CoS, calculated for a
¯
rock salt ͑Fm3m͒ structure with a=4.67 Å.
important. Interestingly, the antibonding region of the S-
S͑↑͒ COHP just above EF is slightly stabilized by spin-
polarization, just as antibonding S-S͑↓͒ is slightly desta-
bilized. Antibonding S-S͑↑͒ state are what pin the Fermi
energy, and are perhaps the most significant states for
discussing half-metallicity in these compounds. S-S states
are pseudomolecular so they not disperse very greatly.
They can be expected to remain in place because there is
no great change in the charge state or in the degree of
charge-transfer in the system as x is increased, as was
observed from the constancy of the S-S distance. For an-
tibonding S-S͑↓͒ states to descend through the Fermi en-
ergy, the S-S bond would have to be elongated.
ferromagnet, despite minority spin states trying to nest in a
pseudogap. The electronic structure is characteristic of so-
called “intermediate spin” systems such as the finite-
temperature electronic structure of the cobalt oxide perov-
skite LaCoO3.39
V. CONCLUSIONS
The low Curie temperatures of Co1−xFexS2 make their use
as spin injectors in spintronic circuitry unlikely.38 This sys-
tem does however offer insights into the design of new half-
metallic ferromagnets. There are two questions which our
results help to address. The first is, what renders a compound
half-metallic? From observing changes on going from ferro-
magnetic Co metal to CoS2, we learn that s and p states at EF
(present in Co) are not good for half-metallic behavior since
they are only poorly exchange split. Compound formation
through removal of s and p electrons is therefore useful. This
suggests that even in systems such as the Heusler com-
pounds, X2YZ, where X and Y are usually transition ele-
ments and Z is a main group element, it might help to have
electronegative substituents at Z (for example, Si rather than
Al).40
In support of our argument that the S22− units play a cru-
cial role in determining the electronic structure of CoS2 and
the series Co1−xFexS2, we have performed first-principles cal-
culations on hypothetical rock-salt CoS, which has approxi-
mately the same atomic topology, and the same formal Co
valence as pyrite CoS2. Figure 8(a) shows the results of the
structure optimization by plotting total energy as a function
of the cubic cell parameter, as well as the corresponding
magnetic moment of Co. The GGA-optimized cell parameter
was determined to be 4.67 Å. The corresponding magnetic
moment is about 4.67 ␮B per Co. Figure 8(b) shows the den-
sities of state of ferromagnetic CoS in the two spin direc-
tions. It is seen that the crystal field in CoS is much smaller
than in CoS2. More importantly, CoS is not a half-metallic
The second question is how the system retains ferromag-
netism and half-metallicity across the substitution range. We
summarize our findings on the unusual electronic structure of
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the pyrites solid solutions Co1−xFexS2 in the scheme dis-
played in Fig. 9. For low filling of eg states (x approaching
1), the electronic structure is characterized by “boxlike”
states above EF, with a very sharp rise in the number of
states with energy, as depicted in Figs. 9(a) and 9(b). The
origins of this sharp rise, as we have demonstrated, are S-
S antibonding states, which persist just above the EF
through the solid solution series. The states are sharp be-
cause they are pseudomolecular. Even small filling of
empty states results in the Stoner criterion being fulfilled6
and the rapid onset of ferromagnetism.4,11 The details of
the insulator-metal transition at very low filling of the eg
band have not been examined by us. Within density func-
tional theory, any finite filling of the eg levels would result
in metallic behavior, and correctly describing the localization
near the FeS2 composition would require methods that go
beyond the present treatment. The important role played
by the shape of the DOS in fulfilling the Stoner criterion
has been examined in detailed for transition metals by
Andersen et al.41
ACKNOWLEDGMENTS
We thank J. Gopalakrishnan for pointing us towards CoS2
and Ryan Hummel (IGERT undergraduate intern) for help
with sample preparation. Discussions with, and help from
Ole Andersen, Nicola Spaldin, Kiril Katsov, and Pio Baettig
are gratefully acknowledged. This work was partially sup-
ported by the MRL program of the National Science Foun-
dation under the Award No. DMR00-80034, including a seed
grant. C.E. thanks Nicola Spaldin and the Materials Research
Laboratory for support.
Electronic address: ramesha@engineering.ucsb.edu
*
18 O. Jepsen and O.K. Andersen, STUTTGART TB-LMTO-ASA Program
version 47, MPI für Festkörperforschung, Stuttgart, Germany,
2000.
†Electronic address: seshadri@mrl.ucsb.edu
‡Electronic address: ederer@mrl.ucsb.edu
§Electronic address: tao.he@usa.dupont.com
ʈElectronic address: mas.subramanian@usa.dupont.com
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