Journal of Magnetism and Magnetic Materials 189 (1998) 69 — 82 Structural and magnetic properties of (Fe 1~x Co x ) 3 P compounds: experiment and theory Hui-ping Liu!,*, P. James", A. Broddefalk#, Y. Andersson!, P. Granberg#, O. Eriksson",$ ! Department of Inorganic Chemistry, Uppsala University, Box 538, SE-751 21, Uppsala, Sweden " Condensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-751 21, Uppsala, Sweden # Department of Materials Science, Uppsala University, Box 534, SE-751 21, Uppsala, Sweden $ Center for Materials Science and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87544, USA Received 6 October 1997; received in revised form 5 May 1998 Abstract The structural and magnetic properties of (Fe 1~x Co x ) 3 P compounds have been investigated by means of X-ray and neutron diffraction experiments, magnetization measurements and first-principles calculations. The saturation magnetization and the transition temperature of (Fe 1~x Co x ) 3 P decrease with increasing Co concentration. The magnetic moments on the three non-equivalent metal sites are determined in detail by means of neutron diffraction experiments and first principles calculations which both show that the moments on the different sites have different magnitudes and they all decrease with increasing Co concentration. Results show that Co preferentially substitutes Fe on two of the metal sites. The complex behavior of the individual magnetic moments and the site preferences of Co substitution are discussed in terms of atomic radius, coordination numbers, and eigenvalue sums. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Magnetism; Crystal structure; First principles calculations; Neutron scattering experiments; Magnetisation measurements 1. Introduction The 3d transition metals and the nonmetallic elements form a large number of compounds, which are magnetically ordered [1]. Attention has mostly been paid to binary and ternary compounds with * Corresponding author. Tel.: #46 18 4713738; fax: 46 18 503056. the metal to non-metal ratios 1 : 1, 1 : 2 and 2 : 1 [1]. M 3 X compounds are commonly formed be- tween transition metals and non-metals (M" transition metal, X"B, Si, Ge, P, As, Sb or S). These compounds normally crystallize in the closely related structure types: Fe 3 P, Ti 3 P, a- and b-V 3 S [2]. Fe 3 P crystallizes in a tetragonal structure [3], with space group I 4 1 and eight formula units per unit cell. The metal atoms are distributed on three crystallographically non-equivalent eight-fold 0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 2 0 3 - 0
Transcript
Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
Structural and magnetic properties of (Fe1~x
Cox)3P
compounds: experiment and theory
Hui-ping Liu!,*, P. James", A. Broddefalk#, Y. Andersson!, P. Granberg#, O. Eriksson",$
! Department of Inorganic Chemistry, Uppsala University, Box 538, SE-751 21, Uppsala, Sweden" Condensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-751 21, Uppsala, Sweden
# Department of Materials Science, Uppsala University, Box 534, SE-751 21, Uppsala, Sweden$ Center for Materials Science and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87544, USA
Received 6 October 1997; received in revised form 5 May 1998
Abstract
The structural and magnetic properties of (Fe1~x
Cox)3P compounds have been investigated by means of X-ray
and neutron diffraction experiments, magnetization measurements and first-principles calculations. The saturationmagnetization and the transition temperature of (Fe
1~xCo
x)3P decrease with increasing Co concentration. The magnetic
moments on the three non-equivalent metal sites are determined in detail by means of neutron diffraction experimentsand first principles calculations which both show that the moments on the different sites have different magnitudesand they all decrease with increasing Co concentration. Results show that Co preferentially substitutes Fe on two ofthe metal sites. The complex behavior of the individual magnetic moments and the site preferences of Co substitutionare discussed in terms of atomic radius, coordination numbers, and eigenvalue sums. ( 1998 Elsevier Science B.V.All rights reserved.
The 3d transition metals and the nonmetallicelements form a large number of compounds, whichare magnetically ordered [1]. Attention has mostlybeen paid to binary and ternary compounds with
the metal to non-metal ratios 1 : 1, 1 : 2 and 2 : 1[1]. M
3X compounds are commonly formed be-
tween transition metals and non-metals (M"
transition metal, X"B, Si, Ge, P, As, Sb or S).These compounds normally crystallize in theclosely related structure types: Fe
3P, Ti
3P, a- and
b-V3S [2].
Fe3P crystallizes in a tetragonal structure [3],
with space group I 41 and eight formula unitsper unit cell. The metal atoms are distributed onthree crystallographically non-equivalent eight-fold
0304-8853/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved.PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 0 2 0 3 - 0
positions, called M(1), M(2) and M(3), and thenon-metal atoms on one eight-fold position. Fe
3P
orders ferromagnetically at about 700 K [4—7] andfrom neutron diffraction experiments the magneticmoments on the three different iron positions atroom temperature 2.12k
B, 1.25k
Band 1.83k
B, re-
spectively, have been determined [8]. Previousmagnetization measurements gave a saturationmoment of 1.70k
Bper Fe atom at room tem-
perature [4,8] and 1.84kB
per Fe atom at 4.2 K[4,7,8].
The Co3P phase does not exist in the binary
Co-P system [9]. Previously, it has been re-ported that Co substitutes Fe up to a maximumCo concentration of about 30% [7] or 60%[10]. Magnetization measurements showed thatthe saturated magnetic moment and the transitiontemperature decrease with increasing Co content[6,7].
In this paper the magnetic properties of thesolid solution of cobalt substitution of iron in(Fe
1~xCo
x)3P have been investigated. The site pref-
erences of the substituted Co atoms, the total andindividual magnetic moments have been studied bymeans of magnetization measurements, neutronpowder diffraction experiments and first principlescalculations.
The paper is organized as follows. In Section 2,the experimental and theoretical aspects are de-scribed and Sections 3 and 4 contain the resultsand a summary.
2. Experiments and theory
2.1. Sample preparation
Master samples with the nominal compositionsFe
3P and FeCo
2P were made by melting stoi-
chiometrically pure iron and cobalt rods and lumpsof red phosphorus (purity 99.999%) in a high-fre-quency vacuum induction furnace by the drop syn-thesis method described by Rundqvist [11].Compounds of (Fe
1~xCo
x)3P with x"0.0, 0.10,
0.20, 0.33, 0.37 were prepared by mixing appropri-ate proportions of the two master samples andannealed at 1220 K in sealed evacuated quartztubes for 4 days, then slowly cooled to room tem-
perature. The heat treatments were repeated untilequilibrium was obtained. Phase analysis wereperformed by recording X-ray powder diffractionphotographs with Guinier—Hagg focusing camerausing CrKa
1radiation, and powdered silicon
(a"5.431065 A_ , 25°C) as internal standard for cal-ibration. All diffraction lines for compositions withx(0.37 could be indexed according to the tetrag-onal Fe
3P-type structure [3].
2.2. Neutron diffraction experiments
The neutron powder diffraction work was car-ried out at the Swedish research reactor R2 atStudsvik. The measurements were performed at 10and 733 K for (Fe
0.90Co
0.10)3P and (Fe
0.67Co
0.33)3P.
The samples were contained in vanadium tubes andthe data sets were collected by two different multidetector systems either with 10 separate 3He de-tectors mounted 3.12° apart or 35 detectors moun-ted 4.00° apart, measuring intensities in 2h steps of0.050° or 0.080°. The neutron flux at the samplewas approximately 106 cm~2 s~1 for the paralleldouble Cu(2 2 0) monochromator system used witha wavelength of 1.470(1) A_ .
Structure refinements of the neutron powderdiffraction patterns were based on the Rietveldmethod [12] using the program FULLPROF [13].The 2h ranges for the refinements were 9.80°—128.04°. A pseudo-Voigt function was used to de-scribe the peak shape. The neutron scatteringlengths used were Fe: 9.45 fm, Co: 2.49 fm, andP: 5.13 fm. Magnetic form factors for Fe andCo were the default values from the FULLPROFprogram. The linewidths were expressed by the full-width at half-maximum, FWHM"º tan2 h#» tan h#¼, where º, » and ¼ are refin-able parameters and h is the Bragg angle. Thebackground was described by a polynomial ex-pression
yi"
5+
m/0
BmA
2hi
90!1B
m. (1)
Correction for absorption was applied using thelr-values, 0.22 and 0.33 for (Fe
0.90Co
0.10)3P and
(Fe0.67
Co0.33
)3P, respectively, as obtained from
transmission measurements at 2h"0.
70 H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
Inspection of the neutron powder diffractionpatterns of (Fe
0.67Co
0.33)3P showed that some
very weak diffraction lines could be identified as(Fe,Co) and (Fe,Co)
2P. Simultaneous refinements
of temperature factors and the Fe/Co distributionled to unrealistic results. Therefore, the temper-ature factors were fixed at the values for which thebest agreement with the nominal composition andthe lowest agreement factors were obtained. In therefinements of the neutron powder diffraction pro-files measured at 733 K, 29 and 35 parameters wererefined for (Fe
0.90Co
0.10)3P and (Fe
0.67Co
0.33)3P,
respectively. Profile parameters: zero point (1),scale factor (1 for (Fe
magnetic and crystal structure at 10 K, the distri-bution of iron and cobalt on the three positionswere fixed at the values obtained from the 733 Kmeasurements. The starting model of the orderedmagnetic structure at 10 K was the magnetic struc-ture of Fe
3P, where the magnetic moments of the
three metal positions were parallel and aligned inthe ab-plane. The individual magnetic moments ofthe three metal positions were refined together withthe profile parameters, atomic coordinates and unitcell parameters mentioned above.
2.3. Magnetization measurements
The magnetic properties of the powder sampleswere measured in a Quantum Design MPMS 5.5 TSQUID magnetometer, operating in fields up to&4400 kA/m and in the temperature range1.5—400 K. At high temperatures a vibrating samplemagnetometer (VSM) was used. The VSM is equip-ped with a high-temperature oven allowing mag-netization measurements in the temperature rangefrom room temperature to 1150 K and in magneticfields up to 1200 kA/m. To measure the saturatedmagnetic moment at low temperatures the magnet-ization was recorded at 10 K as a function of ex-ternal field strength in the SQUID magnetometer.The saturation magnetization was estimated from
a fit of the magnetization at large fields using thelaw of approach-to-saturation [14].
M"M4A1!
b
H2!
c
H3B, (2)
where b and c are fitting parameters and M4is the
saturation magnetization. The Curie temperature,¹
#, of the samples was measured in a small
magnetic field of about 2 kA/m using the VSMapparatus. In these measurements the low-fieldmagnetization was recorded at a constant rate (4data points/min) while the temperature of thesample was continuously and slowly increased atthe rate 5 K/min. In the immediate vicinity of thetransition the temperature increase was approxim-ately 2 K/min. ¹
#was assigned to the location of
the inflexion point in the M versus ¹ curve.
2.4. Details of calculations
In the theoretical calculations, Co concentra-tions of 0, 10, 33, 67 and 100% were considered.For the 33% Co concentration, it was assumed thatCo atoms replace all Fe atoms in a given site.The total energy and the magnetic moment werecalculated for Co in the M(1), M(2) and M(3)positions, respectively. Calculations were alsoperformed for 67% Co where the Fe atoms wereoccupying one of the three possible sites at a time.For the 10% Co concentration, the virtual crystalapproximation method (VCA) was used. In thisapproximation the alloy is represented as a systemwith artificial metal atoms with an atomic numberequal to the average atomic number of the con-stituting metal elements. The VCA has been shownto be well applicable to alloys involving neighbor-ing elements in the periodic table, such as Fe andCo [15,16].
In the present work, the calculations have beenbased on a full-potential linear muffin-tin-orbital(FPLMTO) method [17—19]. Space is divided intonon-overlapping spheres, muffin-tins, centeredaround the atomic sites, and an interstitial region.The basis function used are different in the differentregions. In the muffin-tin, where the charge densityvaries rapidly, the basis functions are linear muf-fin-tin orbitals. The radial part of each muffin-tin
H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82 71
orbital is constructed from the numerical solutionsof the radial Schrodinger equation, /
L(El, r) in
a spherical potential at the fixed energy El and theirenergy derivatives /Q
L(El, r). The index L is a com-
mon index for the principal quantum number n, theorbital quantum number l, the magnetic quantumnumber m. In the interstitial region, where thecharge density varies slowly, the basis functions areBloch sums of Hankel or Neumann functions de-pending on the sign of the kinetic energy. At thesphere boundaries the crystal wave functions in themuffin-tin are connected continuously and differen-tiably to the crystal wave functions in the inter-stitial region.
The variational principle, using the Rayleigh—Ritz method, leads to an eigenvalue problem whichcan be solved by diagonalization of the secularmatrix. For each eigenvalue, e
k, a corresponding set
of optimized coefficients, ct, is obtained yielding
a best representation of the crystal wave function,WkM . s, p and d orbitals were used for Fe, Co as wellas P.
In the generation of the potential and chargedensity, an unrestricted shape was provided by anexpansion of spherical harmonic functions insidethe muffin-tin spheres and by a Fourier series in theinterstitial region. For the integration over the Bril-louin zone a special point sampling was used [20]with a Gaussian smearing of 10 mRy and using32k-points in 1
4th of the zone. Experimental lattice
constants determined from X-ray diffraction ex-periments were used in all calculations. The elec-tron exchange and correlation parts of the potentialwere calculated using the local spin density approx-imation (LSDA) with the Hedin—Lundqvist [21](HL) parameterization.
3. Results
3.1. Structural properties
X-ray powder diffraction data shows that(Fe
1~xCo
x)3P (x(0.37) crystallizes in a tetragonal
structure [2,3]. The range of solid solution is foundto be different from that previously reported [7,10].The substitution of iron with cobalt is associatedwith a decrease in the unit cell volume. The unit cell
dimensions for different compositions are listed inTable 1. The crystal structure is shown in a projec-tion along the c-axis in Fig. 1. The final structuralparameters and agreement factor [22] obtainedfor (Fe
0.90Co
0.10)3P and (Fe
0.67Co
0.33)3P at 733 K
are listed in Tables 2 and 3. The agreement be-tween observed and calculated intensities were notimproved significantly by introducing individual
Table 1Unit cell parameters at 298 K for (Fe
1~xCo
x)3P, x(0.37, ob-
tained from X-ray powder diffraction experiments. Estimatedstandard deviations in parentheses
Composition a (A_ ) c (A_ ) » (A_ 3)
Fe3P 9.1081(3) 4.4606(2) 370.04(3)
(Fe0.90
Co0.10
)3P 9.0915(4) 4.4593(2) 368.59(3)
(Fe0.80
Co0.20
)3P 9.0718(3) 4.4575(2) 366.85(3)
(Fe0.67
Co0.33
)3P 9.0487(5) 4.4552(3) 364.79(5)
(Fe0.63
Co0.37
)3P 9.0418(3) 4.4537(2) 364.11(3)
Fig. 1. The crystal structure of Fe3P projected on the (0 0 1)
plane.
72 H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
Table 2Structure data for (Fe
0.90Co
0.10)3P at 733 K. Estimated stan-
dard deviations in parentheses. The overall temperature factorwas fixed to 1.9 A_ 2. Space group I 41 (no 82) a"9.1174(5) A_ ,c"4.5091(3) A_ . R
temperature factors in the refinements of the inten-sity data recorded at 733 K. The best fit was ob-tained by applying an overall temperature factorof 1.9 A_ 2. The observed and calculated neutronpowder diffraction profiles for (Fe
0.67Co
0.33)3P at
733 K are shown in Fig. 2a. The metal atoms in theFe
3P-type structure are distributed on three crys-
tallographically non-equivalent eight-folded posi-tions denoted M(1), M(2) and M(3), and thephosphorus atoms on one eight-folded position.The cobalt atoms preferentially substitute the ironatoms in the M(3) and M(2) positions, while theM(1) position is less favorable. The averagemetal—metal and metal—phosphorus distances aregiven in Table 4.
3.2. Magnetic properties
The magnitude of the magnetic moments at10 K, as obtained by the neutron measurements,
Table 4The average metal—metal and metal—phosphorus distances inA_ at 10 K. Distances less than 3.4 A_ are listed
Compound M(1)-12M M(2)-10M M(3)-10M
(Fe0.90
Co0.10
)3P 2.72 2.74 2.66
(Fe0.67
Co0.33
)3P 2.72 2.73 2.65
Compound M(1)-2P M(2)-4P M(3)-3P
(Fe0.90
Co0.10
)3P 2.35 2.32 2.33
(Fe0.67
Co0.33
)3P 2.34 2.31 2.32
were refined with the assumption that the cobaltand iron atoms interact in the same manner andcontribute with the same magnetic moment. In thepreliminary refinements, the magnetic moments onthe three metal positions were allowed to vary bothin the ab-plane and in the c-direction. The contri-bution in the c-direction was set to zero in the finalrefinements since this value oscillated around zerowhen refined. The structural and magnetic para-meters of (Fe
0.90Co
0.10)3P and (Fe
0.67Co
0.33)3P
are listed in Tables 5 and 6. The observed andcalculated neutron powder diffraction profiles of(Fe
0.67Co
0.33)3P at 10 K are shown in Fig. 2b. An
overall temperature factor of 0.18 was used in therefinements of (Fe
0.90Co
0.10)3P at 10 K. The best
profile fit of (Fe0.67
Co0.33
)3P at 10 K was obtained
when the individual temperature factor of M(1) wasfixed to a lower value than the other atoms (seeTable 6), but the structural and magnetic para-meters did not change compared to the refinementsusing an overall temperature factor.
In Fig. 3 the magnetization versus applied fieldat 10 K is plotted for three different (Fe
1~xCo
x)3P
powder samples (x"0, 0.10, 0.33). The large mag-netization value and the shape of the M versusH curves are typical for a ferromagnetic ordering.A clear decrease of the saturation magnetizationwith increasing Co concentration is observed.
In Fig. 4 the normalized magnetization at smallfields is plotted versus temperature for all samplesin the series. The distinct transition from ferro- toparamagnetic phase with increasing temperatureindicates a homogeneous Co distribution in thesamples. At high temperatures an offset level of themagnetization is seen which signifies the presence
H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82 73
Fig. 2. Observed and calculated neutron powder diffraction patterns of (Fe0.67
Co0.33
)3P, (a) at 733 K, (b) at 10 K. Observed
intensities are dotted and the calculated profile is in full line. At the bottom of each figure the difference line is shown. The most intenselines originating from (Fe,Co) and (Fe,Co)
2P are indicated above the profile.
74 H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
Table 5Structure data for (Fe
0.90Co
0.10)3P at 10 K. Estimated standard deviations in parentheses. The overall temperature factor was fixed to
0.18 A_ 2. Space group I 41 (no 82) a"9.0715(4) A_ , c"4.4416(2) A_ . R1"0.037, R
of a minor amount of a ferromagnetic impurityphase.
In Fig. 5 the saturation magnetic moment andthe transition temperature, ¹
#, are plotted as func-
tions of cobalt concentration. Both M4
and¹
#show approximately a linear decrease with in-
creasing cobalt concentration. The dependences ofM
4and ¹
#on cobalt concentration are qualitat-
ively in agreement with the results obtained fromGoto et al., [7] but quantitatively a differenceis observed. The decreasing trend is in contrastto the known behavior of Fe
1~xCo
xalloys where
the magnetic moment shows an increase to amaximum value followed by a linear decrease.This is the so-called Slater—Pauling character-istic. The presence of P thus moves the maximum ofthe Slater—Pauling curve to a lower d-electronconcentration. This is a common effect for a non-magnetic material, with hybridizing states whichare lower in energy than the transition metald states [23].
In Fig. 6 the total magnetic moments obtainedfrom the magnetization measurements, neutron dif-fraction experiments as well as from first-principlescalculation are plotted as functions of Co concen-tration. Also included in Fig. 6 is the total momentat room temperature obtained from previousmagnetization measurements on Fe
3P [4,7,8]. The
agreement between theory and experiments is asgood as can be expected from state-of-the-art, firstprinciples theory. For completeness, the momentsfor FeCo
2P and Co
3P have also been calculated.
The theoretical data show that the approximatelinear decrease of the magnetic moment continuesacross the entire concentration interval, which isexpected from band filling arguments of a strongferromagnetic system.
In Fig. 7 the experimental site decomposedmoments of Fe
3P, (Fe
0.90Co
0.10)3P and
(Fe0.67
Co0.33
)3P are compared with those ob-
tained from first-principles theory. The theoreticaldata for the total magnetic moments for
H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82 75
Fig. 3. Magnetization at 10 K as a function of applied field for(Fe
1~xCo
x)3P compounds with x"0, 0.10 and 0.33.
Fig. 4. Normalized magnetization of (Fe1~x
Cox)3P compounds
as a function of temperature, for x"0, 0.1, 0.2, 0.33 and 0.37.H&2 kA/m.
Fig. 5. Saturation magnetization at low temperature and Curietemperature of (Fe
1~xCo
x)3P compounds as a function
of x.
Fig. 6. Total magnetic moment obtained from magnetizationmeasurements, neutron diffraction experiments and first prin-ciples calculations of the (Fe
1~xCo
x)3P compounds as a function
of x.
Fig. 7. Site projected magnetic moments obtained from neutrondiffraction experiments and theoretical calculations. The theor-etical data are weighted with the experimentally obtained sitepreferences.
(Fe0.67
Co0.33
)3P are obtained by averaging the
moments for different sites, weighted with the ex-perimentally obtained site preferences. Also shownin Fig. 7 are the results from the VCA calculations.
76 H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
For the 33% Co composition, the results fromthe VCA can be compared with the results from theweighted moments of the ordered compounds. Thetwo different theoretical treatments give rather sim-ilar site decomposed moments, which supports theuse of the VCA. For the 10% Co composition, theresults from the VCA also show a good agreementwith experiments. In general, experiment and the-ory agree well. The largest discrepancy was foundfor the M(2) moment where the experimental datawere consistently lower than the theoretical values.For the M(3) moments, the agreement betweenexperiment and theory is good except for the 10%
Fig. 8. Theoretical data of the site projected magnetic moments.The upper panel shows the least stable solution when the Coatoms first enters site 1 (33% case) and then sites 1 and 2 (67%case). The lowest panel shows the most stable solution when theCo atoms first enters site 3 (33% case) and then site 2 and 3 (67%case). The middle panel shows the moments when Co atoms firstenters site 2 (33% case) and then sites 1 and 3. The energies givenin the figure correspond to the increase in energy for thatconfiguration relative to the most stable configuration.
Co compound. In view of the experimental errorsthe discrepancy between experiment and theory isreasonable.
For a given alloy composition the three differentsite substitutions correspond to different calculatedtotal energies. The site decomposed moments foreach system are displayed in separate panels ofFig. 8, the most stable system in the lowest paneland the least stable system in the upper most panel.It is seen that initially Co prefers to occupy theM(3) site. The M(2) occupation is only marginallyhigher in energy (0.5 mRy/metal atom). Substitu-ting Co on M(1), however, gives an energy rise of1.7 mRy/metal atom. The preference for the Cosubstitution does not in a clear way correlate withthe magnetic moment of that site, since Co prefer-entially enters M(3), the site with the second largestFe moment in Fe
3P. The resulting Co moment in
M(3) is smaller than Co in M(1) and larger than Coin M(2). Other mechanisms must play a role for thedetermination of the site preference.
For the 67% Co substitution, the preferred sitesfor Co are M(2) and M(3), which are the two lowestenergy sites also for the 33% Co substitution. Forthe most stable system (the lowest panel) the Femoment is rather high in contrast to the two othersystems (the upper and middle panel). Another ob-servation is that the Fe or Co moment of a givensite (say M(1)) is rather insensitive to which atoms(Fe or Co) occupy the other crystallographic sites(M(2) or M(3)). Quite generally the Fe or Co mo-ments are lower on M(2) and larger on M(3).
3.3. Total energy analysis
In this section the experimental and theoreticalsite preference of the Co substitution is analyzed, bymeans of the electronic structure. The free energy ofthe compounds is estimated using two contribu-tions; the zero temperature total energy and thedisorder entropy. With these two entities the freeenergy is calculated as F"E
LSDA!S
$*403$%3¹.
The disorder entropy may be calculated fromS$*403$%3
"!kB
+iciln c
i, where the sum runs over
the three types of atomic sites in the cell and c*is the
element concentration. The total energy of a com-pound where the Co and Fe atoms partially occupythe different sites can be calculated and compared
H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82 77
Fig. 9. Calculated density of states for (Fe1~x
Cox)3P in the Fe
3P-structure. (a) x"0, (b) x"0.33, (c) x"0.67, (d) x"1. In (b) and (c)
the upper panels show the least stable solutions and the lowest panels show the most stable solutions.
to the free energy of the compound with ideal siteoccupation (all Co atoms in one position). Notethat for Fe
2CoP the energy obtained when occupy-
ing M(3) with Co is almost the same as occupyingM(2) with Co (0.5 mRy/metal atom difference only).This value becomes substantially higher when sub-
stituting Co on M(1) instead of M(3) (1.7 mRy/metal atom). These energy differences are consis-tent with the experimental finding that there ishigher Co occupation on M(3) and M(2) comparedto M(1). If the Co substitution on M(2) and M(3)are considered degenerate, the free energy becomes
78 H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
Fig. 9. (continued )
F"(E2#E
3)/2#k
B(0.5 ln 0.5#0.5 ln 0.5)¹,
where E2
and E3
are the LSDA-energies when Coenters M(2) and M(3), respectively. The free energyof the system with experimentally determined c
i’s
can thus be estimated as F"0.4E2#0.4E
3#
0.2E1#k
B(2 ) 0.4 ln 0.4#0.2 ln 0.2)¹. Comparing
this free energy with that for a system with onlyM(2) and M(3) populated with Co, it is found that
the experimental free energy is lower for temper-atures above 800 K. Since the sample was annealedabove this temperature it is reasonable that thehigh-energy position, M(1) also is partly occupiedat low temperatures.
To understand the zero temperature site prefer-ences, the electronic structure is analyzed. The den-sity of states (DOS) for Fe
3P (a), Co
3P (d) and the
H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82 79
Fig. 10. Calculated charge density contours in the (1 1 0) plane of Fe3P.
Fig. 11. Calculated spin density contours in the (1 1 0) plane of Fe3P.
different Co substituted alloys (b and c) are dis-played in Fig. 9. On Co substitution, small changesin the DOS of the Fe positions are observed. Thisis consistent with the fact that the Fe moment ofa given site is rather insensitive to the occupation ofCo or Fe on the other sites.
The expression for the total energy calculationsinvolves a kinetic energy term (¹), an electrostaticterm (E
%-) and the exchange and correlation term
(E9#). The sum of the eigenvalues enters the kinetic
energy term as ¹"+ei!:v
%&&(r)o(r) dr and it fol-
lows that the total energy is not the same as the sumof eigenvalues. Nevertheless, it has been shown thatas long as the second moment of the density ofstates is the same for two structures one may relatethe difference in total energy between two struc-tures to the difference in the eigenvalue sum [24].
To investigate this relationship, the eigenvalue sumof the DOS have been calculated. However, thisanalysis shows that the sum of eigenvalues alonedoes not provide the mechanism for the M(3) pref-erence for Co substitution, since the eigenvalue sumis largest for the M(3) substitutions. Hence, we mustconclude that the site preference of Co substitutiondoes not correlate in a simple way with the mag-netic properties or with the eigenvalue sum of thesesystems, but it can be understood from an atomicsize-factor concept, as will be discussed below.A comparison of the projected DOS plots for Feand Co occupying the same position shows that theDOS of Co is more narrow, as expected.
In Fig. 10 the calculated charge density contourin the (1 1 0) plane is shown for Fe
3P. In this plane
only the charge density around the Fe atoms is
80 H.-p. Liu et al. / Journal of Magnetism and Magnetic Materials 189 (1998) 69—82
seen. Between the two atoms at the top and in themiddle, the inter atomic distance is short and hencethe charge density is large between the atoms. InFig. 11 the corresponding spin density is shown.The spin density has significantly less structure andis more spherical and concentrated around the Featoms. This is consistent with the fact that the spindensity is dominated by the 3d electrons whichhave their main contribution in the vicinity of theFe atoms.
4. Conclusions
In summary, a detailed crystallographic study ofthe (Fe
1~xCo
x)3P-system has been undertaken.
The Fe3P structure is retained for x(0.37. The
magnetic properties of Fe3P and the Co substituted
alloys have been investigated in detail by means ofmagnetization measurements and neutron diffrac-tion experiments. The two types of experiments areconsistent, showing that (Fe
1~xCo
x)3P with
x(0.37 are ferromagnetic in the entire concentra-tion interval. The neutron diffraction experimentsgive detailed information about the individualmagnetic moments on the different sites, which arein agreement with the theoretical calculations. Thesaturation magnetization and Curie temperaturedecrease with increasing Co concentration. Cal-culated magnetic moments are in good agreementwith the experimentally determined data, for allconcentrations.
The results from the neutron diffraction experi-ments showed that the Co atoms preferentiallyoccupy the M(2) and M(3) positions. This is consis-tent with the results from the calculations, whichshow that the total energy for Co substitution onM(1) is higher than on M(2) and M(3) (Table 6 andFig. 8). The M(2) and M(3) positions both have tenclose metal neighbors and the number of closephosphorus neighbors are four and three, respec-tively. The M(1) position is coordinated by twelvemetal atoms and two phosphorous atoms.
Previously, the coordination and bonding in thecrystal structures belonging to the Fe
3P, Ti
3P, a-
and b-V3S-type structures have been discussed in
terms of atomic radius, electro negativity and cohe-sive properties of the elemental transition metal
components [2,25]. The preferential occupation ofCo on the M(3) position, which has the shortestmetal—metal distances (see Table 6), could be ex-plained according to the size-factor concept, as theatomic radius of cobalt is somewhat smaller thanthe radius of iron. On the other hand, with thisargument it is hard to understand the Co prefer-ence for the M(2) site since the shortest metal—metaldistance of this site is similar to one of the M(1) site.However, the M(2) and M(3) sites have a largernumber of P nearest neighbors and the preferencefor Co on these sites indicates a preferred Co—Pbonding over the Co—Co bonding. This is due tothe fact that transition metal d-phosphorous p hy-bridization is large and causes a strong bondingmechanism.
A simple model of the free energy showed thatthe experimental site occupancy has lower energythan the zero temperature occupancy at the anneal-ing temperature.
The total as well as the individual magnetic mo-ments on the three different metal positions ob-tained from experiments and first principlescalculations agree well. The values of the magneticmoments are smaller for cobalt than for iron, asshowed in Fig. 6. The magnitude of the individualmagnetic moments on M(1) and M(3) are consider-ably larger than on M(2). The results correlate withthe number of nearest phosphorous neighbors.M(1), M(2) and M(3) are surrounded by 2, 4 and3 phosphorous atoms, respectively. The phos-phorus—metal hybridization, which is largest for theM(2) position, quenches the magnetic moment.
Acknowledgements
We wish to thank the Swedish Natural ResearchCouncil for financial support. Ha> kan Rundlof atStudsvik is acknowledged for skillful assistance inthe neutron diffraction experiments.
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