Download - Electronic structure and X-ray photoemission spectra of the compounds APtSn I (A=Th, U

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Journal of Magnetism and Magnetic Materials 281 (2004) 281–289

*Corresp

8684524.

E-mail

0304-8853/

doi:10.1016

Electronic structure and X-ray photoemission spectra of thecompounds APtSn I (A=Th, U)

A. Szajeka,*, J.A. Morkowskia, A. Bajorekb, G. Che"kowskab, R. Tro!cc

a Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Pozna !n, PolandbA. Che!kowski Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice, Poland

cW. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410,

50-950 Wroc!aw, Poland

Received 31 March 2004; received in revised form 13 April 2004

Available online 2 June 2004

Abstract

The electronic structure of the actinide compounds ThPtSn and UPtSn is calculated by the tight-binding linear

muffin–tin orbital method, and the X-ray photoemission spectra (XPS) are measured and computed. Rather good

agreement is found. Comparison of XPS for UPtSn and ThPtSn shows the role of 5f electrons. Although electrical

resistivity measurements reported earlier in literature suggested semiconducting behaviour of the (Th,U)PtSn

compounds, the present study finds either very small or even vanishing semiconducting gap in UPtSn. The problem of

gap is discussed and arguments for an antiferromagnetic ground state in UPtSn are presented.

r 2004 Elsevier B.V. All rights reserved.

PACS: 71.20.�6; 82.80.Pv

Keywords: Actinides; Electronic band structure; Photoemission spectroscopy

1. Introduction

The APtM group of equiatomic ternary alloys,where A is Th, U or Ti, Zr and Hf, while M is Sbor Sn, crystallize in the cubic MgAgAs-type crystalstructure (space group F-43m, 4 formula units inthe unit cell). This group of compounds presents arich variety of physical properties, especially

onding author. Tel.: +4861-8695124; fax: +4861-

address: [email protected] (A. Szajek).

$ - see front matter r 2004 Elsevier B.V. All rights reserve

/j.jmmm.2004.04.116

semiconducting behaviour in their transport prop-erties originating from the special symmetry ofcrystal structure [1,2]. These compounds are so-called half-Heusler compounds. Due to the vacantA-site, each second A-site is empty and hence theinversion symmetry in the crystal structure is lost.This leads to the situation that overlap between theelectronic orbitals of the A elements is muchreduced. The large inter-uranium spacing, e.g. inUPtSn of about 0.47 nm, leads to a large reductionin the 5f–Td–Msp hybridization causing a morelocalized kind of behaviour of the uranium 5f

d.

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A. Szajek et al. / Journal of Magnetism and Magnetic Materials 281 (2004) 281–289282

electrons. Indeed, the temperature dependence ofthe magnetic susceptibility of UPtSn shows theCurie–Weiss behaviour towards high temperatureswith an effective moment meff ¼ 3:45 mB and theparamagnetic Curie temperature yp ¼ �125Kderived in a wide temperature range [2], so thatin the paramagnetic state the magnetic propertiesare well described by the localized f-electronmodel. On the other hand, the wðTÞ dependenceof the stoichiometric UPtSn exhibits quite anom-alous behaviour at low temperatures. The suscept-ibility of this compound below about 140K firstshows the tendency for leveling off and then atabout 35K, it increases rapidly to go through asmall maximum at about 20K, probably due tosmall ferromagnetic impurities. At the same timethe heat capacity measurements show withoutambiguity the transition probably into an anti-ferromagnetic order at the same temperature andyield the electronic specific heat coefficient to beabout 10mJ/K2mol [1,3].The results of electrical resistivity measurements

show dramatic and controversial temperaturevariations, as reported by several authors [1–3].As previous measurements showed [1], the beha-viour rðTÞ is characteristic of semiconductors andits temperature dependence at higher temperaturesmay then be described by a gap function,rðTÞEexp ðD=2kBTÞ; where D is 0.34K [1]. Atlow temperatures rðTÞ either decreases [1] or goingthrough a maximum at different temperaturesdepending on a sample measured (60–140K), thenpasses through a minimum at 9–16K and drama-tically increases towards lower temperatures. Inorder to describe the transport properties ob-served, we have previously proposed a simplephenomenological model [2] in which the band gapslowly diminishes and finally is closed at T ¼ 0Kinstead to collapse immediately at TN; as is thecase of UNiSn [4]. This suggests that the orderedstate acts as an additional mechanism in a strongp–f mixing effect [5] towards closing the gap.Previous synchrotron photoemission studies of

valence band spectra [6] were measured in thephoton energy range hn ¼ 222130 eV. Theyshowed the d-like density of states located wellbelow the Fermi level, EF; with the maximumbeing about 4.6 eV. The 5f states are close to the

Fermi energy with a maximum at 0.75 eV and full-width at half-maximum of 1.6 eV. These results areconsistent with a band gap in the paramagneticstate and a small g-value of 10mJK�2mole�1.Oppeneer et al. [7] have adopted a model

approach for a band-structure self-consistentdescription based on the local density approxima-tion of density functional theory generalized withan on-site Coulomb correlation U (LDA+U) andshown that this model approach correctly de-scribes a whole group of similar materials. ForUPtSn they obtained an AF ground state which issemiconducting with a gap of 0.21 eV in theparamagnetic state. In this state the 5f density ofstates has a broad shape with its maximum at0.85 eV, close to that found in the photoemissionexperiment [6].ThPtSn is a suitable reference compound,

because it has not occupied 5f electrons andremains paramagnetic semiconductor to the lowesttemperatures [2].The paper is organized as follows: In Section 2

the calculations of the electronic band structureand X-ray photoemission spectra (XPS) aredescribed. Then results of the measurements ofXPS are reported. The comparison of the mea-sured and calculated XPS for ThPtSn and UPtSnis presented in Section 4. Finally, the controversiesover the existence of an energy gap above thevalence band of UPtSn are discussed.

2. Calculations of the electronic band structure

For the half-Heusler APtSn compounds studiedin this paper the following positional parameterswere assumed for calculations: The A atomoccupies the (4b) site (1

2;12;12); while Pt: (4c), i.e.

(14;14;14) and Sn atoms are in: (4a), i.e. (0, 0, 0). The

above assignments have only a partial support inliterature. The (1

4; 14; 14) position for Pt has been

reported in Refs. [8–10], and no information to thecontrary is available, to our best knowledge.However, for UPtSn had been proposed thefollowing locations: for U atoms in (0, 0, 0) andSn atoms in (1

2; 12; 12) [2].

The tight-binding linear muffin–tin orbital (TB-LMTO) method in the atomic sphere approximation

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Table 1

The Wigner–Seitz radii (in (A) for APtSn compounds and the

muffin–tin overlap

A Pt Sn % of overlap

Th 1.924 1.587 1.924 14.7

U 1.873 1.601 1.873 15.1

A. Szajek et al. / Journal of Magnetism and Magnetic Materials 281 (2004) 281–289 283

(ASA) was used for band structure calculations[11,12]. The exchange-correlation potential in theform proposed by von Barth and Hedin [13] wasassumed for the calculations presented in Figs. 1and 4. The general feature of the band structuresof the series APtSn is an energy gap at the Fermilevel, evident in the DOS plots. The typical valuesfor the calculated gap are in the range between 10and 30meV. However, in the calculations the gapvalue appears to be sensitive to the choice of theexchange-correlation potential. For some forms ofthis potential the gap even vanished. Therefore,the band structure calculations were checkedagainst the choice of the exchange-correlationpotential. In spite of differences in the gap values,the calculated XPS spectra were not sensitive tothe choice of the exchange-correlation potential, atleast to the extent relevant to comparison withexperiments. So that only band structures for theone choice, von Barth and Hedin [13], arepresented in Figs. 1 and 4 in details.Calculations for ThPtSn and UPtSn were done

for 3091 k-points in 124

segment of the BrillouinZone. The initial atomic configuration of Pt wasassumed as (Xe+4f14) core +5d96s; the config-uration of Sn comprised (Kr) core +4d105s25p2.The remaining initial configurations were specifiedas follows: for Th: core +6p66d27s2; and U: core+6p65f36d7s2. As mentioned above, the resultingelectronic band structure depends in some finedetails upon the choice of the form of theexchange-correlation potential and the initialatomic configurations even if self-consistency isachieved within the assumed 0.01mRy error in theenergy eigenvalues. These differences are inherentin the TB-LMTO (ASA) approximations. Somefurther comments will be provided below whilediscussing particular results.The values of the Wigner–Seitz radii and

estimates of the overlapping of the muffin–tinspheres are collected in Table 1. The standardcombined corrections [11] for overlapping muffin–tin spheres were applied. Fully relativistic treat-ment of the core electrons and the scalar relativis-tic approximation for the valence electrons wasused [14]. Integrations in the k-space were done bythe tetrahedron method [15–17]. The experimentalvalues for the lattice constants: a ¼ 6:736 (A for Th

[3], and a ¼ 6:6108 (A for U [3] were used incalculations. For calculating the photoemissionspectra the standard Gaussian broadening wasassumed with the width parameter 0.3 eV, equal tothe experimental resolution.

3. XPS measurements

The samples were prepared by arc meltingappropriate amounts of constituent elementsunder argon gas. After melting the samples werewrapped in Ta foil and annealed in vacuum at850K for a week. The samples were identified byX-ray diffraction and determination of the latticeparameters. Only single phases were detected.The XPS were obtained with monochromatized

Al Ka radiation (1486.6 eV) at room temperature,using a PHI 5700

660Physical Electronics Spectrometer.

The emission spectra were analyzed by a hemi-spherical analyzer with energy resolution about0.3 eV. The samples were fractured mechanically inthe preparation chamber under UHV conditions(5� 10�10Torr) and then moved into main cham-ber. All spectra were recorded immediately afterbreaking in a vacuum about 5� 10�10Torr. Thefractured samples contain a small amount ofoxygen and carbon. The oxidation of all sampleswere checked several times during measurements byobserving the O(1s) spectra. No effects of oxidationduring the data acquisition time were observed.The XPS valence band spectra of the compounds

ThPtSn and UPtSn are shown in Figs. 2 and 5,respectively. For the UPtSn compound the 5f statesare located near the Fermi level ðEFÞ at about�0.42 eV. In the case of the thorium-containingcompound we have not observed f electron densityof states at EF; because in Th the 5f states are notoccupied. The broad peak located about 5 eVbelow EF is typical for the Pt-based compounds.

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Nearby the Fermi level one can observe partialcontributions of the Sn 5p electrons to the totalXPS spectrum. Intensity of this band is quitesmaller in comparison with the Pt band.Fig. 6c shows the U4f core-level spectrum of

UPtSn. The standard procedure of subtracting thebackground was applied and the deconvolution ofthe total core level curve had been made. The U4fspectrum shows two asymmetric lines resultingfrom U4f7/2�377.09 and U4f5/2–388.02 eV levels,split by the spin–orbit interaction; each of these isbeing accompanied by two satellite lines at higherbinding energy sides. According to the Do-niach– $Sunjic theory [18], the asymmetry of themain line is due to the angular dependence ofscreening charges in the electron–hole interactionduring the photoemission process and is describedby a singularity index a: According to the Kotaniand Toyozawa theory [19], this parameter is afunction of the density of states at the Fermi level.For the UPtSn compound the singularity index awas assumed in calculations to be about 0.44. Thestructure consisting of the main line and the satellitelocated about 7 eV higher in the binding energy hasbeen observed in the XPS core-level spectra of anumber of uranium intermetallic compounds [20–22]. The presence of this kind of satellite is an

Fig. 1. (a) The total and local DOS for ThPtSn, (b) partial DOS for T

of (a) plotted in expanded scales shows the energy gap at the Fermi

indication for a decreasing in the 5f-other-electronshybridization and consequently increasing the 5f-electron localization in uranium compounds. Theadditional satellites at about 2.85 eV in higherbinding energy with respect to the main lines havebeen found in our previous several studies [21,22].The structure consisting of the main line and twosatellites is interpreted as resulting from a contribu-tion of 5f2, 5f3 and 5f4 final states in thephotoemission processes [20]. However the intensityof this satellite in the UPtSn studied here isprobably enhanced by the existence in the sampleof small quantity of uranium oxides, satellites ofwhich are located at the same energy range.The Th 4f lines for the ThPtSn compound show

a spin–orbit splitting into 4f7/2 and 4f5/2 lines witha separation of about 9.32 eV. The satellites atabout 334.4 and 344.1 eV may be caused bycontamination with ThO2.

4. Results

4.1. ThPtSn

In Fig. 1 the total, local and partial densities ofstates (DOS) calculated for ThPtSn using von

h, Pt and Sn sites, respectively. The inset in the uppermost panel

level.

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0

1500

3000

4500

-1000 -600 -200

Th(

5p3/

2)

Pt(

4p1/

2)

Th(

4p3/

2)

Sn(

4s)

Sn(

3s) Sn(

3p1/

2)

O(1

s)

Th(4d3/2) Sn(3p3/2)

Th(

4d5/

2)

Pt(

4p3/

2) Sn(

3d)

Th(

4f)

Pt(

4d5/

2)C

(1s)

Th(

5d) Pt(

4f)

Sn(

4d)

ThPtSn

0

0.25

0.50

0.75

1.00

-80 -75 -70 -65

Pt(4f5/2)

Pt(4f7/2)

Inte

nsity

[arb

.uni

ts]

0

500

1000

1500

-350 -340 -330

oxidesPt(4d3/2)

Th(4f5/2)

Th(4f7/2)

Binding energy ( eV)

oxides

(c)

(b)

(a)

Fig. 3. (a) The XPS of ThPtSn in the broad energy range; and


Barth–Hedin exchange correlation potential [13]are summarized. A small energy gap of 32meV atthe top of the valence band is the most importantfeature of the electronic energy spectrum of thiscompound. The calculated values of the gap aresensitive to details of the method being chosen, e.g.for the exchange-correlation potential in the formproposed by Perdew et al. [23] the gap is less than0.001meV; or including the Sn4d electrons to thecore results in zero energy gap. As expected, the 5fstates due to the Th atoms nearly all are lyingabove the Fermi level. The main contributions tothe total DOS in the energy interval from �5.5 eVto the Fermi energy are due to the 5d electronsfrom Pt. The narrow peak at �18 eV comes fromTh 6p electrons which appear to be localized. Alsolocalized are the Sn 4d electrons which aremanifested by a very narrow peak at about�23 eV.As it will be presented in our next paper II, an

interesting feature of DOS(E) for the whole seriesof APtSn compounds studied (A=U, Th, Ti, Zr,Hf) is a rather narrow well separated band, locatedbetween about �10 and �8 eV due predominantlyto the Sn5s electrons.The measured valence band X-ray photoemis-

sion spectrum, presented in Fig. 2a, is accompa-nied by the calculated one, in Fig. 2b. The

0

0.4

0.8

1.2

Sn(4d) ThPtSn

0

0.4

0.8

-25 -20 -15 -10 -5 0

Sn(6s)Th(6p)

Sn(4d)

Binding energy [eV]

Inte

nsity

[arb

. uni

ts]

0

0.1

0.2

-5 0

total →

Pt

Th Sn

→

→ →

(a)

(b)

Fig. 2. The measured (a) and calculated (b) XPS for ThPtSn. In

the inset the total intensity is shown together with the

contributions from Th6d, Pt5d and Sn5d states, respectively.

details of the spin–orbit split lines for Pt 4f (b), and Th 4f (c).

agreement is rather good in the low binding energyregion. The peak due to the fully occupied bandSn4d is not well reproduced by the calculations.The same situation appears also for the UPtSncompound (Fig. 5b) and, most likely, is due tosystematic errors of the TB-LMTO-ASA proce-dure when applied to regions of high bindingenergies.The XPS in the broad energy range is shown in

Fig. 3a. Except for the peaks corresponding to theweights of all the individual constituting elements,a small contamination by oxygen (O1s) andcarbon (C1s) is visible. The peaks Pt 4f and Th4f, split by the spin–orbit interaction are presentedin Figs. 3b and c, respectively. Not a sign ofsatellites to the Th 4f peaks can be recognized inFig. 3c, this is in contrast to such a spectrum inuranium compounds [20–22], shown in Fig. 6.

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Fig. 4. (a) The total and local DOS for UPtSn, (b) partial DOS for U, Pt and Sn sites, respectively. The inset in the uppermost panel of

(a) plotted in expanded scales shows the energy gap at the Fermi level.


4.2. UPtSn

As is evident from Fig. 4, the 5f band inUPtSn is partially occupied. The 5f band issplit by the spin–orbit interaction with anenergy gap of about 11.8meV, visible in the leftuppermost panel of Fig. 4. The occupied valenceband extending from about �5.5 eV to its toptaken as zero of energy is formed by thehybridization of the Pt and Sn d states, whichare dominating, with the Pt and Sn p states, andalso with the U f states as well as with a smallcontribution of s states.The DOS data in Fig. 4 and in Table 2

were calculated for the von Barth–Hedinexchange correlation potential [13]. The gapis of 11.3meV wide in the case of Perdew–Wangpotential [25], but vanishes if the Sn4delectrons are assumed to be a part of thecore. Also, no gap appears at all if the fullpotential approach instead of ASA is used, asdiscussed below.

5. Discussion

The band structure calculations indicate on acomplete filling of the valence band for ThPtSnand UPtSn or, perhaps, for all of the compoundsAPtSn studied by us. Unfortunately, the actualvalue of the gap between the occupied valenceband and the empty conduction band hasappeared to be sensitive to the assumptions madein implementing the local density functional theory(Table 2). Energy gaps calculated using the vonBarth and Hedin [13] or the Perdew et al. [23]exchange-correlation potentials are quite different.The gap appears also to be sensitive to the choiceof an initial atomic configuration of Sn atoms, i.e.they are different if all the ten 4d electrons of Snare included either to ‘‘core’’ or to ‘‘valence band’’.The sensitivity of the energy gap at the top of

the valence band to the details of the TB-LMTO-ASA method chosen for the band structurecalculation was the reason for undertaking com-putations by a different implementation of the

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Table 2

Numbers of occupied states: partial (s, p, d, f), local (A, Pt, Sn) and their sums

APtSn A Pt Sn Total

s p d fP(s, p, d, f) s p d f

P(s, p, d, f) s p d f

P(s, p, d, f)

P(A, Pt, Sn)

ThPtSn 0.474 6.067 2.125 0.717 9.383 0.852 0.743 8.224 0.045 9.864 1.615 2.794 10.195 0.149 14.753 34.000

UPtSn 0.477 6.063 1.895 3.085 11.520 0.927 0.776 8.181 0.069 9.953 1.572 2.625 10.180 0.150 14.527 36.000

0

0.4

0.8

1.2

UPtSn

U(6

p 1/2

) Sn(

4d3/

2)

0

0.4

0.8

-25 -20 -15 -10 -5 0

←U(6p)

←Pt

←

Sn(4d)→

Binding energy [eV]

Inte

nsity

[arb

.uni

ts]

0

0.1

0.2

-5 0

total→

U(6

p 3/2

)Sn(

4d5/

2)

Sn(6s)

U

(a)

(b)

Fig. 5. The measured (a) and calculated (b) XPS for UPtSn. In

the inset the total intensity is shown together with the

contributions from U6d, Pt5d and Sn5d states, respectively.

0

3000

6000

9000

-1000 -750 -500 -250 0(a)

U(N

OV

)

Sn

(MN

N)

O(1

s)

Pt(

4p1/

2) Pt(

4p3/

2)

Sn

(3d

)

Sn

(3p

1/2)

Sn

(3p

3/2)

U(4

d3/

2)

U(4

d5/

2)

U(5

d)Pt(

4d)

U(5

p3/

2)

Pt(

5p)

Pt(

4f)

U(4f)

UPtSn

0

0.4

0.8

1.2

-80 -77 -74 -71 -68 -65

Pt(4f7/2)

Pt(4f5/2)

(b)

Inte

nsi

ty [

arb

. u

nit

s]

0

1500

3000

4500

-400 -390 -380(c)

sat.Isat.Isat.IIsat.II

U(4f5/2) U(4f7/2)

Binding energy [eV]

←

Fig. 6. (a) The XPS of UPtSn in the broad energy range, and

details of the spin–orbit split lines for Pt 4f (b), and U 4f (c).


general LDA treatment. To this end the fullpotential program LmtART 6.50 [24] has beenused for recalculating the band structure ofUPtSn. Unfortunately, no energy gap near theFermi level was found, irrespective of usingdifferent forms of the exchange-correlation poten-tial, taken from Refs. [13] or [23]. Instead, the totaldensity of states at the Fermi level,DOSðEFÞ ¼ 3:758 states/(eV � formula unit) (forthe exchange-correlation potential in the form ofRef. [13]) is pretty large. It gives, e.g., thetheoretical estimate of the electronic specific heatcoefficient gth ¼ 8:85mJ/K2mol, as compared tothe experimental value of 10mJ/K2mol. Also thereis a satisfactory agreement between the calculatedby the LmtART method splittings of the core andsemicore levels for UPtSn with the values found

from the measured XPS (see Fig. 6). Thecalculated splittings, compared with the measuredones (given in brackets) are as follows: U4f:11.02 eV (10.93 eV), Pt4d: 16.83 eV (16.81 eV);Pt4f: 3.56 eV (3.35 eV); Sn3d: 8.7 eV (8.35 eV);Sn4d: 1.07 eV (0.94 eV). The total, local and partialdensities of states calculated by the full potentialLmtART method show shifts of the energypositions of some of the DOS(E) features

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0

0.05

0.10

0.15

-20 -10 0

UPtSn

Sn(4d1/2)

U(6p1/2)

Pt(4d) U(5f)

Sn(5s)

Sn(4d3/2)

U(6p3/2)

Binding energy [eV]

Inte

nsity

[arb

.uni

ts]

Fig. 7. Theoretical X-ray photoemission spectrum of UPtSn

calculated by the LmtART method [24], as described in the text.


presented in Fig. 4. Consequently there are alsodifferences in the calculated photoemissionspectrum.Since some features of the theoretical XPS curve

of UPtSn calculated by the LmtART method (forfull potential version, using von Barth and Hedin[13] exchange-correlation potential with general-ized gradient corrections of Ref. [25]) differ fromthose obtained by TB-LMTO-ASA method, theLmtART result is presented in Fig. 7. As is evidentfrom this figure, the observed structure of thevalence band spectrum is rather better reproducedby this type of calculations. For example, thetheoretical position of the peak U6p3/2 in Fig. 7 isa bit closer to that found experimentally. TheSn4d3/2–Sn4d5/2 splitting is in reasonable agree-ment with experiment, as is also the case of thetheoretical figure for the U6p1/2–U6p3/2 splitting.Summing these observations up one can say incontrast to the experiment [1,2] that strongertheoretical arguments support rather the view thatthere is no gap near EF in the DOS(E) for UPtSn.However, this argumentation is opposed to thatpresented by Oppeneer et al. [7]. As they haveclaimed, the electronic structure calculations tak-ing into account, somewhat arbitrary fixedU ¼ 2 eV as an account of strong on site Coulombinteractions of the 5f electrons, quantitativelyexplained the gap appearance in UPtSn in theparamagnetic state. In effect, the 5f electron DOS

in this LDA+U approach yields a broad shape,with its maximum at 0.85 eV giving good agreementwith the experimental value reported by the authorsof Ref. [6]. The appearance of the differences invarious calculations described above needs that afurther similar studies of the MgAgAs-type com-pounds should be accomplished.Finally, calculations for UPtSn by the LmtART

method [24] have revealed that the lowest totalground state energy has a magnetic state with themagnetic moments of 1.35 on U, �0.039 on Pt,and�0.018 on Sn (in mB). The orbital moments are�2.17, �0.01, and �0.003 for U, Pt and Sn,respectively. It also appeared from this calculationthat the total energy of a non-magnetic state, withall the magnetic moments being suppressed, ishigher by dE ¼ 90meV per formula unit. Thestable magnetic ground state is then an antiferro-magnetic one but the exact type of the antiferro-magnetic ordering has not been determined by ourpresent calculations of the electronic structure.Since the experimental investigations [3] hint on apossibility of an antiferromagnetic ordering, anyconfirmation of such a ground state of UPtSnremains as an interesting challenge for a furtherinvestigation.In the forthcoming part II the electronic band

structure and XPS of the isostructural compounds(Ti,Zr,Hf)PtSn will be discussed. The valence bandspectra for all these compounds appear to benearly identical, not surprising for Ti, Zr and Hfhaving the same electronic configurations of theirouter atomic shells.

Acknowledgements

The research was supported by the KBN GrantNo. 2P03B 024 22. The band structure computa-tions were partly performed in the Supercomputerand Networking Centre (PCSS) in Pozna !n.

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