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Anomalous magnetic behavior of cerium in Ce2Sn5 and Ce3Sn7, two superstructures of CeSn3

Anomalous magnetic behavior of cerium in Ce2Sn5 and Ce3Sn7, two superstructures of CeSn3

ELSEVIER Journal of Magnetism and Magnetic Materials 132 (1994) 289-302 A journal of magnetism IH A EzJnatic materials Anomalous magnetic be...

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ELSEVIER

Journal

of Magnetism

and Magnetic

Materials

132 (1994) 289-302

A

journal of magnetism

IH A

EzJnatic materials

Anomalous magnetic behavior of cerium in Ce,Sn, and Ce,Sn,, two superstructures of CeSn, M Bonnet a, J.X. Boucherle a,‘, F Glvord by**2,F. Laplerre ‘, P LeJay ‘, J. Odin ‘, A.P. Muram d, J. Schwelzer a, A. Stunault a23 a Cl%, Dgpartement de Recherche Fondamentale sur la Matr&e Condensie, SPSMS, MDN, 85X, 38041 Grenoble Cedex, France, b Laboratowe

Louis Nkel, CNRS, 166X, 38042 Grenoble Cedex, France, ’ CRTBT, CNRS, 166X, 38042 Grenoble Cedex, France, d ILL, 156X, 38042 Grenoble Ceder, France

(Received 25 May 1993, m revised form 19 October 1993)

Abstract The two magnetic compounds Ce,Sn, and Ce,Sn, have very slmllar crystallographic structures They are both superstructures of CeSn, with two different cermm sites one, similar to the cermm site m CeSn,, 1s “non-magnetic” or m intermediate valence state, and the other carries a well-defined moment and dominates the magnetic properties at low temperatures Although their macroscopic magnetic propertles under the effect of an applied field look quite similar, the magnetic structures of the two compounds m zero field are totally different In fact, Ce,Sn, presents a modulated structure with moments of maximum value 1 3~~ ahgned along a, whereas Ce,Sn, IS an antlferromagnet with moments of only 0 36~~ parallel to c This difference cannot be attributed to different Crystal Electric Field effects, which, from melastlc neutron spectroscopy measurements, are found to be fairly close m the two compounds A strong amsotropy of the mterlomc exchange coupling 1s evidenced m both compounds from the magnetization curves and neutron data, wlthm a crystal field model Especially, m Ce3Sn7, a negative value 1s found for the c component of the exchange coefficient, leading to strong negative interactions when moments are aligned along c The effects of hybrldlzatlon of the cermm 4f-electron with the band electrons play an Important role m Ce,Sn, and Ce,Sn, In both compounds, besides the mtermedlate-valent behavior of cermm m the CeSn,-type site, Kondo effects are present on the magnetic cermm site, leading to an extra reduction of the cermm magnetic moments These hybrldlzatlon effects are also likely to be at the origin of the amsotropy of the exchange mteractlons and of the reslstlvlty

1. Introduction In

CeSn,,

* Correspondmg author 1 Member of C N R S staff ’ Present address CEA, Dhpartement mentale sur la Mat&e Condenske, Grenoble Cedex, France 3 Present address ESRF, 220X, France

the cermm-tm system, the compound which crystalhses m the AuCu, cubic

structure,

de Recherche FondaSPSMS, MDN, 85X, 38041 38043

0304-8853/94/$07 00 0 1994 Elsewer SSDI 0304-8853(93)E0601-8

Grenoble

Science

Cedex,

1s a Paul1 paramagnet

m which

well known to be m an intermediate [ll

The compounds

with a composition

Ce 1s

valent state richer

m

cermm than CeSn, are magnetic [2-41 Among them, the two closest ones, Ce,Sn, and Ce,Sn,,

B V All rights reserved

290

M Bonnet et al /Journal

of Magnetcsm and Magnetic Materials 132 (1994) 289-302

are very similar and play a particular role They still present some of the intermediate valent character of CeSn,, but they order magnetically below 2 9 and 5 1 K respectively [4] Then macroscopic magnetization curves are very similar [51 In particular, they show the same large amsotropy below and above then ordering temperatures for both compounds, the magnetization 1s the largest along a and the smallest along c Ce,Sn, and Ce,Sn, are superstructures of CeSn, [6] They can be described by a stackmg of the basic CeSn, cells along the b direction with ordered amsotroplc substltutlons of atoms m the (a, c> plane, resulting m both cases m an elongated orthorhomblc cell (Fig 1) Only the frequency of the substltutlons makes the difference between Ce,Sn, and Ce,Sn, An essential peculiarity of these two crystal structures 1s the exlstence of two different cermm sites the site Ce,, with 12 Sn neighbors, has the same environment as Ce m CeSn,, and the site Ce,,, m the substltutlon zone, is surrounded by 2 Ce and 10 Sn atoms This feature mainly entails the peculiar magnetic behavior of Ce,Sn, and Ce,Sn, A key experiment to understand this magnetic behavior was the determination of the magnetlzatlon densltles at low temperatures by polarized neutron diffraction [7] For each of the two compounds, the density maps show unambiguously that there 1s a coexistence of non-magnetic and magnetic cermm atoms the CeSn,-like Ce atoms (Ce, site) do not carry any magnetic moment, whereas all the magnetization 1s concentrated on the Ce atoms m the substltutlon zones (Ce,, site) The ratio of magnetic Ce among all Ce atoms is l/2 for Ce,Sn, and 2/3 for Ce,Sn The presence of these two types of cermm atoms has also been confirmed by the determmatlon of the magnetic structures at low temperatures using neutron scattering [81 The ordered magnetic moments are m both cases carried by the Ce,, atoms only Considering the slmllarltles of the crystal structures and the apparent analogy of the macroscopic magnetic properties of the two compounds, one would expect similar magnetic mteractlons Surpnsmgly, then magnetic structures are very different For Ce,Sn,, the structure 1s modulated along a (7 = (l/8,1,0)),

Ce2Sn5

Ce3Sn7

CeSn3

l Cell 0

Gel

0

Sn

Fig 1 (lattice 35 014 25 742 drawing

Crystallographic and Omagnetx structures of SeSn, parameter a = 4 7.21 A), Ce,Sn, (a = 4 559 4, b = A and c = 4 619 A) and Ce,Sn, (a = 4 524 A, b = .& and c = 4 610 & For Ce,Sn,, the ongm of the has been taken at (l/2 0 0)

the moments are parallel to a with a maximum value of 13~~ In contrast, m Ce,Sn,, the moments are parallel to c with a very small value of 0 36~~ only They are coupled ferromagnetically m the (a, c) planes and antlferromagnetlcally (T = 0) along b (Fig 1) The observed different spontaneous magnetization directions and the very different values of the magnetic moments are m complete contradlctlon with the expected similar magnetic interactions It was then considered worthwhile to have a closer look at some physical measurements which reflect the electronic and magnetic properties of the cermm atoms m these compounds All the experiments were performed on samples (powders as well as single crystals) extracted from the same Ce,Sn, or Ce,Sn, ingot The sample preparation

M Bonnet et al /Journal

of Magnetlsm and Magnetic Materials 132 (1994) 289-302

IS given m Ref [6] In view of a careful analysis of the differences which exist between the equlvalent cermm sites m the two compounds, we first describe the results of the low temperature specific heat and reslstlvlty measurements We then recall the varlatlons of the magnetlzatlons at low temperatures and those of the susceptlblhtles at high temperatures, both measured on single crystals In order to get a good insight on the Crystal Electric Field (CEF) of cermm atoms m both compounds, we report the results of crystal field excltatlons observed by inelastic neutron scattermg Finally, we propose and discuss a quantltatlve model which underlines the slmllarltles and the differences between Ce,Sn, and Ce,Sn,

2. Specific heat Specific heats were measured by an adiabatic method at the CRTBT (CNRS, Grenoble) on Ce,Sn, [9] and Ce,Sn, polycrystalhne samples Their thermal variations between 13 and 28 K (Fig 2) present the characterlstlc contrlbutlon of a magnetic phase transition The transition temperatures shown m more detail m Fig 3 are 2 92 K for Ce,Sn, and 5 07 K for Ce,Sn, These are the NCel temperatures previously found by magnetlzation measurements [4] In the case of Ce$n,, a small extra peak 1s observed around 2 9 K It 1s attributed to the presence of some Ce,Sn, phase m our sample Because of the very closely related structures of the three compounds CeSn,, Ce,Sn, and Ce,Sn,, impurities of the two superstructures are always present in CeSn, [lo], as well as impurities of Ce,Sn, in polycrystalline Ce,Sn, [ll] Linear corrections usmg the measured Ce,Sn, speclflc heat have been done, but without suppressmg completely the extra peak at 2 9 K on the corrected Ce,Sn, specific heat The behavior of the phase as an impurity 1s probably different from the behavior of the pure phase The best result 1s obtained for a mass concentration of 20% of Ce,Sn, The corrected Ce,Sn, specific heat 1s shown m Figs 2(b) and 3(b) (sohd lme) The measured speclflc heat 1s the sum of three contrlbutlons the lattice contrlbutlon pT3 (for

120

O I

10 I

I

291

20 I

100

E‘

30

I /.

60-

8

E 5 0

604O20

-

0 0

10

20

30

T WI

Rg 2 Thermal varlatlon of the specific heat C m Ce,Sn, (a) and Ce,Sn, (b) The sohd hne IS the speclfx heat of Ce,Sn, after correctlon of the Ce,Sn, contammatlon

T +Z 13,), the electronic contrlbutlon yT, and the magnetic contrlbutlon Away from the ordering temperature (T < T,/2 and T > 2T,), y and /? can be obtained from the linear part of the plot of C/T versus T2 Results are different above TN (Fig 4) and below TN (insets m Fig 4) Values of low temperature (It) and high temperature (ht) coefflclents are gathered m Table 1, as well as the Debye temperatures 8, deduced from & For comparison, values previously found by other authors on CeSn, [12,131 and Ce,Sn, [141 are also given The values of the low temperature coefflclents are not very slgmflcant because of the proxlmlty of the Nkel temperatures They have still been useful for the calculation of the low temperature entropy (see below) Our values of the high temperature coefflclents are very close to those of Dhar et al [14], who have also shown that a Schottky anomaly associated with a CEF sphttmg of 100 K or 150 K would not much affect these coefflclents The Debye temperatures are

292

M Bonnet et al /Journal

of Magnetwn and Magnetic Materials 132 (1994) 289-302

quite lower than m CeSn, the lowest 1s that of Ce,Sn,, the structure of which 1s the most dlfferent from that of CeSn, The high temperature electronic contrlbutlon m Ce,Sn, 1s very similar to that m CeSn, with a large y value charactenstic of Kondo or valence fluctuation compounds

[I51 The magnetic entropies have been calculated for the two compounds from then magnetic specific heats obtained after subtraction of the high temperature lattice and electronic contrlbutlons ylt and Pit were used for evaluating the contnbutlon below 1 3 K The magnitude of the magnetic entropy S, per mole of Ce, up to 20 K, 1s found

to be much smaller than the expected R In 2 for a doublet ground state it 1s around l/2 m Ce,Sn, and 2/3 m Ce,Sn, It confirms the polarized neutron result [7], mdlcatmg that only one of the two Ce sites contributes to the magnetic ordering The magnetic entropy per magnetic Ce (&/A, with A = l/2 for Ce,Sn, and A = 2/3 for Ce, Sn,) 1s shown m Fig 5 Saturation 1s obtained at N 0 82 R In 2 for Ce,Sn, and N 0 90 R In 2 for Ce,Sn, In both cases, there subsists a lack of entropy, which has to be attributed to a reduction of the Ce moments of the magnetic site Ce,, This reduction 1s larger for the compound Ce,Sn, which 1s the closest neighbor to the intermediate

./:.i., : /+ m r-l 04 Ce,Sn,

(a) Ce,Sn,

E‘

6

a,

ii4

3.

02

20

E u

l

=I’

LO 5 0

l

01 ’ 2345676

t











20),,,

1

2

3

T (W Fig 3 Ordermg temperature Ce,Sn, corrected for Ce,Sn,

4

5

2

6

3

4

5

6

7

6

T W)

TN m Ce,Sn, (a) and Ce,Sn, (b), from the thermal varlatlons of the specific heat C (sohd hne IS for contammatlon), the resrstwlty p along e (crosses are for dp/dT) and the susceptlblhty x along a

M Bonnet et al /Journal

of Magnetlsm and Magnetic Materials 132 (1994) 289-302

N

5

293

10

2 fn=06

cl6

2 ,o

04

5 o_ 2

02

z? iz

00 0

5

.

10

15

20

T W)

Fig 5 Magnetrc entropy S, per magnetic cermm versus temperature m Ce,Sn, and Ce,Sn, A IS the ratlo of magnetrc cermm per formula (A = l/2 for Ce,Sns and A = 2/3 for Ce,Sn,)

0

100

200

400

300

500

smooth m Ce,Sn,, whereas magnetic order appears more suddenly m Ce,Sn,

T2 (K’) Fig 4 C/T varlatlon versus T2 m Ce,Sn, (a) and Ce,Sn, (b) Insets show the low temperature varlatlons The straight lines (C/T = -y + fir’) gwe the y and p coefflclents

valent compound CeSn, The shapes of the magnetic entropy curves are also different the transltlon to the ordered magnetic state IS rather

Table 1 Electronic y and lattice p speclflc heat coefficients below (lt) and above (ht) the ordering temperature for Ce,Sns and Ce,Sn,, as well as thevalues pubhshed for CeSn, and Ce,Sns Bo IS the Debye temperature deduced from pht by the relation Pht = (12/5)7r4nR(l/0,)3, where n 1s the number of atoms per formula and R is the perfect gaz constant (R = 8320 mJ/mole K) Compound

YII (mJ/ mole Kz)

PI, (mJ/ mole K4)

CeSn3 [121 CeSn3 [13] Ce,Sn, Ce,Sn,

1141 [this work]

376

300

Ce,Sn,

[this work]

- 0

265

Yht

(mJ/ mole K2)

$J/ mole K4)

!I$

73 53

05 -

252 _

44 56

31 31

164 164

63

146

-0

3. Electrlcat resistivity Electrlcal reslstlvltles were measured on smgle crystals, at the CRTBT (CNRS, Grenoble) between 1 and 300 K, on Ce,Sn, and Ce,Sn,, and on the non-magnetic lsotype compounds La,%, and La,%, Measurements were performed usmg the four-probe ac techruque on small rods with the conventional method, and on platelets with the Van der Pauw method [16] Because of the crystal structures of these compounds, which involve cells piled up along the b direction, cleavages made it impossible to get rods along the b axis Only rods of N 0 3 mm’ m section and N 1 mm m length along a or c could be cut Platelets of N 0 5 mm width (measurements do not depend on the other dlmenslons) were obtained perpendicular to b Electric contacts, done with a sdver spray under argon atmosphere, were very difficult to achieve because of the strong tendency of these compounds for oxldatlon Preliminary experiments had shown the systematic presence of a drastic drop m the reslstlvlties at 3 7 K, due to the superconductlvlty of free tin m our samples This effect was ehmmated by performing the low temperature measurements m

M Bonnet et al /Journal

294

120

I

I

I

a

t

(a) Ce,Sn,

.

.

l

l

Ii

.*

c.

Lb

80

E 5a

of Magneturn and Magnetrc Matenals 132 (1994) 289-302

II a LapSn5 CeSn, LaSn,

40

-

-

_ _

0

80

60

5 a 1 a

40

20

0 0

100

200

300

400

T W)

Fig 6 Thermal variation of the resistlvlty p along different crystallographx axes m Ce,Sn, (a) and Ce,Sn, (b), m the lsomorphous La compound, as well as m CeSn, and LaSn,

a field of 0 04 T (the crltlcal field for tm 1s N 0 03 T at 1 K [17]) produced by a permanent magnet Because of the oxldatlon problems, because of cleavages that led to rods which are not very long compared to their section, and because also of the difficulty to measure precisely the distances between the contacts on the rods, the absolute values of the measured reslstlvltles should be considered with great caution However, It 1s very interesting to look at the shapes of their thermal variations m the two compounds In Fig 6(a) are reported the electrical reslstlvlties versus temperature measured on Ce,Sn, along a, c and on a platelet perpendicular to b The reslstlvltles measured on a platelet of La,Sn,, and, for comparison, on CeSn, and LaSn, [181 are drawn The variation observed for La,Sn, 1s very similar to those of CeSn, and LaSn,, with a room temperature value around 35 PR cm For

Ce,Sn,, the variation along a 1s also very similar, but along c the room-temperature value reaches 110 cm The curve obtained with the (a, c) platelet 1s between the two previous ones The detailed variation of the reslstlvlty along c at low temperatures 1s shown m Fig 3 it presents a smgularlty around 3 K, and the derivative dp/dT drops at 2 90 K correspondmg to the magnetic ordering temperature T, The equivalent measurements for Ce,Sn, and La&, are reported m Fig 6(b) The La,%, reslstlvlty exhibits quite a large value at room temperature (N 70 ~0 cm), even larger than those measured on Ce,Sn, along c or on the platelet The reslstlvltles measured on Ce,Sn, have thermal variations quite different from those of CeSn, or LaSn, Below 100 K, the values measured on the platelet are between those measured along c and a, as for Ce,Sn, The low temperature reslstlvlty (Fig 3) changes drastically around 5 K and the very sharp drop of dp/dT defines TN at 5 12 K Measured reslstlvltles are all very close to each other above 100 K They reach values between 60 and 70 @ cm at room temperature The magnetic contrlbutlon to the reslstlvlty pm can be determined by subtracting the reslstlvlty of a reference non-magnetic compound from the Ce-compound reastmlty, assuming that they have the same phonon and defect contrlbutlons The choice of the La-compound as reference 1s usual, but may be discussed as, for instance, m the case of La,Rh, [19], because of the non-lmeanty of its thermal variation near room temperature [20] Furthermore, as already pointed out, some of the absolute values we have measured are probably somewhat erroneous, but the general shape of the pm variations 1s not much affected by the various normahzatlons that can be done [11,191 Fig 7 shows the magnetic reslstlvltles obtained for Ce,Sn, and Ce,Sn, along a, and for CeSn, In the case of Ce,Sn,, the La&, contrlbutlon has been normalized to 60 kfi cm at room temperature CeSn, presents a monotonic variation that tends to saturate around 10 PQ cm above 200 K Such a behavior 1s usually observed m mtermedlate valent compounds (see for instance CeNl [21l

M Bonnet et al /Journal

295

of Magneturn and Magnetic Materials 132 (1994) 289-302

4. Magnetization

00

/ 0

200

100

300

T 6)

Fig 7 Magnetic reslstlvlty pM versus and along a m Ce,Sn, and Ce,Sn,

temperature

m CeSn3,

or CePd, [22]) The varlatlon obtained for Ce,Sn, exhlblts a well-defined maximum around 50 K The presence of a maximum 1s characterlstlc of Kondo-type compounds [23] Ce,Sn, behavior 1s intermediate between the two previous ones with a smooth maximum between 150 K and 300 K It 1s very similar to that of CeRu,Sl, [24], which 1s a magnetic compound but at the limit of the onset of magnetism In conclusion, these reslstlvlty measurements have evidenced an evolution of the behavior of Ce m these three compounds CeSn, presents a magnetic reslstlvlty typical of an intermediate valence compound For Ce,Sn7, the onset of the magnetic ordering on the Ce,, atoms at TN appears clearly and the magnetic reslstlvlty 1s characteristic of Kondo-type effects probably on these same Ce,, atoms For Ce,Sn,, the magnetic ordering settling 1s not as perceptible, the reslstlvlty variation being smoother The magnetic reslstlvlty 1s between those of an intermediate-valent compound and a Kondo-type one A very similar variation of the shape of the magnetic reslstlvltles has been observed m the system CeIn,Sn,_, [25] m which, substltutmg In to Sn changes the Ce state from intermediate valent (X = 0) to Kondotype (X = 1) The reslstlvlty obtained for x = 0 4 1s comparable to that of Ce,Sn, and that for x = 10 1s comparable to Ce,Sn,

Magnetization measurements were performed on single crystals m the temperature range 13300 K [5] Fields were applied along the three principal crystallographic directlons up to 7 T at the Louis N&e1 Laboratory (CNRS, Grenoble), and up to 18 T at the SNCI (Grenoble) The susceptlblhtles of Ce,Sn, and Ce,Sn,, measured along the a dlrectlon, exhibit a maximum (Fig 3), mdlcatmg an antiferromagnetic type of ordering below 2 9 and 5 1 K respectively The NCel temperatures are given by the mflexlon point Just before the maximum However, this maximum 1s sharper m Ce,Sn, The same kmd of difference between the two compounds was observed on their specific heats or on then reslstlvlties at the transition temperature No trace of Ce,Sn, impurity can be detected on the susceptlblhty of Ce,Sn, around 2 9 K this fact indicates that the single crystals are purer than the polycrystalline sample used for the speclflc heat measurements

-h

6

a;”

100

0

I

0



-x .

0

I

A

*

.

A

.

A .

.

.

a

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.

O-.

R

500x

o

0.

L

2 t

0

0

l

.*

I

0

100

0

100

(a)

I

I

Ce,Sn,

0

I

I

200

300

200

300

1

100

0

-I- W

Fig 8 Thermal varlatlon of the reciprocal susceptlbthtles x-l m Ce,Sn, (a) and Ce,Sn, (b), along the three prmclpal symmetry axes Crosses represent the values calculated wlthm our model

296

M

Bonnet et al /Journal

of Magnetrsm and Magnetic Materials 132 (1994) 289-302

Reciprocal susceptlb&y curves above the ordermg temperature and magnetization curves m the ordered state are shown m Figs 8 and 9 They are characterized by a large amsotropy up to room temperature For both compounds, the magnetization 1s the largest along a and the smallest along c At 13 K, no spontaneous magnetlzatlon 1s present m zero field but transitions with the applied field appear m the two compounds, at very low fields along the a direction, and m high fields along c (Fig 9) The magnetization curves look very similar m Ce,Sn, and Ce,Sn,, especially as concerns the amsotropy the magnetization 1s the largest along a for both compounds This fact 1s m agreement with the magnetic structure of Ce,Sn, It 1s m

I



20

.

* 15

apparent contradlctlon with that of Ce,Sn,, m which the spontaneous direction of the moments 1s found to be along c, and the moments (0 36~~) are much smaller than the measured magnetlzatlon The large observed amsotroples suggest that CEF effects on the Ce,, ions should play an important role Therefore, it was interesting to undertake a thorough comparison of the CEF effects m the two compounds by means of melastic neutron spectroscopy

5. Inelastic neutron scattering Inelastic neutron scattering experiments were performed to determine the sphttmg of the 4f’

9. a

(a) Ce,Sn,

T=l.3K

(b) Ce,Sn,

T=1.3K

.

10

.

05 /

00 00

40

2

10

l



.

no 30 m

40

30

0 2 c 20 9 fij Y

20

E 0) ‘0

10

1

1

2

00 1 00

00 10

2

00

50

100

150

20 0

Ha(7 Fig 9 Magnetlzatlon curves m the ordered state m CeaSnS (a) and Ce,Sn, (b), for fields apphed along symmetry axes Lmes are a guide for the eye and crosses represent the values calculated wlthm our model

the three

pnncipal

M Bonnet et al /Journal

of Magnetwm and Magnetic Materials 132 (1994) 289-302

ground state J multlplet m the presence of the Crystal Electric Field These experiments were carried out using the time-of-flight spectrometer IN4 at the ILL (Grenoble) with an incident neutron energy of 67 meV Spectra were collected at various temperatures from 10 K to 150 K, for scattering angles 28 ranging from 4” to 100” m order to follow the angular dependence of the magnetic as well as the phonon scattering Measurements m a high resolution mode were necessary for a good separation of all the peaks For Ce,Sn,, the samples were small single crystalline blocks extracted from the ingot close to the prevlous single crystals, and the absence of Ce,Sn, impurities has been checked by low temperature susceptlblhty measurements The spectral responses exhibit two mam peaks (Fig 10) A third peak, much broader and spreaded, 1s also observed centered on 40 meV, especially m Ce,Sn, It may be attributed to the Ce, (CeSn,-type site) contnbutlon, as observed m CeSn, [26], but it 1s difficult to evaluate its quantitative contrlbutlon m the present experiment The measured spectra were corrected by a standard procedure [26] using spectra obtained for vanadium, cadmium and an empty sample holder The phonon contrlbutlon was also corrected for, using the measurements obtained on the lsomorphous La-compounds which gave mformation on the evolution of the phonons as function of energy and scattering angle From the high scattering angle spectra collected on the Ce-compounds and using the variation between high and low angles found m the La-compounds, it 1s possible to deduce the low scattering angle contrlbutlon of phonons m the Ce-compounds Fig 10 shows the corrected spectral responses obtained for Ce,Sn, and Ce,Sn, at 28 = 12 6 andat T=lOK The comparison between the spectra obtained at various temperatures and various scattering angles allows the ldentlflcatlon of the two welldefined peaks as magnetic peaks In fact, m the orthorhomblc symmetry, the ground Ce multlplet J = 5/2 is decomposed by the CEF mto 3 doublets, leading to two possible transitions at 10 K The positions of the peaks represent the energy transfers from the ground doublet to the two

297

excited ones These are AE, = 5 5 meV (64 K) and AE, = 13 6 meV (159 K) for Ce,Sn,, and AE, = 6 4 meV (74 K) and AE, = 13 8 meV (161 K) for Ce,Sn, The detailed explanations for the spectral fits are given m Section 6 Although the relative intensities of the two peaks are different m the two compounds, the CEF effects are very close, as could be expected from the slmllarlty of their crystallographic structures and of their magnetizations The CEF effects cannot explain the difference m the spontaneous Ce moment dlrectlons Other effects, such as amsotroplc exchange mteractlons, are then to be considered to account for the peculiar behavlour of Ce,Sn,

8, -

6-

II

-10

8 , G5

6-

-10

I

1

(4 Ce,Sn,

1

I

I

I

I ”

T=lOK

0

10

20

30

40

I,

I

I

I

I

30

40

1

I

!

t

0

(W

10

Ce,Sn,

20

Energy Transfer (meV) Fig 10 Magnetic spectral response obtamed at 10 K, for an Incident energy of 67 meV at 6 = 12 6”, m Ce*Sn, (a) and Ce$n, (b) Solid hnes are calculated wlthm our model and dotted hnes represent separately the contrlbutlons of the two magnetic and the quasIelastIc peaks The long dashed hne 1s a gmde for the eye representmg the elastic peak

298

M Bonnet et al /Journal

6. Quantitative

of Magnetwn and Magnettc Materials 132 (1994) 289-302

model: analysis and results

The magnetic behavior of the Ce,, atoms 1s essentially entailed by the CEF and the exchange mteractlons acting on these ions On the one hand, the inelastic neutron results obtained at 10 K provide mformatlon on the CEF scheme, but these experiments do not allow a unique determlnation of the CEF parameters because of the large number of parameters involved On the other hand, magnetization and susceptlblhty are the sum of two contrlbutlons due to the Ce, and Ce,, atoms The Ce, magnetization 1s unknown but should be close to that of CeSn,, almost constant up to 300 K The Ce,, magnetization 1s related to the CEF and exchange parameters Above 150 K, the Ce, contrlbutlon 1s not neghglble compared to that for the Ce,,, whereas at low temperatures (below 50 K), the Ce,, contrlbutlon 1s at least one order of magnitude larger than the Ce, one Below 50 K, we can then use the CeSn, magnetization values for the Ce, contrlbutlon and deduce the Ce,, magnetization These two types of measurements, neutron spectroscopy and magnetization, were combined to refine the CEF and exchange parameters m Ce,Sn, and Ce,Sn, A least square method was used The evaluation of the exchange contrlbutlon to the Hamlltoman was done by a self-consistent calculation with convergence on the values of the three components of the magnetic moment 6

1

represents the Zeeman couplmg between the 4f magnetic moment and the applied magnetic field H (external field corrected for demagnetization effects) XB = -M

H,, = -gJpBJ

He,

1s the Helsenberg-type bilinear interaction Hamlltoman written m the mean field approxlmatlon as a function of the exchange field He, The last term i (M > He, 1s for not counting twice the same interaction energy m the total energy of the spm system In the paramagnetlc region, or at sufflclently high applied magnetic fields m the ordered state, the exchange field writes H,, = nM = ng,pB( J>, where n 1s the bilinear exchange parameter, representing the sum of all mteractlons We have been led to assume amsotroplc bilinear couplmgs to explain the discrepancy between magnetic structure and CEF effects m Ce,Sn, The components of the exchange field can then be written as

fG=n,g,~B(Jx), H,Y= n,m+(J,),

HA = n,gJpB(Jz)

Higher order couplmgs, such as magnetoelastlc or two-ion quadrupolar lpteractlons, have been neglected 6 2 Results

Model

The Hamiltonian describing the magnetic properties of the Ce,, 4f shell writes as He, X = zCEF +~z+ZB+~ where XcEF 1s the CEF term In the orthorhomblc symmetry of the Ce,, sites it can be expressed as

where the 0;“are the Stevens operators, Vfm the CEF parameters and (Ye, pJ the Stevens coefficients (rJ = 0 for J = 5/2) [271 &?z = -M H = -gJpBJ H

The saturation magnetlzatlons per Cell atom at 1 3 K, obtained by subtracting a Ce, contnbutlon equal to the CeSn, magnetization from the value measured along a, 1s 158~~ m Ce,Sn, and in Ce,Sn, These values are reduced 186P, compared to the value of the free Ce3+ ion (gJ/-+ = 2 14/+J The five CEF Vnm parameters have been obtamed by fitting together the melastlc neutron scattering spectra and the Cell magnetlzatlons along the three dlrectlons a, b and c, below 50 K and m high fields The neutron spectra are calculated with the CEF parameters taking into account various possible shapes of the magnetic excitation lines (Lorentzlan or Gaussian-type)

M Bonnet et al /Journal

of Magnetwn and Magnetic Materials 132 (1994) 289-302

with half-width r/2 and a quasielastic scattering with half-width r,/2, describing the fluctuations m the ground state level The magnetlzatlon data are strongly connected to the exchange parameters The a direction was taken as the quantifying direction for all the calculations Both cases, with lsotroplc or amsotroplc exchange mteractlons, have been tested for the two compounds No satisfactory solution could be obtained unless a moment reduction factor k of Kondo-type [28] was introduced This factor should tend towards one as the Kondo effect 1s softened by apphcatlon of a magnetic field However, there 1s no simple way to take this field variation mto account Results were consistent enough with the same reduction factor for all the types of measurements The best solution was found with amsotroplc exchange mteractlons m Ce,Sn, as well as m Ce,Sn, Results are summarized m Table 2, and calculated points used for the fits are reported m Fig 10 (solid line) for the neutron spectra and m Figs 8 and 9 (crosses) for the magnetization data Two other sets of CEF parameters can lead to close values of the total agreement factor, with similar fits of the neutron spectra, but then agreement with the magnetization measurements m Ce,Sn, 1s not as good 6 3 Analyszs of the results As could be predicted from the similar melastic spectra m the two compounds, as well as from their similar crystallographic structures, the CEF

299

parameters are very close m Ce,Sn, and Ce,Sn, Especially, with these parameters, the easy magnetization direction m absence of exchange mteractions 1s a for both compounds However, the line shapes of the CEF spectra appear to be different fits are better with Lorentzlans m Ce,Sn, and with Gausslans m Ce$n,, and the quaslelastlc peak 1s broader m Ce,Sn, These two features are coherent [29] with the fact that Ce,Sn, contains a larger proportion of Ce, to Ce,, atoms (l/2), and that the magnetic behavior of the Ce,, atoms m Ce,Sn, presents a stronger Kondo couplmg or hybrldlzatlon than m Ce,Sn, This IS also confirmed by the values of the Ce,, moment reduction k the moment 1s reduced more m Ce,Sn, than m Ce,Sn, Amsotroplc exchange mteractlons are found m both compounds Interactions are stronger along the b direction, and besides, negative mteractlons appear along c m Ce,Sn, The values given m Table 2 correspond to calculations m which all the Ce,, moments were assumed to be equivalent and represent the sum of all the mteractlons In Ce3Sn7, a negative value for n, thus means that, for moments aligned along c, negative mteractions are preponderant and can lead to an antiferromagnetic structure However, to describe this structure, it 1s necessary to introduce other exchange parameters nb, ((Y= a, b or c) instead of n,, which take mto account the fact that the Ce,, site 1s divided mto two sublattlces ferromagnetic (a, b) planes coupled antlferromagnetlcally along c (Fig 1) If A,, represents the mteractlons mslde the plane and A,, the mteractlons

Table 2 CEF V,” and paramagnetlc exchange parameters n, b,c in Ce&s and Ce-,Sn, For the neutron spectra hne shape (L = Lorentzlan and G = GaussIan) and halfwldth r/2 of the excitation hnes, and r,/2 of the quaslelastlc contrlbutlon k IS the moment reduction factor and X2 the agreement factor (X2 = (&p,(Ipb” - I, ca’c12)/(N - K) with p, = l/u,‘, N = number of data and K = number of parameters) Compound

CEF parameters v;

Ce,Sn,

Ce,Sn,

132 (1) 141 (2)

Neutron spectra parameters (meV)

(K)

v;

v4O ::,

-18 (7)

::, 20 (1)

v4

vb’

Shape

-87

-115

L

(9) -63 (9)

(3) -113 (4)

G

r/2

Exchange parameters rO/2

170

48

(0 11)

(11)

179 (0 04)

73 (0 7)

k

X2

(T/&

na

nb

137 (0 12)

40 (0 8)

“c

23 (2 6)

0789 (0 003)

17

156 (009)

-33 (3 3)

0 905 (0 004)

11

(:47)

M Bonnet et al /Journal

300

of Magnetrsm and Magnetrc Materials 132 (1994) 289-302

between the planes, the exchange parameters nh m zero field can be written [30] n’=A -A Aa, whereas n, = A,, + A,, a A vke of .’ has been estimated from the value of the mo’ment along c measured m the magnetic structure determination (0 36~~) A value of nb 1s deduced from the transition m a very low field applied along a m 0 1 T, the structure changes from the antlferromagnet with moments along c to a ferromagnet with moments along a A limit for n6 1s given by the fact that the free energy has to be the smallest along c Values of 12, and n; for Ce,Sn,, as well as the deduced h,, and h,, along the three dlrectlons, are given m Table 3 Interactions between the ferromagnetic planes are in fact strongly negative for moments along c They induce the observed antiferromagnetic structure By using the CEF and exchange parameters of Table 2, one can calculate the Ce,, susceptlblhties above 150 K By subtracting them from the measured susceptlblhtles, one can get an estlmatlon of the Ce, susceptlblhtles Results are drawn m Fig 11 for Ce,Sn, and Ce,Sn,, and compared to the CeSn, susceptlblhty [lo] In Ce,Sn,, the Ce, susceptlblhty 1s almost the same along the three directions, and 1s very close to that of CeSn, In Ce$n,, an amsotropy of the Ce, susceptlblhty appears although the error bars are quite large, the Ce, susceptlblhty 1s the largest along a and the smallest along c, showing the same amsotropy as the Ce,, susceptlblhty This difference m the Ce, susceptlblhtles m Ce,Sn, and m Ce,Sn, can be attributed to a difference m the mteractlons between Ce,, and Ce, atoms Although then crystallographic structures are very similar, the difference (Fig 1) lies m the dlsTable 3 Ce,Sn, amsotroplc state na and m the mteractlons m the planes A,, ((Y = a, AXIS

exchange parameters m the paramagnetlc antlferromagnetlc state n:, and deduced ferromagnetic planes A,, and between b or c)

(T//-d

; c

156 71 -33

,

I

I

i=

_2

10

100

I

(a)

150 I (b)

x

I

1

I

Ce,Sn,

:

200

250

300

I

I

I

Ce,Sn,

%

I 350

l

a

A

b

1 0

I

100

150

I

I

I

200

250

300

350

T W Fig 11 Calculated thermal varlatlon of the susceptlblhty x of the Ce,-type atoms m Ce,Sn, (a) and Ce,Sn, (b), along the a, b and c axes The sohd hne represents the measured CeSn, susceptlblhty [lo]

tances between the pairs of Ce,,-(a, c) planes surrounding the Ce, sites and m the ratio of number of Ce, to Ce,, atoms The Ce, atoms are more numerous m Ce,Sn, than m Ce,Sn,, and especially, one complete CeSn,-type cell is still present m Ce,Sn, The Ce,,-Ce, mteractlons which are negligible m Ce,Sn,, can be strong enough m Ce,Sn, to transmit the amsotropy of the Ce,, to the Ce, susceptlblhty However, the precision on our Ce, susceptlblhty values, obtamed from differences, 1s not good enough to give a quantitative estimation of this Ce,,-Ce, magnetic interaction

7. Discussion

and concluslon

(T/id ,

n,

10

n,

0 85 <112 13 0

h Fo

1 20 < 9 45 4 85

A Aa

0 36 >-175 -8 15

In the two compounds Ce,Sn, and Ce,Sn,, which are both superstructures of the basic compound CeSn,, there is a coexistence of two types of cermm atoms located on two different sites

M Bonnet et al /Journal

of Magneturn and Magnetrc Materials 132 (1994) 289-302

the same mtermedlate valent cermm as m CeSn,, and a magnetic cermm m the substltutlon zones, leading to magnetic ordering at low temperatures Hybridization of the Ce4f electron with the non-f band electrons, 1s at the orlgm of the mtermediate valence behavior of CeSn, It results m a quite characteristic magnetic susceptlblhty m this compound its thermal variation 1s almost constant, with a broad maximum around 135 K [lo], at low temperatures, Its value 1s much smaller than that of a paramagnetlc atom, but rather large for a non-magnetic compound A very slmllar susceptibility 1s found for the cermm atoms of the CeSn,-type site m Ce,Sn, and Ce,Sn, However, there are slight changes m the case of Ce3Sn7, and, m particular, anisotropy effects This difference should be related to the difference m the crystallographic structures of the two compounds, especially to the number of magnetic and non-magnetic cermm atoms around these sites The magnetic behavior of the two compounds at low temperatures 1s essentially related to that of the cermm atoms m the substitution zones For this site, magnetic properties are characterized by a competltlon between the effects of the Crystal Electric Field and anisotropic exchange mteractlons From the neutron spectroscopy experiment, it 1s clear that the CEF 1s very similar for both compositions The anisotropy due to the CEF 1s very large and implies the largest value of the moments along a and the smallest along c On the contrary, the amsotropy of the exchange mteractlon 1s different m the two compounds In Ce3Sn7, a negative value for the c component imposes an antiferromagnetic structure with a spontaneous direction of the moments along c The moment 1s then reduced to 0 36~~ only A similar situation has already been found by Bonvllle et al [31] m YbNdn, where the dlrectlon of the spontaneous magnetization 1s also imposed by amsotroplc exchange mteractlons and the value of the moment is reduced because of the CEF effects The origin of the strong exchange amsotropy 1s attributed to the hybridization of the Ce-4f electron with the band electrons, which leads to unusual anisotropic magnetic ordering [32] This

301

effect 1s particularly striking here, because of the differences observed m the magnetic structures of Ce,Sn, and Ce,Sn, These hybrldlzatlon effects are also responslble for Kondo-type behavior of the magnetic cermm atoms m both compounds Such behavior 1s evidenced by all the different types of measurements reported here, as well as Its evolution when gomg from the Ce,Sn, compound to Ce,Sn, The amsotropy observed m the reslstlvlty measurements confirms the important effects of the hybrldlzatlon effects [33] Moreover, It has been necessary to introduce an extra-reduction factor k of the cermm moments, besides the reduction due to the CEF effects This extra-reduction 1s larger for Ce,Sn, (k = 0 79) than for Ce,Sn, (k = 0 91), showing the decrease of the hybrldlzatlon effects as the cermm content 1s Increased The values of k are m total agreement with the reduction found on the magnetic entropies 0 82 for Ce,Sn, and 0 90 for Ce,Sn, As a general feature, as concerns both types of cermm, this evolution 1s confirmed by the decrease of the electromc term y of the specific heat from CeSn, to Ce,Sn, Finally, as shown m Fig 3 by the shapes of the specific heats, the reslstlvltles and the susceptlblhtles at the ordermg temperatures, the magnetic character of Ce,Sn, 1s much less pronounced than that of Ce,Sn, In conclusion, due to the existence of the closely related structures of CeSn,, Ce,Sn, and Ce&,, it has been possible to study the evolution of the hybrldlzatlon effects m the Ce-Sn system As the magnitude of the hybrldlzatlon decreases from CeSn, to Ce$n,, the magnetic character of the compound 1s enhanced, as usually expected Simultaneously, increasing amsotroplc exchange mteractlons have also been evldented, a property which 1s not so commonly observed

Acknowledgements

The authors wish to thank P Haen for fruitful dlscusslons and G Fllhon for his constant mterest m this study

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of Magnetwn and Magnetrc Materials 132 (1994) 289-302

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