CeSn3_xlnx and Celn3

T T4!cesn3T42 K

3.1.3. CeSn3_xlnx and Celn3

In connection with CeSn3 we will also discuss the experiments performed on the intermetallic alloys CeSn3_xInx. Whereas CeSn3 has weak VF properties, CeIn3 behaves as a K o n d o or H F compound. There have been extensive investigations of the magnetic properties (Lawrence 1979, Dijkman et al. 1980), heat capacity, and resistivity (Elenbaas et al. 1980). Some of the results of the different authors are collected in fig. 43, showing the evolution of a characteristic temperature T~ [as defined by Lawrence (1979) through the scaling behavior of the effective moment

ffz= Tz/C

by the condition /j2(T~)= 0.5"] and of Tma x [the temperature of the maximum in z(T)]. Also shown is the evolution of the linear coefficient 7 of the specific heat and the x-dependence of the antiferromagnetic ordering temperature TN for the In-rich side. Three distinct concentration regimes seem to exist:

(1) (0 ~< x ~< 1): the characteristic temperature T~ and Tm,x decrease almost linearly with increasing x, accompanied by a linear increase of 7,

(2) (1 ~< x ~< 2.6): ? peaks around x ~ 1; then there is a steady decrease of 7 with x and a nearly constant characteristic temperature (with minor variations due to alloying effects, as also found in LaSn 3 xIn~); in the first two regimes no long-range magnetic ordering has been found,

44 M. LOEWENHAUPT and K.H. FISCHER

(3) (2.6 ~< x ~< 3): 7 and T(~ stay constant with x; long-range antiferromagnetic order appears, with TN steeply increasing with x; TN = 10 K for CeIn3.

Neutron scattering investigations have been performed mainly in the first regime and for CeIn 3. We discuss first the results of inelastic magnetic scattering. Murani (1987a, b) has shown that the position A of the hump in the low-temperature spectra moves towards smaller values for increasing x (up to x = 1), in line with the decrease of T~ and T~ax (large, open circles in fig. 43). Let us remind that the hump in CeSn3 is at an energy around 45 meV, corresponding to 522 K. This is 3.7 times T~nax or 2.6 times T~. The hump position decreases to A = (18 _+ 2), (13 _+ 1), and (9 _+ 1) meV for x = 0.5, 0.75, and 1, respectively (Murani 1987a, b). This corresponds to roughly three times Tma x. Hence there seems to be a scaling relation between the position of the hump and Tmax, the temperature where )~(T) has a maximum. In addition to the reduction of the hump position Murani (1987a, b) claims that there is also a reduction of quasi-elastic intensity for increasing x. An experiment performed on a CeSn2In single crystal at T = 5 K by Murani et al. (1990a) reveals only an inelastic line of Lorentzian shape with A = (8 _+ 1) meV and ½F = (7 _ 1) meV and no quasi-elastic scattering. The value of A as deduced from the single crystal experiment, is consistent within error with the value given above for the polycrystalline sample for x = 1. The magnetic response of the single crystal was measured at different Q values. The shape of the magnetic response seemed to be independent of Q. There was, however, a slight Q dependence of the intensities, indicating the possible presence of short-range spin correlations. Temperature-dependent measurements on all samples showed the characteristic evolution of the inelastic features into a broad quasi-elastic response at elevated temperatures as usually observed for VF compounds.

Murani (1987b) also observed a change from inelastic to quasi-elastic scattering already of the low-temperature response when going from concentrated CeSn2.25- Ino.Ts to dilute Cel yLaySn2.zsIn0.75 with y = 0.2 and 0.4. Whether this change of line shape is caused by the loss of periodicity in the dilute Ce lattice or by a reduction of the K o n d o temperature for Ce ions surrounded by La ions (connected with a shift of intensity towards lower energy transfers) is not yet clear.

Preliminary inelastic neutron data for the 2 F 5 / 2 __+

2F7/2

spin-orbit transition in CeSn3 xIn~, obtained with high incident-neutron energies of 600 meV on the H E T spectrometer of the ISIS spallation source by Murani et al. (1990b), are shown in fig. 44. The energy of the spin-orbit transition for a free Ce ion is 280 meV (see Osborn et al. 1991). An inelastic transition with about this splitting is observed for x = 1 to 3 (CeSnzIn up to CeIn3). F o r x = 0.5 there is still an inelastic transition visible, although already considerably broadened and shifted to higher energies (315 meV). In addition, a tail on the low-energy side is developing for increasing Sn concentration. This is reminiscent of the broad magnetic scattering within the J = I ground-state multiplet. F o r CeSn3 the tail is the only observed scattering intensity. No inelastic line seems visible. It is not clear whether the spin-orbit transition is totally absent in CeSn3 or whether it is present but even further broadened or shifted and is thus lost in the statistical scatter of the data.

F o r m factor measurements have been performed on CeSn2In (Benoit et al. 1985) and CeIn 3 (Boucherle et al. 1983, Boucherle and Schweizer 1985). In contrast to

V F A N D H F 4f S Y S T E M S 45

2 c 0

> , L

.~ -2 8 -g 03 6

2 0 -2

' l ' • . . . . • ~ '

CeSn 3 × In x = 3.0 Celn 3

_t t CeSn 3

i I i

i _ 1

• ~ . ~ k 1 , i h J -2

h ' i , T ~ - - I '

4 L x = 1.0 ~,~, CeSn 2In

- 2

4 [ ~ x = 0 . 5 l

0

-2 , ] , _._.J , I ~ J

100 200 300 400 500 100 200 300 400 500

ENERGY TRANSFER (meV) ENERGY TRANSFER (meV)

Fig. 44. S p i n - o r b i t transition in CeSn 3 ~In~ m e a s u r e d at 7 ' = 20 K with E0 = 600 meV on the H E T spectrometer (redrawn from M u r a n i et al. 1990b).

0.10 | , I - - ~ - -

~

- CelnSn 2 T = 5.5 K - 0.08 ~-- H = 4 . 6 T - -

-

O ~ e l

o e l

0.06

o - ~ " 4 ~

~

^{0.04 -}

0.02

a

0 ~ I , I

0.2 0.4 0.6

sin e / X (,&-~)

0.10 I ' I ' I '

C e l n S n 2 T = 7 5 K

0 . 0 8 H = 4 . 6 T

g

0.06 §

20.04 ~

0,02

0 L ~ I , I

0.2 0.4

sin 0 / X (•--1)

Fig. 45. Magnetic form factor of C e S n 2 I n at T - 5 . 5 and 7 5 K . Solid line is 4f form factor for free Ce ion. Mag- netic susceptibility measure- m e n t d a t a on the same sample have been added at sin 0/2 = 0.6 0. N u m b e r s indicate Bragg

indices (Bcnoit et al. 1985).

CeSn3 there is no

significant

5d-like contribution at low temperatures for both compounds. Data taken at 5.5 and 75 K on a CeSnzIn single crystal can be fitted essentially with a 4f form factor (solid line in fig. 45). There is a slight deviation from this line of the data point for the (001) reflection (within error bars for T = 75 K, just outside error bars for T = 5.5 K). This corresponds to a 5d contribution of at most 10% to the total magnetization density. There is also only a small upturn in the susceptibility at low temperatures measured on the same sample. N o anisotropies of the form factor due to crystal field effects have been reported. The same isotropic behavior was found for CeSn3 and CePd3, indicating that all six levels of the 2 F5/2

46 M . L O E W E N H A U P T a n d K . H . F I S C H E R

0.12 0,10

g

"~ 0.08 o 0.06 0,04 :::L

0.02

' V ~ - ~ - I ' - r - - F

c C e l n 3 T = 1.8 K

= oo

~, e 9 ^-

- ~ ~ " " g ~ ~ -

",, , , ~ o g -

" ' . ~ g ~ ' 7. g©

- ~ ~ . o a ~ ~

, I ,_ I , I " ~ ~ I ~ } , 0.2 0,4 0.6 0.8

sin e / k (~-1)

1.0

Fig. 46. Magnetic form factor for Celn 3 at T = 1.8 K in the magnetically ordered phase. Solid circles: data points, open circles: calculated with I' 7 ground-state wave function.

Dashed and solid line: upper and lower boundary for aniso- tropy. Numbers indicate Bragg indices (Boucherle and Schweizer 1985).

multiplet are involved in the formation of the ground-state wave function. This is not the case for Celn3. Although Celn3 cannot be considered as a "normal" rare earth compound, it is definitely different from CeSn3. There are signatures in Celn3 that its ground state is split by the cubic crystal field into a low-lying /77 and an excited Fs level around 10 15 meV. The form factor measured in the magnetically ordered state at 1.8 K is strongly anisotropic (fig. 46). All (h00) reflections lie above and all

(Okk)

reflections lie below the average 4f form factor. This is what one expects from a F7 crystal field ground state (the opposite anisotropy is expected for a /'8 ground state or isotropic behavior for the full J = 2 s multiplet). This interpretation is strongly supported by the fact that the magnetic entropy per mol Ce is close to R l n 2 at the ordering temperature (Elenbaas et al. 1980), as expected for a F7 (doublet), in contrast to R in 4 for £8 (quartet) or R In 6 for the full multiplet. F r o m the slight discrepancy between the calculated and measured form factor for the two low-Q reflections (111) and (200), Boucherle et al. (1983) estimate an additional 5d contribution of 18% to the total magnetization density in Celn3. N o error is quoted for this estimate, but the error must be rather large, since it relies on discrepancies for reflections where the 5d contribution is already very weak. No data are given for the more decisive reflections (001) and (011). These reflections are rather weak and thus difficult to be measured, because the nuclear scattering lengths of Ce and In are nearly equal. We are also not aware of any form factor measurements at elevated temperatures, which could give information whether the 5d contribution is still present or not.

The magnetic structure of Celna has been determined by Lawrence and Shapiro (1980) and by Benoit et al. (1980). Celn 3 is a simple antiferromagnet with propagation

~! ! !~ i.e. the Ce moments are aligned in opposite directions in adjacent vector ~,2, 27 217

(111) planes. The spin directions within the planes could not be determined from the experiments. Lawrence and Shapiro (1980) report for the Ce moments a value of (0.65 4- 0.1)#B at T = 5 K, Benoit et al. (1980) a value of (0.48 +_ 0.08)#B at T = 3 K.

Both values are somewhat smaller t h a n the expected 0.71#B for a F v state. Lawrence and Shapiro (1980) also investigated the critical scattering around TN = 10.2 K. They observed a strong suppression of critical fluctuations and nearly mean-field behavior.

Finally, we discuss the inelastic magnetic response of CeIn3. The F 7 --+ F s crystal

VF A N D H F 4f SYSTEMS 47

field transition was measured by Lawrence and Shapiro (1980) as function of temper- ature. They observed a rather broad inelastic line at 15 meV with a width of about 10 meV at low temperatures (5 K, 15 K), shifting to 11-12 meV at elevated temper- atures (50 K, 160 K). The width of the crystal field transition was originally interpre- ted by Lawrence and Shapiro (1980) as a measure of a spin-fluctuation energy kB Tsv with TsF ~_ 100 K. This value, however, seems to be much too high for Celn 3. The quasi-elastic scattering, which could not be resolved in the experiments by Lawrence and Shapiro (1980), was measured by Lassailly et al. (1985) with better energy resolution at T = 60, 140, and 240 K. The width and the intensity of the quasi-elastic line are strongly Q-dependent and temperature dependent. This behavior suggests that spin-spin correlations are the main origin for the spin dynamics and that line broadening due to hybridization effects is of minor importance in CeIn3. The Q- dependence of the intensity is strongest for T = 60 K; it is still observed at 140 and 240 K, although much weaker for increasing temperatures. The Q-dependence of the line width is indicative of spin diffusion processes. A typical value for the line width in the region around 1-2 N - 1 is 1 meV at T - - 60 K and 2 3 meV at T = 140, 240 K.

The value of 1 meV at 6 0 K is of the same order as kBTN (10.2K~-0.9meV).

Unfortunately there are no data for the quasi-elastic scattering below 60 K, which might allow to extract a residual width due to K o n d o broadening in comparison to spin spin interactions. F r o m the data of Lassailly et al. (1985) we can estimate an upper limit for the K o n d o temperature of CeIn3 of TK ~< 10 K. The increase of the line width with temperature can be understood from the increasing contribution from the F 8 excited state to the quasi-elastic scattering. The quasi-elastic scattering within the F 8 level must be considerably broader than that within the F7 level. This is in line with the observation of the rather large line width of the FT-Fs crystal field transition. The quasi-elastic scattering is always separated from the inelastic scatter- ing. Lassailly et al. (1985) report a value of 10 meV for the energy of the crystal field transition, in agreement with the findings of Lawrence and Shapiro (1980). In addi- tion, Lassailly et al. (1985) claim that they have observed a second inelastic magnetic line around 20-25 meV. We feel, however, that this line is not of magnetic origin but most likely due to an improper subtraction of p h o n o n scattering. It should be noted that In is a strong neutron absorber, which makes all experiments with In-containing samples rather difficult.

3.1.4. CeBe13

While CePd3 and CeSn 3 have been studied very thoroughly over the past 15 years, there are only few data available for CeBe13, although it exhibits similar magnetic properties. CeBel3 was classified as VF compound quite early with an (over-esti- mated) valence of 3.2--3.3 from lattice parameter systematics (Borsa and Olcese 1973, Krill et al. 1980). New estimates of the valence from Lm X-ray absorption give 3.04 (R6hler 1987), a value much more close to the integral valence of + 3, similar to CeSn3. The crystal structure is of cubic NaZn13-type with the Ce ions forming a simple cubic lattice. The shortest C e - C e distance is 5.1 N. There are no Ce Ce near- neighbors since Be ions form cages around the Ce ions. The structure may be viewed as Ce ions embedded in Be metal.

48 M. LOEWENHAUPT and K.H. FISCHER

The susceptibility of CeBel3 is rather flat at low temperatures with a very b r o a d maximum at Tmax= 1 4 0 K and a paramagnetic Curie temperature 0 p = 2 0 0 K (Kappler and Meyer 1979). Inelastic neutron scattering experiments have been per- formed by Holland-Moritz et al. (t 982) on polycrystalline samples with cold neutrons (D7, Eo = 3.5 meV). The spectra could be fitted with just one broad quasi-elastic line.

The line width is 17 meV at room temperature and increases with decreasing temper- atures, reaching a value of about 28 meV at 100 K. F o r lower temperatures it could only be stated that the magnetic response must stay broad and/or develops inelastic features. Unfortunately no inelastic neutron data are available at low temperatures with sufficiently high incident energies. There are, however, N M R data reported as function of temperature from 300 K down to 4 K (Panissod et al. 1988). N M R basically probes the imaginary part of the dynamic susceptibility, )('(co)/co, as does neutron scattering. But while N M R probes a Q-average of this quantity at low energy (co~*:>#eV, nuclear L a r m o r frequency), neutron scattering probes it for different Q- values and in a much higher energy range (0.1 to 100meV, depending on the spectrometer). If an electronic relaxation rate (corresponding to a quasi-elastic line width) is deduced from N M R - T 1 measurements, usually two important assumptions are made:

- there are no correlations between different spins, i.e. the magnetic response is independent of Q, and

the magnetic response is of purely relaxational form (quasi-elastic spectrum of Lorentzian shape).

F o r CeBe13 the N M R data yield a line width around 70 meV for temperatures between 4 and 50 K. It then decreases with increasing temperature to 55 meV (100 K), 35 meV (200 K), and 25 meV (300 K). This is the same behavior as observed for the line widths deduced from neutron scattering, but with larger absolute values for the N M R - d e d u c e d line widths. The discrepancy between the values for both methods increases for decreasing temperatures. It is rather unlikely that correlation effects are the origin of the discrepancies. It is more likely that the shape of ;g"(~o) changes with temperature. We therefore suspect that the magnetic response of CeBe13 changes from a more or less quasi-elastic spectrum at high temperatures to a spectrum with quasi-elastic and inelastic features at low temperatures, as it was observed in CePd3 and CeSn 3 .

3.1.5. (a, ~, 7)-Ce and its alloys with Sc, Y,, La, Th

Ce metal in its different phases exhibits already the wide span of properties of the Ce-based compounds, ranging from welt-localized moments via K o n d o lattice up to heavily valence fluctuating and non-magnetic. Vice versa, the behavior of Ce com- pounds has been classified as p-, 7-, and a-like. Simple measurements, however, like the temperature dependence of the magnetic response of a certain phase, are ham- pered by the peculiarities of the phase diagram. At ambient pressure and room temperature it is possible to produce Ce samples in the/~-phase (dhcp, ao = 3.68 A, Co = 11.92 &) and in the ~-phase (fcc, ao = 5.16 A). At decreasing temperatures both transform into the a-phase (fcc, ao = 4.85 A). At r o o m temperature 7-Ce transforms upon application of a pressure of about 8 kbar into a-Ce. F o r more details of the

VF A N D HI" 4f SYSTEMS 49

phase diagram and the description of even more phases we refer the reader to the review articles by Koskenmaki and Gschneidner (1978) and by Gschneidner and Daane (1988). To overcome the limitations of the phase diagram and allow, e.g., temperature-dependent measurements over a wide range of temperatures, a simple trick has been applied: alloying. For instance, alloying with Y stabilizes the/#phase, while alloying with Th prevents the formation of the/?-phase. (Ce,Th)-alloys therefore show only the ~/~c~ phase transition. Further addition of La to (Ce,Th) then even allows some "fine tuning" of the y--+ c~ transition and eventually the suppression of the transition. Alloying, however, always introduces disorder, different local environ=

ments, etc. These effects often complicate the interpretation of work on alloys compared to experiments on chemically ordered intermetallic compounds. We there- fore discuss only briefly neutron investigations performed on Ce metal and its alloys with Sc, Y, La, and Th in its different phases.

3.1.5.1. fi-phase. In fi-Ce the 4f electron can be considered as well localized. Rapid quenching to low temperatures allows one to deduce that fi-Ce orders antiferromag- netically around 12 13 K (Burghardt et al. 1976). For C%_~Yx the ordering temper- ature decreases with x (Panousis and Gschneidner 1972). On a polycrystalline sample of Ceo.75Yo.25 neutron diffraction experiments by Gibbons et al. (1987) yield an antiferromagnetic ordering below TN----7 K with a propagation vector of 0.5"c10 o.

Inelastic neutron scattering by Gibbons et al. (1989) on the same sample shows narrow quasi-elastic scattering (width is 1.3 meV at T = 20 K) and well-defined crystal field transitions at 8 and 16.5 meV. Gibbons et al. (1989) analyze this in terms of a F7 ground state and an excited F 8 state at 16.5 meV (197 K) for the cubic sites and a l+_½) ground state and a [+-3) excited state at 8 meV (97 K) for the hexagonal sites. This model explains why the ordered moments lie in the basal plane (as found in the diffraction experiment), but predicts somewhat larger moments (1.29#n and 0.71#B ) than found experimentally (0.91#u and 0.38#B for the hexagonal and cubic sites, respectively).

3.1.5.2. y-phase. The lattice and spin dynamics of a 7-Ce single crystal have been studied at room temperature by Stassis et al. (1979c). When compared to the p h o n o n dispersion curves of Th, a relative p h o n o n softening of some branches had been stated. Yet is was not clear whether this observation could be uniquely related to a valence-fluctuation effect. The magnetic response could be fitted with just one broad quasi-elastic line of Lorentzian shape and a width of 16 meV. Rainford et al. (1977) reported a width of 10 meV deduced from an experiment on a polycrystalline sample.

Form factor measurements by Stassis et al. (1978) revealed at room temperature a 4f free-ion Ce 3 + form factor.

For obvious reasons there are no measurements of 7-Ce at low temperatures. It is, however, believed that the residual quasi-elastic line width would only be a few meV and an inelastic crystal field transition would be observable. This can be inferred from the results of inelastic neutron scattering experiments on Ce0. 9 xLaxTho. 1 (for x = 0.14, 0.20, 0.40) by Grier et al. (1980, 1981). The addition of La suppresses the 7~c~ transition of Ceo.9Tho.~. The spectra below 110 K were

50 M. LOEWENHAUPT and K.H. FISCHER

fitted with a quasi-elastic and an inelastic line of the same width. The inelastic line was interpreted as a/77 ~ F 8 crystal field transition with an energy around 12, 14, and 15meV and a width around 5, 6, and 8 m e V for x = 0 . 4 0 , 0.20, and 0.14, respectively. Position and width are nearly temperature independent for all x for temperatures between 40 and 110 K. Below 40 K a moderate increase of position and line width is observed for the samples with x = 0.40 and 0.20, while a drastic increase is observed for the 0.14 sample (A = 21 meV, width = 12 meV at 5 K). The different behavior of the 0.14 sample is connected to the still present ~-~ e transition (although of second order instead of first order as in Ce-metal). Grief et al. (1981), however, indicate that the increase in crystal field splitting cannot be understood quantitatively on these grounds.

3.1.5.3. y ~ e transition.

Ceo.74Tho.26

undergoes a first-order valence transition at T = 150 K. For this sample detailed neutron investigations have been performed.

Inelastic neutron scattering experiments are reported by Shapiro et al. (1977) between 100 and 250 K using thermal neutrons and by Loong et al. (1987) between 10 and 200 K using epithermal neutrons with incident energies up to 1.2 eV. In both phases (e below, 7 above 150 K) the magnetic response consists of a broad quasi-elastic spectrum with no indication of inelastic crystal field transitions. In both phases the line width increases with decreasing temperatures. It is typically 20 meV in the 7-phase and around 100 meV in the e-phase. At T = l0 K the magnetic response of the e-phase is somewhat better described by a broad inelastic line at A = 140 meV and a width of 90 meV. This is reminiscent of the hump observed at low temperatures in the excitation spectra of CePd 3 and CeSn3.

A form factor measurement by M o o n and Koehler (1979) on Ceo.74Tho.26 revealed a 4f free-ion Ce 3 + form factor in the y-phase at T = 180 K and deviations from the 4f form factor at the two low-Q reflections (111) and (200) in the c~-pbase at T =

50 K. The results at 50 K suggest that the induced moment in the e-phase has two components, one 4f-like and the other 5d-like, as also found for CePd3 and CeSn 3.

3.1.5.4. c~-phase. The determination of the magnetic response in e-Ce has been a challenge for neutron scatterers for many years. There is no final answer yet, but there is agreement that there is magnetic scattering intensity in the c~-phase of Ce and that the magnetic response is very broad in energy, presumably extending up to the eV region. Fillion et al. (1985) report an inelastic scattering experiment at T - - 8 K with polarized neutrons and polarization analysis (D5, ILL). They obtained a weak magnetic intensity for all data points between 0 and 180 meV, followed by a steplike increase of magnetic intensity for three data points at 200, 230, and 250 meV (the upper limit of the experiment). The steplike increase of intensity between 180 and 200 meV is somewhat surprising in view of the coarse energy resolution of 150 meV ( F W H M ) in this region, which should produce a much smoother variation of intensity with energy transfer (even if the underlying scattering law would be a step function). Fillion et al. (1985) conclude from their data that the magnetic response in e-Ce is essentially inelastic and rule out a purely quasi-elastic response (of width around 200 meV). This is consistent with the observation of Loong et al. (1987) for