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NMR and magnetic susceptibility of the intermetallic pseudo-binary compounds Ce1−xRxAl3 with R=Gd, Tb and Er
J. Phys.Chem.Solids, 1973,Vol.34, pp. 961-967. PergamonPress. Printedin Great Britain
NMR AND MAGNETIC SUSCEPTIBILITY OF THE INTERMETALLIC PSEUDO-BINARY COMPOUNDS Cel-~RxAI3 W I T H R = Gd, Tb A N D Er V. NICULESCU and IULIU POP University of Cluj, Romania
and M. ROSENBERG University of Bucharest, Romania
(Received 11 May 1972; in revised form 13 July 1972) Abstract--The N M R and magnetic susceptibility of the intermetallic pseudo-binary compounds Cel_zGd~,Als (x = 0.01; 0"03; 0-05; 0.07), Ce0.asTbo.o~Al3and Ce0.975Er0.02~13 were investigated. The susceptibility is given by the sum of a temperature independent term and a Curie-Weiss one. The last one results from the contribution of the localized free-ion magnetic moments of all the rare-earth ions which are also responsible for the strong temperature dependent Knight shifts of the N M R lines of 27A1 nuclei via the exchange polarization of the conduction electrons. The 27A1 NMR spectra exhibit besides the line due to AI sites surrounded in the first coordination sphere as in CeAIa a second peak with a lower Knight shift due to A1 nuclei positioned in the vicinity o f a Gd, Tb or Er ion.
1. INTRODUCTION
THE LANTHANIDE intermetallic compounds and among them the lanthanide aluminides RAI~[I-7] have received an increasing attention in recent years as very suitable materials for the investigation of the mechanism of exchange interaction between the localized moments of the rare-earth ions and the conduction electrons [8-11]. In the present investigation we studied the influence of the substitution of Ce by small amounts of Gd, Tb and Er in CeAl3, which crystallizes in the Ni3Sn hexagonal structure[12]. The small difference in the ionic radius of Ce, Gd, Tb and Er (1.18:1.11:1.09:1.04,~) makes it possible to prepare stable solid solutions of the Cel_xRxAl3 type (with R = Ce, Gd, Tb, Er) for x ,~ 1, preserving the Ni3Sn structure, and forming pseudo-binary intermetallic compounds. The 27A1 N M R and the temperature dependence of the magnetic susceptibility have shown that in the investigated pseudo-
binary compounds the rare-earth ions preserve their individuality, all of them contributing with the free ion magnetic moments to the magnetic susceptibility and by exchange polarization of the conduction electrons to the Knight shift of the N M R line of 27A1. At low concentrations of the substituting rareearth element, the N M R makes it possible to distinguish between AI nuclei positioned in the neighbourhood of an RE ion, and the majority of A1 nuclei surrounded by Ce ions only as nearest neighbours. 2. EXPERIMENTAL
Six compositions in the series Cel-xRxAl3 were investigated: For R = Gd, x = 0.01 : 0-03 : 0-05:0.07, for R = T b , x--0.05 and for R = Er, x = 0.025. The compounds were prepared in vacuum in a Tamann furnace, starting from the metallic components. The samples checked by metallographic and X-ray analysis were found as single phase. 961
962
V. NICULESCU et al.
The N M R spectra of 2rAl nuclei were recorded on powders in a 15.085 MHz JNM-3 spectrometer, improved by a broad-line attachment WB-10, at several temperatures in the range 100-475~ in a special designed dewar[13]. The magnetic susceptibility was measured from liquid nitrogen to 1200~ with a 10-acm3/g sensitivity Faraday type magnetic balance.
z-z z.o
a CeoeeGdooI AL3
1"9
b Ceo.e~Gdo.o3ALs
1.8
c ~Gdoo~
1"7
d Ceo~Gdo.gr AL3
//// ///
AL3
//
P'6 ~
i-s
i
i,4 1"3
~.
.
/ //
/ // o
/
"
J //
//
i //
/
/"
b / d~ f // // ~ , , O "
1.2
• o.E
o,',
3. RESULTS AND DISCUSSION
oe
(a) Magnetic susceptibility The temperature dependence of the magnetic susceptibility is shown in Fig. 1 for the Cel-xGdxAl3 compounds and in Fig. 2 for Ceo.95Tb0.05A13and Ceo.975Ero.o25Ala. A least square fit of the experimental data is in good agreement with a dependence expressed by X = Xo+C(T--Op)
o.i 0.3 o.2
o.i
,'o Joe
o,
,
600 T,
"tOO
' Joo ,o'~ '
8OO
The room temperature values of X and of the Curie-Weiss 'term in (1) together with the paramagnetic Curie temperature and the magnetic moment per molecule /xee in Bohr
where Xo is temperature independent.
1"8
1.6
1"4 T o~ '~
I-2
E
?" o
I'0
X 0"8
0"6
0"4
0'2
0
I
I00
I
;too
I
300
I
400
tloo
~
Fig. 1. The temperature dependence of the magnetic susceptibility for the compounds Cel_~GdxA13.
(1)
-1
I,
30O
I
I
500
T,
600
i
700
I
8oo
I
900
I
tooo
"K
Fig. 2. The temperature dependence of the magnetic susceptibility for Ceo 95Tbo.osAla and Ceo.grsEro.o2~Al3.
NMR AND MAGNETIC SUSCEPTIBILITY OF Cel_xRxA13 WITH R = Gd, Tb AND Er magnetons are given in Table 1. T h e values of /zez computed under the assumption that the Curie-Weiss term is due to the R E free ion moments only are given in the last column of Table 1. The very good agreement with the experiment/z~s is quite obvious, thus providing us with a straight evidence for the high degree of localization of the 4 f electrons o f the R E ions in the investigated compounds. An interesting feature is the gradual change in the sign and value of 0p for increasing G d concentrations from a negative value of - 25~ for CeAl3 to a positive one o f + 12~ for Ceo.93Gdo.07A13. T h e substitution with E r and T b yields to a more drastic effect on 0v than that of Gd. Regarding the temperature independent term X0 one can try to fit its value by taking into account all the additive contributions to the susceptibility, known as being temperature independent, i.e. writing the susceptibility Xo as p,d -'~ Xvv ~ "q-XL "~-Xdia, Xo = XP-'~ Xorb
corresponding values for CeA13. Thus, the ionic diamagnetism of the Ce 3+ and AI 3+ ions gives Xdia = - - 0 " 1 17. 10-6 e.m.u./g. T h e strong localization of the 4 f electrons allows us to take for X~ the value of 5 0 . 1 0 -6 e.m.u./mol of the free Ce 3+ ion given by Van Diepen et al. [5]. Assuming that the contribution of the outer p electrons o f AI and d electrons of Ce is the same in the intermetallic compound as in the pure metals one obtains for the orbital contribution of A1 X~orb= 0" 15. 10-6 e.m.u./g. The orbital contribution o f the Ce 5d electron computed with the expression given by G a r d n e r and Penfold[14] is Xorb 5d = 38"8. 10-6 e.m.u./mol. The Landau term, computed for free electrons is XL = - - 0 " 127. 10-6 e.m.u./g. Subtracting all the above mentioned terms from X0, one obtains for the Pauli paramagnetism of CeA13 a value XJ, = 1 . 3 . 1 0 -6 e.m.u./g which is 2.8 times that of Xp for free conduction electrons. The enhancement of the Pauli paramagnetism was interpreted in terms of e l e c t r o n electron and e l e c t r o n - p h o n o n interactions by Clogston who gives [15 ]:
(2)
where Xp is the Pauli paramagnetic term, XorbV'd the orbital contribution of the collective outer p and d electrons, X~ the contribution of the Van-Vleck paramagnetism o f the localized 4 f electrons, XL the Landau diamagnetic term, and Xaia the contribution o f the diamagnetic ionic cores of the AI and R E atoms. The figures for the different terms in (2), excepting Xp are probably v e r y close to the
f = (X~/Xp~ = [1--No(EF)(/3--~)] -1, (3) where No(EF) is the free electron density of states, /3 and E the coupling parameters for electron-electron and respectively e l e c t r o n phonon interactions. T h e lowering o f X0 with an increasing content in G d shows that the enhancement factor
Table 1. The values of some magnetic features o f the compounds Cel-xGdxAl3, Ceo.95Tbo.osA13 and Ceo.975Ero.o25A13 as compared with CeAl3. The susceptibilities are given in 10 -e e.m.u.[g Compound CeAI3 Ceo.aaGd0.01A13 Ce0.97Gd0.0aA13 Ceo.9~Gdo.o~13 Ceo.93Gd0.oTA17 Ce0.95Tb0.o~A13 Ce0.9rsEr0.02sAl3
M 221.16 221-31 221.66 221.8 222.14 222-014 221.82
963
X (300~
Xo
11.6 13.8 15.4 16.5 20 20.10 16.5
1.3 1.3 1.25 1.15 1.1 1.35 1.3
Xf(300~ 10.6 12.5 14.15 15.35 18.9 18.75 15.2
0v(K) /zes(exp) /za(calc) --25 -6 +5 +8 + 12 + 25 +6
2.525 2"673 2"95 3"005 3"21 3' 16 2.933
2.56 2.67 2-87 3.06 3-23 3.3 2.94
964
V. N I C U L E S C U et al.
f decreases from 2.8 to 2.3 for 7 per cent of the Ce atoms substituted by Gd. This may be understood in terms of a decrease in the density of states at the Fermi level owing to the presence of Gd which in the metallic state exhibits a very low value of the electronic specific heat (6.7mJ/mol~ ~) as compared with that of the metallic Ce (42 mJ/mol~ (b) N M R line shape and Knight shift The room temperature N M R spectra of the Gd substituted compounds are shown in Fig. 3. The NMR half line width taken as the full width at half maximum for the absorption curve for Ce0.99Gd0.01A13 is shown in Fig. 4. In contrast to the central symmetric line of CeAI3 with a half line width of about 6 G with a weak temperature dependence between 150 and 450~ and a positive Knight shift
\
Fig. 3. N M R line shapes at the room temperature for the Cel-xGdxAl3 compounds.
,o
8 7
,o 6
I
I00
I
I
2OO
300 T,
I
400
*ff
Fig. 4. The temperature dependence of the N M R half line width of the main line of Ce0.~aGd0.olAl3.
K = 0.196 per cent at room temperature, the Gd, Tb and Er substituted compounds exhibit besides a strong central line, a high field satellite more or less well resolved. The presence and the position of the satellite line may be explained by assuming that there are two inequivalent surroundings of the AI sites, i.e. A1 nuclei either further (site AI I) or closer (site AI II) in respect to the Gd ions. For small concentrations of Gd the amount of AI II sites is low, but well defined. For higher concentrations of Gd the distinction between the two types of sites grows gradually blurred and the resolution of the satellite line becomes more difficult. The Knight shift of the satellite taken from its peak is smaller than that of the central line, the former lying closer to that of the calibrating diamagnetic AIC13. For the 1% Gd substituted compound it was possible to record the Knight shift for both central and satellite lines, as shown in Fig. 5. For the other Gd substituted compounds an overall Knight shift was taken from the middle of the broadened line on the field axis and its temperature dependence is plotted in Fig. 6. For all the investigated compounds the Knight shift K.S. is proportional to the Curie-Weiss term of the magnetic susceptibility, i.e. to the susceptibility of the localized 4 f electrons. Such a behaviour is consistent with a R K K Y mechanism of enhancement of the hyperfine field at the AI nuclei[8-11]
NMR AND MAGNETIC SUSCEPTIBILITY OF Cel-~R~rAI3 WITH R = Gd, Tb AND Er
0-26 r /
la
!o.2o r
o
can be explained in terms o f a crude model as follows: Assuming that the spin polarization of the conduction electrons is enhanced through the exchange interaction with the localized 4 f electron spins S o f the R E ions, the total Knight shift K is related to the 4 f susceptibility per R E ion through [11 ]
o
.~ 0-24~-
9 ~
p
~. o.m
I
I\Ir
o-,41-
012 0
"
1
0
0
T,
•
-'~
..iT "
,
~
owing to the exchange polarization of the conduction electrons by the localized f electrons. The appearance o f the satellite line and its evolution with increasing G d concentration
0"30
~, Ceo.e7 Gdo.os AI 3
0"28
9 Ceo.ss Gdo-oe AL3
\i
=~. 0"24
K = Ko[1
+Jss(gs-- 1)XA(2gsnd~B2)], (4)
where gs is the 4f-electron Land6 g-value and K0 is the K.S. due to Pauli paramagnetism. Considering only an elementary exchange interaction with an exchange integral F, the phenomenological exchange constant becomes
*K
Fig. 5. The temperature dependence of the K.S. for Ce0.agGd0.0~Al3. (a) K.S. of the main line (b) K.S. of the whole line. (c) K.S. of the satellite line.
0"26
965
0"22 0"20 E v 0"18 0"16
J~r= --6rrZF ~ F (2kCRaz.Re),
(5)
RE
where
F(p) =
p cos p -- sin p
p4
(6)
with kF the Fermi wave vector and RA]-REthe distance between a R E ion and the AI site at which is measured the K.S. Lets assume that, owing to their low concentration one may consider the G d ions distributed regularly in the Cel-xGdxAl3 lattice. As a first approximation the exchange polarization of the conduction electrons at an Al site can be expressed as the sum of two contributions, the first due to the exchange interaction with the Ce 4f-electrons and the second one to the exchange interaction with the 4f-electrons of the G d ions. T h e corresponding exchange integrals are denoted by Fce and Fca and the total K.S. becomes
K = Ko { 1 - (3~z~B-~) [rce(gj,c. - 1)
0-14 X
0"12 0"10
0
-1
Xat,cegJ,ee Z F (2kvRAL,E) Ce
I
I00
I 200
T,
I
I
300
400
-1 + F~a(ga,Ga--1 )Xat,GdgJ,Gd
*K
Fig. 6. The temperature dependence of the K.S. of the whole line for CeI_,Gd,AI3 (x = 0-03; 0.05).
XXF(2k~RALGa)]}, Gd
(7)
966
V. N I C U L E S C U et al.
where Xat.ce and Xat.Gd are the magnetic susceptibilities per atom of the corresponding RE ions. Similar expressions can be written for the Tb and Er substituted CeAI3. The factors a=(ga--1)ga-lXat.aE are about 30 times larger for Gd and Tb and 16 times larger for Er than for Ce. Since as usual in the lanthanide trialuminides Jss < 0, F and E have the same sign. ae For low concentrations of the substituting RE elements, a great number of A1 sites have in the first coordination sphere a non-cerium RE neighbour. Owing to the high value of the ratios aRJace and the positive value of gT,1a and assuming that the F of Ce and Gd are similar, the contribution of the Gd-term in (7) may be important thus giving rise to a negative contribution to the K.S. at the A1 II sites. But, for the majority of the A1 sites which are A1 I type the Ce-term in (7) must prevail and with gJ.ce -1 < 0, gives a positive contribution to the K.S. as in CeA13. As the Ce ions give the most important contribution to the Curie-Weiss susceptibility of the 4felectrons in all the investigated compounds, a proportionality of the K.S. with Xs is to be expected from (7), neglecting the Gd term and taking into account that Xat.ce ~ Xr. Such a behaviour is observed for the Gd substituted compounds as shown in Fig. 7. The temperature dependence of the half line width for the strong line in the case of Ceo.99Gd0.01Al~ is similar to that of "rA1 in CeA13. The larger broadening at lower temperatures for the other investigated compounds where the satellite line is not resolved is probably due to the different temperature dependences of the K.S. at the A1 I and A1 II sites. 4. CONCLUSIONS The main effects of the substitution of Ce in CeAla by small amounts of RE elements from the second half of the lanthanide series, such as Gd, Tb and Er are the following: (1) All the RE ions contribute with the magnetic moments of their localized ~ f
0"28
r/
0.26 0'24 0"22 0 "20 0"18 0"I6 0"14
gr- o.r2 ~
OqO 0"08
m
0'06 0-04
h
0 "02
I
0"5
I
I-5
1
2
X,-• 10~ e . m . u . / g
Fig. 7. The K.S. plotted vs Xs for the compounds Cel-xGdxAl~(.) K.S. of the main line for Ce0.99Gdo.01A13; (0) K.S. for Ce0.gaGdo.01A13; (A) K.S. for Ce0.97Gd0.03A13.
electrons to the Curie-Weiss term in the magnetic susceptibility, thus giving rise to an increased magnetic moment per molecule and to positive values of the paramagnetic Curie point as compared to the magnetic moment of CeAl3 and its negative paramagnetic Curie temperature. (2) The localized 4 f electrons are also responsible for the strong temperature dependent K.S. of the N M R lines of 27A1 nuclei via the exchange polarization of the conduction electrons. (3) The presence of a higher-field satellite in the N M R spectra lying close to the main line is explained in terms of inequivalent Al sites, differing by their distance in respect to the RE ions. The smaller K.S. of the satellite as compared to that of the main line is explained by assigning the former to A1 nuclei located in the neighbourhood of the Gd, Tb or Er ions. (4) The substitution of Ce by Gd seems to have an inhibiting effect on the Pauli paramagnetism of the conduction electrons as
N M R A N D M A G N E T I C S U S C E P T I B I L I T Y O F Cel-xRxAlz WITH R = Gd, Tb A N D Er
compared to CeAI3. This may be interpreted as a decrease in the density of states at the Fermi level. REFERENCES 1. J A C C A R I N O V., M A T T H I A S B. T., P E T E R M., S U H L H. and W E R N I C K J. H., Phys. Rev. Lett. 5, 251 (1960). 2. J A C C A R I N O V., J. appl. Phys. 32, 1028 (1961). 3. V A N D I E P E N A. M., D E W l J N H. W. and BUSCHOW K. H. J., J. chem. Phys. 46, 3460 (1967). 4. B U S C H O W K. H. J., FAST I. F., V A N D I E P E N A. M. and D E WlJN H. W., Phys. Status Solidi 24, 715 (1967). 5. V A N D I E P E N A. M., D E WlJN H. W. and BUSCHOW K. H. J., Phys. Status Solidi 29, 189 (1968).
967
6. N I C U L E S C U V., POP I U L I U and R O S E N B E R G M., Phys. Lett. 34A, 265 (1971). 7. N I C U L E S C U V., POP I U L I U and R O S E N B E R G M., Studia Univ. Babes-Bolyai, Set. fiz. fasc. 2, 59 (1971). 8. R U D E R M A N M. A. and K I T T E L C., Phys. Rev. 96, 99 (1954). 9. K A S U Y A T., Prog. theor. Phys. (Kyoto) 16, 45 (1956). 10. Y O S I D A K., Phys. Rev. 106, 893 (1957). 11. DE G E N N E S P. G.,J. Phys. Rad. 23, 510 (1962). 12. V A N V U C H T J. H. N. and B U S C H O W K. H. J. J. less-common Metals 10, 98 (1965). 13. N I C U L E S C U V., M A N D A C H E S. and POP I U L I U , Studii Cerc. Fiz. 23, 1123 (1971). 14. G A R D N E R W. E. and P E N F O L D J., Phil. Mag. 11, 549 (1965). 15. C L O G S T O N A. M., Phys. Rev. 136, A8 (1964).
NMR AND MAGNETIC SUSCEPTIBILITY OF THE INTERMETALLIC PSEUDO-BINARY COMPOUNDS Cel-~RxAI3 W I T H R = Gd, Tb A N D Er V. NICULESCU and IULIU POP University of Cluj, Romania
and M. ROSENBERG University of Bucharest, Romania
(Received 11 May 1972; in revised form 13 July 1972) Abstract--The N M R and magnetic susceptibility of the intermetallic pseudo-binary compounds Cel_zGd~,Als (x = 0.01; 0"03; 0-05; 0.07), Ce0.asTbo.o~Al3and Ce0.975Er0.02~13 were investigated. The susceptibility is given by the sum of a temperature independent term and a Curie-Weiss one. The last one results from the contribution of the localized free-ion magnetic moments of all the rare-earth ions which are also responsible for the strong temperature dependent Knight shifts of the N M R lines of 27A1 nuclei via the exchange polarization of the conduction electrons. The 27A1 NMR spectra exhibit besides the line due to AI sites surrounded in the first coordination sphere as in CeAIa a second peak with a lower Knight shift due to A1 nuclei positioned in the vicinity o f a Gd, Tb or Er ion.
1. INTRODUCTION
THE LANTHANIDE intermetallic compounds and among them the lanthanide aluminides RAI~[I-7] have received an increasing attention in recent years as very suitable materials for the investigation of the mechanism of exchange interaction between the localized moments of the rare-earth ions and the conduction electrons [8-11]. In the present investigation we studied the influence of the substitution of Ce by small amounts of Gd, Tb and Er in CeAl3, which crystallizes in the Ni3Sn hexagonal structure[12]. The small difference in the ionic radius of Ce, Gd, Tb and Er (1.18:1.11:1.09:1.04,~) makes it possible to prepare stable solid solutions of the Cel_xRxAl3 type (with R = Ce, Gd, Tb, Er) for x ,~ 1, preserving the Ni3Sn structure, and forming pseudo-binary intermetallic compounds. The 27A1 N M R and the temperature dependence of the magnetic susceptibility have shown that in the investigated pseudo-
binary compounds the rare-earth ions preserve their individuality, all of them contributing with the free ion magnetic moments to the magnetic susceptibility and by exchange polarization of the conduction electrons to the Knight shift of the N M R line of 27A1. At low concentrations of the substituting rareearth element, the N M R makes it possible to distinguish between AI nuclei positioned in the neighbourhood of an RE ion, and the majority of A1 nuclei surrounded by Ce ions only as nearest neighbours. 2. EXPERIMENTAL
Six compositions in the series Cel-xRxAl3 were investigated: For R = Gd, x = 0.01 : 0-03 : 0-05:0.07, for R = T b , x--0.05 and for R = Er, x = 0.025. The compounds were prepared in vacuum in a Tamann furnace, starting from the metallic components. The samples checked by metallographic and X-ray analysis were found as single phase. 961
962
V. NICULESCU et al.
The N M R spectra of 2rAl nuclei were recorded on powders in a 15.085 MHz JNM-3 spectrometer, improved by a broad-line attachment WB-10, at several temperatures in the range 100-475~ in a special designed dewar[13]. The magnetic susceptibility was measured from liquid nitrogen to 1200~ with a 10-acm3/g sensitivity Faraday type magnetic balance.
z-z z.o
a CeoeeGdooI AL3
1"9
b Ceo.e~Gdo.o3ALs
1.8
c ~Gdoo~
1"7
d Ceo~Gdo.gr AL3
//// ///
AL3
//
P'6 ~
i-s
i
i,4 1"3
~.
.
/ //
/ // o
/
"
J //
//
i //
/
/"
b / d~ f // // ~ , , O "
1.2
• o.E
o,',
3. RESULTS AND DISCUSSION
oe
(a) Magnetic susceptibility The temperature dependence of the magnetic susceptibility is shown in Fig. 1 for the Cel-xGdxAl3 compounds and in Fig. 2 for Ceo.95Tb0.05A13and Ceo.975Ero.o25Ala. A least square fit of the experimental data is in good agreement with a dependence expressed by X = Xo+C(T--Op)
o.i 0.3 o.2
o.i
,'o Joe
o,
,
600 T,
"tOO
' Joo ,o'~ '
8OO
The room temperature values of X and of the Curie-Weiss 'term in (1) together with the paramagnetic Curie temperature and the magnetic moment per molecule /xee in Bohr
where Xo is temperature independent.
1"8
1.6
1"4 T o~ '~
I-2
E
?" o
I'0
X 0"8
0"6
0"4
0'2
0
I
I00
I
;too
I
300
I
400
tloo
~
Fig. 1. The temperature dependence of the magnetic susceptibility for the compounds Cel_~GdxA13.
(1)
-1
I,
30O
I
I
500
T,
600
i
700
I
8oo
I
900
I
tooo
"K
Fig. 2. The temperature dependence of the magnetic susceptibility for Ceo 95Tbo.osAla and Ceo.grsEro.o2~Al3.
NMR AND MAGNETIC SUSCEPTIBILITY OF Cel_xRxA13 WITH R = Gd, Tb AND Er magnetons are given in Table 1. T h e values of /zez computed under the assumption that the Curie-Weiss term is due to the R E free ion moments only are given in the last column of Table 1. The very good agreement with the experiment/z~s is quite obvious, thus providing us with a straight evidence for the high degree of localization of the 4 f electrons o f the R E ions in the investigated compounds. An interesting feature is the gradual change in the sign and value of 0p for increasing G d concentrations from a negative value of - 25~ for CeAl3 to a positive one o f + 12~ for Ceo.93Gdo.07A13. T h e substitution with E r and T b yields to a more drastic effect on 0v than that of Gd. Regarding the temperature independent term X0 one can try to fit its value by taking into account all the additive contributions to the susceptibility, known as being temperature independent, i.e. writing the susceptibility Xo as p,d -'~ Xvv ~ "q-XL "~-Xdia, Xo = XP-'~ Xorb
corresponding values for CeA13. Thus, the ionic diamagnetism of the Ce 3+ and AI 3+ ions gives Xdia = - - 0 " 1 17. 10-6 e.m.u./g. T h e strong localization of the 4 f electrons allows us to take for X~ the value of 5 0 . 1 0 -6 e.m.u./mol of the free Ce 3+ ion given by Van Diepen et al. [5]. Assuming that the contribution of the outer p electrons o f AI and d electrons of Ce is the same in the intermetallic compound as in the pure metals one obtains for the orbital contribution of A1 X~orb= 0" 15. 10-6 e.m.u./g. The orbital contribution o f the Ce 5d electron computed with the expression given by G a r d n e r and Penfold[14] is Xorb 5d = 38"8. 10-6 e.m.u./mol. The Landau term, computed for free electrons is XL = - - 0 " 127. 10-6 e.m.u./g. Subtracting all the above mentioned terms from X0, one obtains for the Pauli paramagnetism of CeA13 a value XJ, = 1 . 3 . 1 0 -6 e.m.u./g which is 2.8 times that of Xp for free conduction electrons. The enhancement of the Pauli paramagnetism was interpreted in terms of e l e c t r o n electron and e l e c t r o n - p h o n o n interactions by Clogston who gives [15 ]:
(2)
where Xp is the Pauli paramagnetic term, XorbV'd the orbital contribution of the collective outer p and d electrons, X~ the contribution of the Van-Vleck paramagnetism o f the localized 4 f electrons, XL the Landau diamagnetic term, and Xaia the contribution o f the diamagnetic ionic cores of the AI and R E atoms. The figures for the different terms in (2), excepting Xp are probably v e r y close to the
f = (X~/Xp~ = [1--No(EF)(/3--~)] -1, (3) where No(EF) is the free electron density of states, /3 and E the coupling parameters for electron-electron and respectively e l e c t r o n phonon interactions. T h e lowering o f X0 with an increasing content in G d shows that the enhancement factor
Table 1. The values of some magnetic features o f the compounds Cel-xGdxAl3, Ceo.95Tbo.osA13 and Ceo.975Ero.o25A13 as compared with CeAl3. The susceptibilities are given in 10 -e e.m.u.[g Compound CeAI3 Ceo.aaGd0.01A13 Ce0.97Gd0.0aA13 Ceo.9~Gdo.o~13 Ceo.93Gd0.oTA17 Ce0.95Tb0.o~A13 Ce0.9rsEr0.02sAl3
M 221.16 221-31 221.66 221.8 222.14 222-014 221.82
963
X (300~
Xo
11.6 13.8 15.4 16.5 20 20.10 16.5
1.3 1.3 1.25 1.15 1.1 1.35 1.3
Xf(300~ 10.6 12.5 14.15 15.35 18.9 18.75 15.2
0v(K) /zes(exp) /za(calc) --25 -6 +5 +8 + 12 + 25 +6
2.525 2"673 2"95 3"005 3"21 3' 16 2.933
2.56 2.67 2-87 3.06 3-23 3.3 2.94
964
V. N I C U L E S C U et al.
f decreases from 2.8 to 2.3 for 7 per cent of the Ce atoms substituted by Gd. This may be understood in terms of a decrease in the density of states at the Fermi level owing to the presence of Gd which in the metallic state exhibits a very low value of the electronic specific heat (6.7mJ/mol~ ~) as compared with that of the metallic Ce (42 mJ/mol~ (b) N M R line shape and Knight shift The room temperature N M R spectra of the Gd substituted compounds are shown in Fig. 3. The NMR half line width taken as the full width at half maximum for the absorption curve for Ce0.99Gd0.01A13 is shown in Fig. 4. In contrast to the central symmetric line of CeAI3 with a half line width of about 6 G with a weak temperature dependence between 150 and 450~ and a positive Knight shift
\
Fig. 3. N M R line shapes at the room temperature for the Cel-xGdxAl3 compounds.
,o
8 7
,o 6
I
I00
I
I
2OO
300 T,
I
400
*ff
Fig. 4. The temperature dependence of the N M R half line width of the main line of Ce0.~aGd0.olAl3.
K = 0.196 per cent at room temperature, the Gd, Tb and Er substituted compounds exhibit besides a strong central line, a high field satellite more or less well resolved. The presence and the position of the satellite line may be explained by assuming that there are two inequivalent surroundings of the AI sites, i.e. A1 nuclei either further (site AI I) or closer (site AI II) in respect to the Gd ions. For small concentrations of Gd the amount of AI II sites is low, but well defined. For higher concentrations of Gd the distinction between the two types of sites grows gradually blurred and the resolution of the satellite line becomes more difficult. The Knight shift of the satellite taken from its peak is smaller than that of the central line, the former lying closer to that of the calibrating diamagnetic AIC13. For the 1% Gd substituted compound it was possible to record the Knight shift for both central and satellite lines, as shown in Fig. 5. For the other Gd substituted compounds an overall Knight shift was taken from the middle of the broadened line on the field axis and its temperature dependence is plotted in Fig. 6. For all the investigated compounds the Knight shift K.S. is proportional to the Curie-Weiss term of the magnetic susceptibility, i.e. to the susceptibility of the localized 4 f electrons. Such a behaviour is consistent with a R K K Y mechanism of enhancement of the hyperfine field at the AI nuclei[8-11]
NMR AND MAGNETIC SUSCEPTIBILITY OF Cel-~R~rAI3 WITH R = Gd, Tb AND Er
0-26 r /
la
!o.2o r
o
can be explained in terms o f a crude model as follows: Assuming that the spin polarization of the conduction electrons is enhanced through the exchange interaction with the localized 4 f electron spins S o f the R E ions, the total Knight shift K is related to the 4 f susceptibility per R E ion through [11 ]
o
.~ 0-24~-
9 ~
p
~. o.m
I
I\Ir
o-,41-
012 0
"
1
0
0
T,
•
-'~
..iT "
,
~
owing to the exchange polarization of the conduction electrons by the localized f electrons. The appearance o f the satellite line and its evolution with increasing G d concentration
0"30
~, Ceo.e7 Gdo.os AI 3
0"28
9 Ceo.ss Gdo-oe AL3
\i
=~. 0"24
K = Ko[1
+Jss(gs-- 1)XA(2gsnd~B2)], (4)
where gs is the 4f-electron Land6 g-value and K0 is the K.S. due to Pauli paramagnetism. Considering only an elementary exchange interaction with an exchange integral F, the phenomenological exchange constant becomes
*K
Fig. 5. The temperature dependence of the K.S. for Ce0.agGd0.0~Al3. (a) K.S. of the main line (b) K.S. of the whole line. (c) K.S. of the satellite line.
0"26
965
0"22 0"20 E v 0"18 0"16
J~r= --6rrZF ~ F (2kCRaz.Re),
(5)
RE
where
F(p) =
p cos p -- sin p
p4
(6)
with kF the Fermi wave vector and RA]-REthe distance between a R E ion and the AI site at which is measured the K.S. Lets assume that, owing to their low concentration one may consider the G d ions distributed regularly in the Cel-xGdxAl3 lattice. As a first approximation the exchange polarization of the conduction electrons at an Al site can be expressed as the sum of two contributions, the first due to the exchange interaction with the Ce 4f-electrons and the second one to the exchange interaction with the 4f-electrons of the G d ions. T h e corresponding exchange integrals are denoted by Fce and Fca and the total K.S. becomes
K = Ko { 1 - (3~z~B-~) [rce(gj,c. - 1)
0-14 X
0"12 0"10
0
-1
Xat,cegJ,ee Z F (2kvRAL,E) Ce
I
I00
I 200
T,
I
I
300
400
-1 + F~a(ga,Ga--1 )Xat,GdgJ,Gd
*K
Fig. 6. The temperature dependence of the K.S. of the whole line for CeI_,Gd,AI3 (x = 0-03; 0.05).
XXF(2k~RALGa)]}, Gd
(7)
966
V. N I C U L E S C U et al.
where Xat.ce and Xat.Gd are the magnetic susceptibilities per atom of the corresponding RE ions. Similar expressions can be written for the Tb and Er substituted CeAI3. The factors a=(ga--1)ga-lXat.aE are about 30 times larger for Gd and Tb and 16 times larger for Er than for Ce. Since as usual in the lanthanide trialuminides Jss < 0, F and E have the same sign. ae For low concentrations of the substituting RE elements, a great number of A1 sites have in the first coordination sphere a non-cerium RE neighbour. Owing to the high value of the ratios aRJace and the positive value of gT,1a and assuming that the F of Ce and Gd are similar, the contribution of the Gd-term in (7) may be important thus giving rise to a negative contribution to the K.S. at the A1 II sites. But, for the majority of the A1 sites which are A1 I type the Ce-term in (7) must prevail and with gJ.ce -1 < 0, gives a positive contribution to the K.S. as in CeA13. As the Ce ions give the most important contribution to the Curie-Weiss susceptibility of the 4felectrons in all the investigated compounds, a proportionality of the K.S. with Xs is to be expected from (7), neglecting the Gd term and taking into account that Xat.ce ~ Xr. Such a behaviour is observed for the Gd substituted compounds as shown in Fig. 7. The temperature dependence of the half line width for the strong line in the case of Ceo.99Gd0.01Al~ is similar to that of "rA1 in CeA13. The larger broadening at lower temperatures for the other investigated compounds where the satellite line is not resolved is probably due to the different temperature dependences of the K.S. at the A1 I and A1 II sites. 4. CONCLUSIONS The main effects of the substitution of Ce in CeAla by small amounts of RE elements from the second half of the lanthanide series, such as Gd, Tb and Er are the following: (1) All the RE ions contribute with the magnetic moments of their localized ~ f
0"28
r/
0.26 0'24 0"22 0 "20 0"18 0"I6 0"14
gr- o.r2 ~
OqO 0"08
m
0'06 0-04
h
0 "02
I
0"5
I
I-5
1
2
X,-• 10~ e . m . u . / g
Fig. 7. The K.S. plotted vs Xs for the compounds Cel-xGdxAl~(.) K.S. of the main line for Ce0.99Gdo.01A13; (0) K.S. for Ce0.gaGdo.01A13; (A) K.S. for Ce0.97Gd0.03A13.
electrons to the Curie-Weiss term in the magnetic susceptibility, thus giving rise to an increased magnetic moment per molecule and to positive values of the paramagnetic Curie point as compared to the magnetic moment of CeAl3 and its negative paramagnetic Curie temperature. (2) The localized 4 f electrons are also responsible for the strong temperature dependent K.S. of the N M R lines of 27A1 nuclei via the exchange polarization of the conduction electrons. (3) The presence of a higher-field satellite in the N M R spectra lying close to the main line is explained in terms of inequivalent Al sites, differing by their distance in respect to the RE ions. The smaller K.S. of the satellite as compared to that of the main line is explained by assigning the former to A1 nuclei located in the neighbourhood of the Gd, Tb or Er ions. (4) The substitution of Ce by Gd seems to have an inhibiting effect on the Pauli paramagnetism of the conduction electrons as
N M R A N D M A G N E T I C S U S C E P T I B I L I T Y O F Cel-xRxAlz WITH R = Gd, Tb A N D Er
compared to CeAI3. This may be interpreted as a decrease in the density of states at the Fermi level. REFERENCES 1. J A C C A R I N O V., M A T T H I A S B. T., P E T E R M., S U H L H. and W E R N I C K J. H., Phys. Rev. Lett. 5, 251 (1960). 2. J A C C A R I N O V., J. appl. Phys. 32, 1028 (1961). 3. V A N D I E P E N A. M., D E W l J N H. W. and BUSCHOW K. H. J., J. chem. Phys. 46, 3460 (1967). 4. B U S C H O W K. H. J., FAST I. F., V A N D I E P E N A. M. and D E WlJN H. W., Phys. Status Solidi 24, 715 (1967). 5. V A N D I E P E N A. M., D E WlJN H. W. and BUSCHOW K. H. J., Phys. Status Solidi 29, 189 (1968).
967
6. N I C U L E S C U V., POP I U L I U and R O S E N B E R G M., Phys. Lett. 34A, 265 (1971). 7. N I C U L E S C U V., POP I U L I U and R O S E N B E R G M., Studia Univ. Babes-Bolyai, Set. fiz. fasc. 2, 59 (1971). 8. R U D E R M A N M. A. and K I T T E L C., Phys. Rev. 96, 99 (1954). 9. K A S U Y A T., Prog. theor. Phys. (Kyoto) 16, 45 (1956). 10. Y O S I D A K., Phys. Rev. 106, 893 (1957). 11. DE G E N N E S P. G.,J. Phys. Rad. 23, 510 (1962). 12. V A N V U C H T J. H. N. and B U S C H O W K. H. J. J. less-common Metals 10, 98 (1965). 13. N I C U L E S C U V., M A N D A C H E S. and POP I U L I U , Studii Cerc. Fiz. 23, 1123 (1971). 14. G A R D N E R W. E. and P E N F O L D J., Phil. Mag. 11, 549 (1965). 15. C L O G S T O N A. M., Phys. Rev. 136, A8 (1964).