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29Si NMR study of the dense Kondo system Ce-Si
Journal of Magnetism and Magnetic Materials 52 (1985) 349-352 North-Holland, Amsterdam
349
29Si N M R S T U D Y OF T H E D E N S E K O N D O S Y S T E M C e - S i Y. K O H O R I ,
K. A S A Y A M A
Department of Physics, Faculty of Science, Kobe University, Nada-Ku, Kobe 657, Japan T. K O H A R A
College of Liberal Arts, Kobe University, Nada- Ku, Kobe 657, Japan N. S A T O , H. Y A S H I M A ,
H. M O R I a n d T. S A T O H
Department of Physics, Faculty of Science, Tohoku Unioersity, Sendal 980, Japan
Nuclear spin lattice relaxation rate, 1 / T 1, of 29Si has been measured in CeSi x for x = 1.7-2.0. The result shows that the trivalent state is stable for 1.7-1.8 at high temperature, and that the system is in the Fermi liquid state at low temperature for x > 1.86.
1. Introduction The rare-earth intermetallic compound CeSi 2 has a tetragonal a-ThSi 2 type structure and exhibits various anomalies associated with the intermediate valence or the K o n d o effect [1]. The magnetic property was found to be highly sensitive to the stoichiometry. The specific heat and the susceptibility measurements were extended to the Si-deficient CeSi x systems. It was found that the spin fluctuation temperature, T K, decreases with decreasing Si content and that the system undergoes a ferromagnetic state for the composition x < 1.83 [2,3]. In order to get further insight into the magnetic property of Ce ions, it is desirable to study the system from the microscopic point of view. In this paper we report the result of 29Si N M R measurements. The Knight shift, K, and the nuclear spin lattice relaxation time, T 1, provide the static and dynamical information of the magnetic environment of the nuclei. A special interest lies in obtaining a unified view of the microscopic nature of unstable Ce ion systems in which T K changes over the range of a few hundreds kelvin.
2. Experimental The polycrystalline specimens were prepared by melting the constituents together in an arc furnace and annealing the product at 950°C for 3 weeks. The speci0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
mens were then crushed into powder for the N M R experiment. The measurement was performed with a standard phase coherent spectrometer at a resonance frequency of 10 M H z over the temperature range 1.3-300 K. The Knight shift was measured with respect to the 11B resonance in B(COH3) 3 by assuming the ratio of the gyromagnetic ratios y ( 2 9 S i ) / y ( N B ) = 8.458/13.660. T 1 was measured at the peak position of the spectrum by recording the recovery of the spin echo intensity after the saturating pulses.
3. Results and discussions 3.1. Knight shift Fig. l a shows the 29Si N M R spectrum of the stoichiometric sample, x = 2.0. The position of the peak is nearly temperature independent indicating that x = 2.0 is non-magnetic. As seen in fig. la, there is a small tail in the low field side whose width increases with decreasing temperature. This tail would be attributed to the magnetic Ce ion which may be associated with a small amount of Si vacancies. Fig. l b shows the temperature dependence of the spectrum of x = 1.86. The spectrum has positive shift and is anisotropic. The anisotropic spectrum is considered to be due to the distribution of Ce moments. We determine the shift at the first moment of the spectrum
Y. Kohori et al. / Dense Kondo system C e - Si
350
~
K=O
A
,,•
O I.--
...... , ~ t , /
52K
Z
33 K
Z
CeSi 2.0
n,"
eSi 1.86
42K
z
J~ 4.2K
I
I
I
114
I
116
I
I
11.8 H(k0 e )
1 .0 H(kOe)
Fig. 1. (a) 29Si spectra in CeSi2o at 4.2, 52 and 84 K; (b) 29Si spectra in CeSil.~6 at 4.2, 33 and 52 K.
from K = 0, which is plotted in fig. 2 against the susceptibility with t e m p e r a t u r e as an implicit parameter. T h e results of other Si concentration are also shown in fig. 2. For each sample, the K n i g h t shift is nearly p r o p o r t i o n a l to the susceptibility. F r o m the slope in the K n i g h t shift vs. susceptibility plot, the hyperfine field is o b t a i n e d to be 6.0 k O e / # B, which is nearly i n d e p e n d e n t of the Si content.
In a system in which the local m o m e n t s reside on the crystal lattice, the isotropic shift is induced by the c o n d u c t i o n electron spin polarization. In the CeSi~ system the coupling of Ce spin and Si nuclear spin via c o n d u c t i o n electrons is considered to be larger than the coupling of the dipole interaction, which is calculated to be 0.5 k O e / # B.
3.2. T:
:i
1.5
% 1.0
A 2.0 × O •
,,~ 0.5
1.9 1.86 1.7
Ahf = 6.0 kOe//U B I
00
'
'
'
5
'
'
I
]
10
I '
I '
I
'5
x10
-3
,,~ ( e m u / m o l e ) Fig. 2. 29Si Knight shift vs. bulk molar susceptibility in CeSi.,.
T 1 of 29Si was measured in the p a r a m a g n e t i c state a n d the t e m p e r a t u r e d e p e n d e n c e is shown in fig. 3. F o r x = 2.0, 1 / T 1 is p r o p o r t i o n a l to T at 1.3-300 K. For x = 1.9, 1 / T 1 is proportional to T at 1.3-90 K a n d deviates slightly to smaller values from the Korringa relation above 90 K. For x = 1.86, 1 / T 1 is proportional to T at 1.3-10 K a n d deviates to smaller values above 10 K. For x = 1.8 and 1.7, the system sets in the ferromagnetic state a r o u n d 10 K. W e observe 29Si N M R a b o v e 20 K in these compounds. F o r x = 1.8, 1 / T 1 is nearly t e m p e r a t u r e i n d e p e n d e n t at 2 0 - 3 0 0 K. For x = 1.7, 1 / T 1 is nearly p r o p o r t i o n a l to 1 / T at 3 0 - 1 0 0 K b e c o m i n g t e m p e r a t u r e i n d e p e n d e n t above 100 K. The observed 1 / T 1 is considered to be the sum of the relaxation due to Ce spin fluctuations, (1/T1)4t, a n d that due to the c o n d u c t i o n electron at the Si site, (1/T1)si ' 1 / T 1 = ( I / T 1 ) 4 r + (1/T1)si. (1/T1)4f may be o b t a i n e d by a subtraction of ( I / T 1)si from the observed 1/T~. ( 1 / T l ) s i is usually estimated from T 1 of the
Y. Kohori et aL / Dense Kondo s~'stern Ce- Si isostructural non-magnetic compound. For this purpose we measured 1/7"1 of :gsi in LaSi 2 and YSi 2, which are 0.64T s -~ and 0.025T s - L respectively. 1/7"1 in'LaSi~ is 2 times larger than in CeSi 2, moreover, 30 times larger than in YSi 2. The value is so sensitive to the species of cation that we could not estimate (1/T1)si for CeSi x from the non-magnetic compounds. So we try to estimate (1/T])si in CeSi.~ from an analysis of the temperature dependence of T] of x = 1.7 at high temperature as follows. Between 30 and 100 K, 1/T~ becomes nearly proportional to l / T , which indicates that the Korringa relaxation of the Ce spin is responsible for the temperature dependence. On the other hand 1/T~ becomes nearly temperature independent at higher temperature. This temperature independent 1/7"1 may be explained as the superposition of (1/T~)4~ and ( 1 / T 1)si which are proportional to 1 / T and T, respectively. The observed relaxation rate is well explained in this way as shown in fig. 3. Then (1/T])si for x = 1.7 is estimated to be 0.31T s ~ by subtracting (1/Tt)4~, that is extrapolated from the region of 7"1 ec T, from the observed 1/7"1. In CeSi~ system, it seems natural to take this value for (1/T~)si in the first approximation. The value of (1/T])si thus deduced is nearly equal to the value of 1/T~ for x = 2.0. For x = 2.0, (l/T1)4f is considered to be much smaller than ( 1 / T ~ ) s r Nextly we shall analyze (1/7"1)4~ to obtain the information about the fluctuation of Ce spin. In the standard
'
'
' ''"'1
'
'
' ''"'1
'
'
'
'
%. 1.7
'1"-~o4"-~.o.3~T
ooo~ o 1.8
.....
e
"~,-~,-'~
100
O, 0 ~, <><> ¢ 0<>0 ¢ ~ / ~ ,
,"
o. ~><><>
~10
=-
C. , / 1.86 ,6"
relaxation theory [4], 1/T] is expressed as
1/7"i = 2y2A~fkBTx'reff,
where Ahf is the hyperfine coupling constant, Yn is the nuclear gyromagnetic ratio, X is the susceptibility and Telf is the effective electronic spin correlation time. For the quantitative analysis, the value of the hyperfine coupling is necessary. The dipole coupling between each Ce 4f moment and 29Si moment can be easily calculated. On the other hand the contribution of the R K K Y coupling is difficult to be estimated. In this system the latter contribution seems to be larger than the former as discussed previously. We tentatively assume A hf = 6.0 kOe/t~B deduced from the Knight shift data. Using T~, Ah] and X [2], we estimate t~f] from eq. (1). The obtained 1/'r~ff for x = 1.7, 1.8, 1.86 and 1.9 are shown in fig. 4. For x = 1.7, 1/%ff varies proportionally to T as 2.7 × 10lIT s - L indicating that the Korringa relaxation is responsible for the temperature dependence. The trivalent state is stable in x = 1.7. For x = 1.8, 1/'re, follows the Korringa relation at high temperature, while it deviates to larger values above 120 K. The fact that the deviation starts at higher temperature in x = 1.8 than x = 1.7 suggests that the deviation from the Korringa law is associated with the Kondo effect. For x = 1.86, 1/%ff decreases gradually below 300 K and becomes temperature independent at low temperatures. For x = 1.9, 1/~'~, is nearly temperature independent below 170 K, which is larger than that for x = 1.86. The temperature independent 1/'r~, corresponds to the Tlinear behavior of (I/T1)4r. This means that the system is in the Fermi liquid state ( T < TK). Then 1/?~ff may be of order kBTK/h in this temperature range. For x = 1.86, 1/1-~, corresponds to = 150 K, which is larger than = 50 K in another estimation [2]. We consider that
M" z~ /
i
,~/,, "I.,.0.31-T
,"
..
i
1.9
,
' ' ' " l
'
x
Tu 1(~4
1.9, .~." /
-29Si
"2.0
,
,,
" ~
NMR
,
10
,
,,,,,11
¢
'~
f =IO.OMHz
,~,1
o o,,'-
CeSix
~'""
,
'''"1
A
I.-
/ z x""
'
N
-
,= tx"~"
7_
(1)
,~,z,"
,/ /0"
Tu
~"
351
o
I~
i
I
I
100 T(K)
Fig. 3. The temperature dependence of 1/7"1 of 298i in CeSi,.
i
i
~"
o 0 o ,w -I ¢ O0o~' oo o o e , , . ~ " ~ e f p c T
~' o
i
0
°°"
ol.8e
iiiJlI
i~../
L /L
10
.,.
L ll,,,I
i
i
i
100 TCK)
Fig. 5. The temperature dependence of the Ce spin fluctuation rate, 1/~"¢u, in CeSi,.
352
Y. Kohori et al. / Dense Kondo system C e - Si
this descrepancy is attributed to an overestimation of the hyperfine coupling constant. In conclusion, the main features of (1/T1)4f a n d 1/%ff are well explained with the model of dense K o n d o system in which T K decreases rapidly with decreasing Si concentration.
References [1] H. Yashima, T. Satoh, H. Mori, D. Watanabe and T. Ohtsuka, Solid State Commun. 41 (1982) 1.
[2] H. Yashima and T. Satoh, Solid State Commun. 41 (1982) 723. [3] H. Yashima, H. Mori, T. Satoh and K. Kohn, Solid State Commun. 43 (1982) 193. [4] J. Aarts, F.R. de Boer and D.E. MacLaughlin, Physica 121B (1983) 162.
349
29Si N M R S T U D Y OF T H E D E N S E K O N D O S Y S T E M C e - S i Y. K O H O R I ,
K. A S A Y A M A
Department of Physics, Faculty of Science, Kobe University, Nada-Ku, Kobe 657, Japan T. K O H A R A
College of Liberal Arts, Kobe University, Nada- Ku, Kobe 657, Japan N. S A T O , H. Y A S H I M A ,
H. M O R I a n d T. S A T O H
Department of Physics, Faculty of Science, Tohoku Unioersity, Sendal 980, Japan
Nuclear spin lattice relaxation rate, 1 / T 1, of 29Si has been measured in CeSi x for x = 1.7-2.0. The result shows that the trivalent state is stable for 1.7-1.8 at high temperature, and that the system is in the Fermi liquid state at low temperature for x > 1.86.
1. Introduction The rare-earth intermetallic compound CeSi 2 has a tetragonal a-ThSi 2 type structure and exhibits various anomalies associated with the intermediate valence or the K o n d o effect [1]. The magnetic property was found to be highly sensitive to the stoichiometry. The specific heat and the susceptibility measurements were extended to the Si-deficient CeSi x systems. It was found that the spin fluctuation temperature, T K, decreases with decreasing Si content and that the system undergoes a ferromagnetic state for the composition x < 1.83 [2,3]. In order to get further insight into the magnetic property of Ce ions, it is desirable to study the system from the microscopic point of view. In this paper we report the result of 29Si N M R measurements. The Knight shift, K, and the nuclear spin lattice relaxation time, T 1, provide the static and dynamical information of the magnetic environment of the nuclei. A special interest lies in obtaining a unified view of the microscopic nature of unstable Ce ion systems in which T K changes over the range of a few hundreds kelvin.
2. Experimental The polycrystalline specimens were prepared by melting the constituents together in an arc furnace and annealing the product at 950°C for 3 weeks. The speci0304-8853/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
mens were then crushed into powder for the N M R experiment. The measurement was performed with a standard phase coherent spectrometer at a resonance frequency of 10 M H z over the temperature range 1.3-300 K. The Knight shift was measured with respect to the 11B resonance in B(COH3) 3 by assuming the ratio of the gyromagnetic ratios y ( 2 9 S i ) / y ( N B ) = 8.458/13.660. T 1 was measured at the peak position of the spectrum by recording the recovery of the spin echo intensity after the saturating pulses.
3. Results and discussions 3.1. Knight shift Fig. l a shows the 29Si N M R spectrum of the stoichiometric sample, x = 2.0. The position of the peak is nearly temperature independent indicating that x = 2.0 is non-magnetic. As seen in fig. la, there is a small tail in the low field side whose width increases with decreasing temperature. This tail would be attributed to the magnetic Ce ion which may be associated with a small amount of Si vacancies. Fig. l b shows the temperature dependence of the spectrum of x = 1.86. The spectrum has positive shift and is anisotropic. The anisotropic spectrum is considered to be due to the distribution of Ce moments. We determine the shift at the first moment of the spectrum
Y. Kohori et al. / Dense Kondo system C e - Si
350
~
K=O
A
,,•
O I.--
...... , ~ t , /
52K
Z
33 K
Z
CeSi 2.0
n,"
eSi 1.86
42K
z
J~ 4.2K
I
I
I
114
I
116
I
I
11.8 H(k0 e )
1 .0 H(kOe)
Fig. 1. (a) 29Si spectra in CeSi2o at 4.2, 52 and 84 K; (b) 29Si spectra in CeSil.~6 at 4.2, 33 and 52 K.
from K = 0, which is plotted in fig. 2 against the susceptibility with t e m p e r a t u r e as an implicit parameter. T h e results of other Si concentration are also shown in fig. 2. For each sample, the K n i g h t shift is nearly p r o p o r t i o n a l to the susceptibility. F r o m the slope in the K n i g h t shift vs. susceptibility plot, the hyperfine field is o b t a i n e d to be 6.0 k O e / # B, which is nearly i n d e p e n d e n t of the Si content.
In a system in which the local m o m e n t s reside on the crystal lattice, the isotropic shift is induced by the c o n d u c t i o n electron spin polarization. In the CeSi~ system the coupling of Ce spin and Si nuclear spin via c o n d u c t i o n electrons is considered to be larger than the coupling of the dipole interaction, which is calculated to be 0.5 k O e / # B.
3.2. T:
:i
1.5
% 1.0
A 2.0 × O •
,,~ 0.5
1.9 1.86 1.7
Ahf = 6.0 kOe//U B I
00
'
'
'
5
'
'
I
]
10
I '
I '
I
'5
x10
-3
,,~ ( e m u / m o l e ) Fig. 2. 29Si Knight shift vs. bulk molar susceptibility in CeSi.,.
T 1 of 29Si was measured in the p a r a m a g n e t i c state a n d the t e m p e r a t u r e d e p e n d e n c e is shown in fig. 3. F o r x = 2.0, 1 / T 1 is p r o p o r t i o n a l to T at 1.3-300 K. For x = 1.9, 1 / T 1 is proportional to T at 1.3-90 K a n d deviates slightly to smaller values from the Korringa relation above 90 K. For x = 1.86, 1 / T 1 is proportional to T at 1.3-10 K a n d deviates to smaller values above 10 K. For x = 1.8 and 1.7, the system sets in the ferromagnetic state a r o u n d 10 K. W e observe 29Si N M R a b o v e 20 K in these compounds. F o r x = 1.8, 1 / T 1 is nearly t e m p e r a t u r e i n d e p e n d e n t at 2 0 - 3 0 0 K. For x = 1.7, 1 / T 1 is nearly p r o p o r t i o n a l to 1 / T at 3 0 - 1 0 0 K b e c o m i n g t e m p e r a t u r e i n d e p e n d e n t above 100 K. The observed 1 / T 1 is considered to be the sum of the relaxation due to Ce spin fluctuations, (1/T1)4t, a n d that due to the c o n d u c t i o n electron at the Si site, (1/T1)si ' 1 / T 1 = ( I / T 1 ) 4 r + (1/T1)si. (1/T1)4f may be o b t a i n e d by a subtraction of ( I / T 1)si from the observed 1/T~. ( 1 / T l ) s i is usually estimated from T 1 of the
Y. Kohori et aL / Dense Kondo s~'stern Ce- Si isostructural non-magnetic compound. For this purpose we measured 1/7"1 of :gsi in LaSi 2 and YSi 2, which are 0.64T s -~ and 0.025T s - L respectively. 1/7"1 in'LaSi~ is 2 times larger than in CeSi 2, moreover, 30 times larger than in YSi 2. The value is so sensitive to the species of cation that we could not estimate (1/T1)si for CeSi x from the non-magnetic compounds. So we try to estimate (1/T])si in CeSi.~ from an analysis of the temperature dependence of T] of x = 1.7 at high temperature as follows. Between 30 and 100 K, 1/T~ becomes nearly proportional to l / T , which indicates that the Korringa relaxation of the Ce spin is responsible for the temperature dependence. On the other hand 1/T~ becomes nearly temperature independent at higher temperature. This temperature independent 1/7"1 may be explained as the superposition of (1/T~)4~ and ( 1 / T 1)si which are proportional to 1 / T and T, respectively. The observed relaxation rate is well explained in this way as shown in fig. 3. Then (1/T])si for x = 1.7 is estimated to be 0.31T s ~ by subtracting (1/Tt)4~, that is extrapolated from the region of 7"1 ec T, from the observed 1/7"1. In CeSi~ system, it seems natural to take this value for (1/T~)si in the first approximation. The value of (1/T])si thus deduced is nearly equal to the value of 1/T~ for x = 2.0. For x = 2.0, (l/T1)4f is considered to be much smaller than ( 1 / T ~ ) s r Nextly we shall analyze (1/7"1)4~ to obtain the information about the fluctuation of Ce spin. In the standard
'
'
' ''"'1
'
'
' ''"'1
'
'
'
'
%. 1.7
'1"-~o4"-~.o.3~T
ooo~ o 1.8
.....
e
"~,-~,-'~
100
O, 0 ~, <><> ¢ 0<>0 ¢ ~ / ~ ,
,"
o. ~><><>
~10
=-
C. , / 1.86 ,6"
relaxation theory [4], 1/T] is expressed as
1/7"i = 2y2A~fkBTx'reff,
where Ahf is the hyperfine coupling constant, Yn is the nuclear gyromagnetic ratio, X is the susceptibility and Telf is the effective electronic spin correlation time. For the quantitative analysis, the value of the hyperfine coupling is necessary. The dipole coupling between each Ce 4f moment and 29Si moment can be easily calculated. On the other hand the contribution of the R K K Y coupling is difficult to be estimated. In this system the latter contribution seems to be larger than the former as discussed previously. We tentatively assume A hf = 6.0 kOe/t~B deduced from the Knight shift data. Using T~, Ah] and X [2], we estimate t~f] from eq. (1). The obtained 1/'r~ff for x = 1.7, 1.8, 1.86 and 1.9 are shown in fig. 4. For x = 1.7, 1/%ff varies proportionally to T as 2.7 × 10lIT s - L indicating that the Korringa relaxation is responsible for the temperature dependence. The trivalent state is stable in x = 1.7. For x = 1.8, 1/'re, follows the Korringa relation at high temperature, while it deviates to larger values above 120 K. The fact that the deviation starts at higher temperature in x = 1.8 than x = 1.7 suggests that the deviation from the Korringa law is associated with the Kondo effect. For x = 1.86, 1/%ff decreases gradually below 300 K and becomes temperature independent at low temperatures. For x = 1.9, 1/~'~, is nearly temperature independent below 170 K, which is larger than that for x = 1.86. The temperature independent 1/'r~, corresponds to the Tlinear behavior of (I/T1)4r. This means that the system is in the Fermi liquid state ( T < TK). Then 1/?~ff may be of order kBTK/h in this temperature range. For x = 1.86, 1/1-~, corresponds to = 150 K, which is larger than = 50 K in another estimation [2]. We consider that
M" z~ /
i
,~/,, "I.,.0.31-T
,"
..
i
1.9
,
' ' ' " l
'
x
Tu 1(~4
1.9, .~." /
-29Si
"2.0
,
,,
" ~
NMR
,
10
,
,,,,,11
¢
'~
f =IO.OMHz
,~,1
o o,,'-
CeSix
~'""
,
'''"1
A
I.-
/ z x""
'
N
-
,= tx"~"
7_
(1)
,~,z,"
,/ /0"
Tu
~"
351
o
I~
i
I
I
100 T(K)
Fig. 3. The temperature dependence of 1/7"1 of 298i in CeSi,.
i
i
~"
o 0 o ,w -I ¢ O0o~' oo o o e , , . ~ " ~ e f p c T
~' o
i
0
°°"
ol.8e
iiiJlI
i~../
L /L
10
.,.
L ll,,,I
i
i
i
100 TCK)
Fig. 5. The temperature dependence of the Ce spin fluctuation rate, 1/~"¢u, in CeSi,.
352
Y. Kohori et al. / Dense Kondo system C e - Si
this descrepancy is attributed to an overestimation of the hyperfine coupling constant. In conclusion, the main features of (1/T1)4f a n d 1/%ff are well explained with the model of dense K o n d o system in which T K decreases rapidly with decreasing Si concentration.
References [1] H. Yashima, T. Satoh, H. Mori, D. Watanabe and T. Ohtsuka, Solid State Commun. 41 (1982) 1.
[2] H. Yashima and T. Satoh, Solid State Commun. 41 (1982) 723. [3] H. Yashima, H. Mori, T. Satoh and K. Kohn, Solid State Commun. 43 (1982) 193. [4] J. Aarts, F.R. de Boer and D.E. MacLaughlin, Physica 121B (1983) 162.