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29Si nuclear magnetic resonance and relaxation in the paramagnetic state of CeCu2Si2
Physica 121B (1983) 162-168 North-Holland Publishing Company
%i NUCLEAR MAGNETIC STATE OF CeCu& J. AARTS
and F.R.
RESONANCE
AND RELAXATION
IN THE P ARAMAGNETIC
de BOER
Natuurkundig Laboratorium der Uniuersitei? van Amsterdam, 1018 XE Amsterdam, The Netherlands
D.E.
MacLAUGHLlN
Physics Department, University of California, Riverside, California 925.21, USA Received 17 September 1982 Revised IS November 1982 *‘Si nuclear magnetic resonance (NMR) and relaxation studies of the unstable-moment compound CeCuzSiz have be-n carried out to probe the electronic state of the nearly-trivalent Ce ions. Isotropic and anisotropic NMR shifts indicate effects of both crystalline electric fields (CEF) and low-temperature moment reduction on the Ce ionic states. A relatively large anisotropic shift was observed at low temperatures, and also obtained from a CEF-state calculation in the molecular-field approximation. The hyperfine coupling also appears to be anisotropic, although this is not manifested in the temperature dependence of the shift due to changing CEF-state populations. NMR estimates of the Ce-spin fluctuation time vary with temperature in a manner similar to the neutron quasielastic scattering linewidth at high temperatures, but suggest the onset of spatially coherent fluctuations.
The
compound
position
among
intermetallics
CeCu& the
[l].
occupies
unstable-moment
No magnetic
ved; there is almost
order
no anomaly
a unique
reported
Ce-based
[3].
is obser-
related
in the difference
will
static susceptibility
Nuclear
spin-lattice
data of Lieke relaxation
to the Ce ionic spin fluctuation
be
compared
to
the
width
r/2
quasielastic
would be indicative
The samples were prepared by arc stoichiometric quantities of the elements
and
at 0.6 K a transition
conducting to involve
occurs
valence into
(IV);
a super-
state which, most remarkably, seems Cooper pairing between 4f electrons
[ 1,3]. Further information on the microscopic behavior of this unusual compound is clearly of interest. In previous resonance
work
(NMR)
[4-61
nuclear
and relaxation
magnetic
measurements
have been used to probe the local static and dynamic magnetism of unstable-moment systems. This paper reports the results of 29Si NMR in CeCuzSiz and LaCuzSiz. The *‘Si resonance is well suited to NMR measurements, since I = 4 and there is no quadrupole interaction. Determination of spectrum centroids and saturation in pulsed spin-lattice relaxation measurements are thereby simplified. NMR paramagnetic shifts will be discussed
in connection
037%4363/83/000~000/$03.00
with the previously0
1983 North-Holland
trum as reported
are
time, and
between the thermal expansion of CeCu& and the non-magnetic isomorph LaCu2Si2 [2], which of intermediate
line in the neutron
et al.
rates of
scattering
the spec-
by Horn et al. [7]. melting Cu, Si,
and Ce or La. They were subsequently annealed at 1120°C for 100 h to improve sample quality [3]. As a result no indications of a second phase could be found in Guinier-De Wolff X-ray NMR absorption spectra and measurements. relaxation
rates
in the
300 K were obtained [S]. The
temperature
using spin-echo
shift was measured
range
I.5
techniques
with respect
to the
27Al resonance in a saturated AK& solution, assuming the ratio of gyromagnetic ratios -y(29Si)/y(27Al) = 8.458/l 1.094 [8]. Fig. 1 gives the temperature dependence of the isotropic static molar susceptibility ,Y,, of a polycrystalline specimen of CeCu$$, obtained after correcting the measured susceptibility for an impurity contribution as decribed previously [3]. Fig. 2 gives the dependence of the 29Si isotropic
J. Aarts et al. I “Si NMR
% t=. L. I
r
1 +I
LOO
xm l .
50[
10-g m3 mole1 .
200
tc*y
/y
//
,Y
100
T [Kl -
n I ,’
I
"0
n
I
200
100
300
”
Fig. 1. Temperature dependence of the impurity-corrected bulk molar susceptibility ,y,,, of CeCu&. Circles: measured susceptibility. Triangles: measured inverse susceptibility. Dash-dot curve: inverse susceptibility (,&JO calculated from eq. (3) in the presence of CEF splitting of the Ce3’ J = 5 manifold. Dashed lines are guides to the eye.
frequency shift Ki, on x,,,, with temperature as an implicit parameter. Above 77 K our results agree well with those of Sampathkumaran et al. [9]. Kisstim) is found to be linear from room temperature down to 7 K, as expected from the relation
(1)
Kiss = (HdNPB)Xm 0.91 0.8-
I
I
I
I 292
0.70.6-
I
I
I 78
,
I
I
TlKl -
I 1 107 ‘/
t K,sol%~
0.5-
0’
0.1 -
0.
I
I
**
_
P0
t**
03-
+4
Ce Cu2 Si2
4+*
1 -01I I I I I 1 1 1 1 X cofr [l”-g$e
0
50
--
100
Fig. 2. Dependence of the ‘%i isotropic frequency shift Ki, on bulk molar susceptibility x,,, in CeCu2Siz. Circles: this work. Crosses: ref. [9]. Triangle: Ki, and x,,, of LaCuzSi2 at 77 K. The line is a guide to the eye.
and relaxation in CeChSi2
163
for the shift due to a single, temperature-independent, transferred hyperfine field & [8]. Here N is Avogadro’s number and pa in the Bohr magneton. The linearity of Kimtim) in CeCu& is in contrast to the behavior of Kim in another unstable-moment system, CeAl*, [5], where crystalline electric field (CEF) splitting of the Ce3+ J = $ manifold, together with anisotropy in Hhf, leads to a pronounced departure from linearity. The present results seem to suggest that Hhf is sensibly isotropic in CeCu&, since appreciable CEF splitting has been established by inelastic neutron scattering [7]. (See, however, the discussion of anisotropic shift measurements below.) The value of Hhf obtained from the slope of Kiwhm) is 5.1 ? 0.3 kOe/pB. A small anomaly is discernible at low temperatures in fig. 2, where Kim lies above the extrapolated high-temperature line for the four points measured below 7 K. Such an increase is also observed in a number of well-characterized IV compounds [lo], where it is tentatively attributed to the onset of hyperfine-coupling enhancement in a correlated 4f state. In CeCu& this anomaly occurs at comparatively low temperatures, due perhaps to a low spin-fluctuation temperature: Td- 10 K from the low-temperature quasielastic neutron linewidth [4, 111. It should be noted, however, that the susceptibility correction [3] involves application of high fields ~BH - k,T,. The correction technique is invalid if these high fields significantly alter the state of the system. It should also be noted that the observed anomaly between 4 and 7 K (AKobs-0.04%) cannot be accounted for by the demagnetization correction [5,8] (AK,,,, - 0.008%) calculated using the measured (uncorrected) susceptibility [3]. But AKobs and AK,, are comparable between 2 and 4 K. The value of Kim extrapolated to x,, = XPauli(LaCU*SiZ) = 3 X 10d9 m3/mole is very small compared to the much larger shift in LaCu& [12], also shown in fig. 2. If the conduction bands of the two compounds were similar, one would expect these quantities to be comparable, in which case Kiwkm) would have to be curved above 300 K. This might indeed occur as an effect of CEF and an anisotropic Hhf [5], especi-
J. Aarts et al. / “Si NMR
164
ally since large CEF splittings (-300 K) are found from neutron scattering (71. Further shift and susceptibility measurements are under way to investigate this point; see also the shift data of ref. [c)]. At low temperatures the NMR line developed considerable anisotropy, as shown in fig. 3. The anisotropic shift K, was extracted from the Van Hove singularities in the powder-pattern spectrum, taking Gaussian broadening into account [ 131, and is given in fig. 3(c). At 4.2 K the observed values of K, = -0.2% are an order of magnitude larger in absolute value than the dipolar contribution (Ka)dip = -0.015%, calculated as previously described [14]. This suggests that anisotropy of the static susceptibility is important, if one assumes that Z&f is isotropic. We have calculated the ground-state susceptibility using a CEF scheme suggested by the neutronscattering data [7], and we indeed find considerable anisotropy. This might be expected, since the crystallographic unit cell is tetragonal. Our calculation is based on the following from of the CEF Hamiltonian: Y&F = z$o;
+ sllop
+ B$O$ ,
(2)
where the operators B:: and 0: are as defined by Hutchings [lS]. The values used for the B:: were taken from ref. [7], and the resulting level splittings and wave functions are given in table I. Our result is diflicult to compare directly with since the calculated powderK,, however, average (i.e. isotropic) susceptibility 2 Cvisohl
=
1
(3)
j XI + j XII
and relaxation
7L2
BUZ
-3.5 8.5
89
-0.40 0.37
11)=1*1/2), B%
-6.25 5.7
7L3
736
739
7L2
Fig. 3. (a) “Si spectrum in CeCu2Sil at 4.2 K. The Van Hove singularities, from which the anisotropic shift K, is obtained. are indicated. (b) %i spectrum at 77 K; the anisotropic shift is too small to be resolved. (c) Temperature dependence of K,.
considerably overestimates the measured susceptibility of a polycrystalline specimen (see fig. 1). Here xl and XII are the calculated CEF susceptibilities perpendicular and parallel to the tetragonal c axis, respectively. The reduction in the measured susceptibility presumably arises either from moment instability (Kondo-lattice formation or IV), or from antiferromagnetic correlations between uncompensatred Ce moments at high temperatures. Either of these mechanisms could give rise to a negative paramagnetic Curie-Weiss temperature as observed (0, = -140 K). In either case a phenomenological description of the resulting susceptibility might be attempted with the help of a molecular-field-like parameter A:
Table I CEF parameters, energy splittings, and wave functions (b) alternative CEF scheme (see text) 12) = cl\ f S/2) - c,I 5 3/2),
in CeCu&
IO) = c,l
for: (a) CEF scheme
”
from ref. [7];
S/2) + ~215 3/2)
Ei1,- Eli,, (W
EIZ)- ElII) (W
Cl
Q
144 144
360 360
0.83 -0.49
0.56 0.87
J. Aarts et al. / “Si NMR and relaxation
in CeCuL%
165
IIIIII~~~
I,,,III,I
-i _i
(4)
_I,
Note that A simply extends a Curie-Weiss-like description of the susceptibility to the case of non-zero CEF splittings, and does not necessarily signify an exchange interaction between spins. The values of A obtained by setting hi,)A given by eq. (4) equal to the experimental A,,, are shown in fig. 4. The temperature dependence of A below 60 K signifies a breakdown of CurieWeiss behavior. Nevertheless, we shall use A(T) below 60 K to obtain an estimate of the anisotropic susceptibility from the expression
(5) assuming that A is isotropic. The quantity xti is plotted in fig. 5, together with K, and xao= k&+ It can be seen that Ati, in contrast to ~~(1, has the same temperature dependence as K, [after subtraction of a constant term K,(T = 0) = -O.lS%], at least below -5OK. However, the slope (dKJdxaA) is an order of magnitude larger than found for the isotropic shift and susceptibility (dKi,/dXm) from the data of fig. 2, which is in conflict with the hypothesis of an isotropic Hhf. Obviously susceptibility measurements on single-crystal samples are needed for a direct determination of the anisotropy of Hhf. We have also checked the sensitivity of xan to the CEF parameters by calculating it in another CEF scheme, chosen as follows: Assuming that
I
I
I
I
t
0
100
200
I
I
300
Fig. 4. Temperature dependence of the molecular-field-like parameter A, obtained from fits of the experimental bulk susceptibility of CeCurSir to eq. (4). The dashed line is a guide to the eye.
50-
?,
\
/
\ \
-
0 -:
_
Ia1 Ibl
[,()-gd-1
/ ‘\
(dl
0
0
TIKI 50
l
t K,I%l
l
--01
0
t l
0
0
I I I I I 0
.
\ ,/--‘_M
IIIIIIII1
0 0
/’
-2 -1
1
-5-\
N-L \
/’
I I I I
ICI
1
r----.
I/ I’
‘... . .. . -.-._ _----__ : ; I I r7 :>
t x, bo-g * moe
t xalj”-g&j-
TIKI-
IIIIIIIII 50
Fig. 5. (a) Theoretical anisotropic susceptibility xa,, (dash-dot line) and xti (dashed line) of CeCurSir. The latter is calculated in the molecular-field approximation, eq. (5) of the text. The h’s used are those obtained with the CEF parameters of ref. 171. (b) x.*, as in (a) above, on an expanded scale. (c) x.~ from the alternative CEF scheme discussed in the text. (d) Experimental ?ji anisotropic shift in CeCurSir.
the level splittings are determined by the neutron scattering data [7], there are still a number of possibilities for B$!, II:, and B%. For constant Bj/BO, there are two sets of CEF parameters, which naturally yield quite different wave functions. These are also given in table I. The procedure described above was then used to calculate A(T) and xar_ It is interesting to note that A(T) was found to be insensitive to the choice of CEF parameters. The results for Aa,, obtained from both sets of CEF parameters are shown in fig. 5, and it can be seen that the second set gives a result which differs qualitatively from the observed K,(T). Although this result corroborates the original choice of CEF parameters [7], the caveats of the previous paragraph should be kept in mind. Turning now to spin-lattice relaxation measurements, fig. 6 gives the temperature dependence of the ?Gi spin-lattice relaxation rate T;‘. These data resemble T;‘(T) found in another unstable-moment compound, CeAI, [5]. Below 30 K, relaxation measurements were
J. Aarts et al. / 29SiNMR And relaxation in CeCu&
166
Ce Cu2G2
* I
505
_
LO{ . 30L 1 2o
IO0
1
T;lkl 3
0
I 50
I 100
I 5
I 10
3q
1 0
i-
TIKI I 150
TLKI I 15
I 200
20
Fig. 6. (a) Temperature dependence of the “Si nuclear spinlattice relaxation rate Ti’ in CeCurSir. (b) Anisotropic spinlattice relaxation rates observed at low temperatures. Triangles show Ti!, squares show Til{.
made at the powder-pattern singularities which correspond to Si-site tetragonal axes perpendicular and parallel to the applied field. These measurements yielded the relaxation rates T;: and T$, respectively. The spectrometer bandwidth was adjusted to be much smaller than the splitting. It can be seen from fig. 6 that anisotropy is also present in the relaxation. In analogy with the definitions of Kim and K, we define
duction-electron contributions to the observed Ki, and T;‘. NMR data obtained from LaCu& shown in table II, can be used as estimates of the corresponding values in CeCu&, and the 4f components (Ki,), and (T;‘)t can then be obtained by subtraction. Alternatively, the nearly zero Kiwhm) intercept of fig. 2 can be taken as evidence for negligible conductionelectron contributions to both Ki, and T;’ in CeCu&. Fig. 7 gives the temperature dependence of h/~,~ calculated on both of these hypotheses, as well as the width r/2 of the quasielastic neutron scattering line [7]. Several features emerge from this analysis: corrections, not sur(1) The conduction-electron prisingly, are most important at high temperatures. The NMR estimates of h/7,* lie above r/2, as is (2) also found for CeAI*. continue to depend on (3) The NMR estimates -10 K, and even lie temperature below somewhat below the quasielastic neutron linewidth r/2( T + 0) = 1 meV [7]. At high temperatures fluctuations of neighboring Ce spins should not be substantially correlated. In this case, the fact that each 2’Si Ce nucleus is coupled to several neighboring
and
An NMR estimate of the effective Ce-spin fluctuation rate T;A can be obtained from T;‘, Kis”, and x,,, as described previously [4, S]. The relation between these quantities is 7;; = 2Ny*ks[(K,,):lT,~TIxmrl
3
where the subscript f indicates the 4f component of the quantity involved. It is difficult, however, to determine the con-
Fig. 7. Temperature dependence of estimated Ce spinfluctuation rates (expressed in energy units) in CeCu&. Open circles: Estimates obtained from NMR data and eq. (7). Filled circles: Estimates obtained from NMR data, corrected for conduction-electron contributions to K, and Ti’ using Nh4R measurements in LaCu&. Triangles: neutron quasielastic linewidth r2. Drawn lines are guides to the eye.
J. Aarts et al. / 29Si NMR
Table I1 %i isotropic Knight shift Ki, and spin-lattice relaxation time-temperature product TIT in the nonmagnetic reference compound LaCu2Siz, measured for comparison with data from CeCuzSiz T (K) 4.2 71.3
Kim (%) 0.084 * 0.01 0.087 5 0.02
TIT (s K) 39.5 -t 49?8
1.3
and relaxation
in C&u&
167
from CEF effects. Around the latter temperature a small increase in transferred hyperfine interaction, as well as the changing ratio (h/~,&(r/Z), suggest the onset of spatial correlation between Ce spins. Further experiments will probe the effect of superconductivity on the magnetic environment of “3Cu nuclei, via nuclear quadrupole resonance in zero applied field.
Acknowledgements spins results in a ratio (h/~,&(r/2) which is greater than unity [4,5]. The experimental ratio is uncertain by at least the correction discussed above, but is comparable to the number of 5 nearest Ce neighbors to a Si site. The difference in temperature dependence between h/~,~ and r/2 at low temperatures is probably due to the onset of spatial correlation between Ce-spin fluctuations. The fact that h/~~~ continues to vary below -10 K suggests that the low-temperature coherent ground state is not yet fully formed at this temperature. As for the observed anisotropy in T;‘, from eqs. (1) and (7) we note that
We are grateful for several useful discussions with P.F. de Chitel, G.J. van het Hof, M.J. Lysak, and 0. Peiia. One of us (J.A.) would like to thank the staff of the Physics Department of the University of California, Riverside, for their hospitality and assistance during his stay there, which was made possible by a grant of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM). This work was supported by the U.S. National Science Foundation, Grant No. DMR-7810301, and by the FOM.
References that if Hhf and T,~ are isotropic the anisotropy in T;’ should be the same as that in x, hence in K. But the ratio (KJKi,) becomes more negative with decreasing temperature, whereas (T;pT;f) remains roughly constant. This may indicate the onset, below 10 K, of anisotropy in the fluctuation rate itself: fluctuations parallel to the tetragonal axis may live longer than fluctuations perpendicular to it. But anisotropy in h/~,~, like anisotropy in Hhf, can only be determined through susceptibility measurements in single crystals. In summary, considerable structure has been found in NMR shifts and relaxation rates in paramagnetic CeC@i. After taking the anomalously reduced susceptibility (for which no satisfactory explanation has been given) into account, the evidence points to an electronic state of the system which remains essentially unchanged from 300 K down to about 10 K, apart so
[l] F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz and H. Sch%fer, Phys. Rev. Letters 43 (1979) 1982. [2] W. Franz, A. Griessel, F. Steglich and D. Wohlleben, Z. Phys. 31 (1978) 7. [3] W. Lieke, U. Rauchschwalbe, C.D. Bredl, F. Steglich, J. Aarts and F.R. de Boer, J. Appl. Phys. 53 (1982) 2111. [4] D.E. MacLaughlin, F.R. de Boer, J. Bijvoet, P.F. de Chltel and W.C.M. Mattens, J. Appt. Phys. 50 (1979) 2094. [5] D.E. MacLaughlin, 0. PeRa and M. Lysak, Phys. Rev. B23 (1981) 1039. [6] 0. PeRa, M. Lysak, D.E. MacLaughlin and Z. Fisk, Solid State Commun. 40 (1981) 539. [7] S. Horn, E. Holland-Moritz, M. Loewenhaupt, F. Steglich, H. Scheuer, A. Benoit and J. Flouquet, Phys. Rev. B23 (1981) 3171. [8] G.C. Carter, L.H. Bennett and D.J. Kahan, Metallic Shifts in NMR, Progr. Mat. Sci. 20 (1977) 1. [9] E.V. Sampathkumaran, L.C. Gupta and R. Vijayaraghavan, Phys. Letters 70A (1979) 356. [lo] D.E. MacLaughlin, in: Valence Fluctuations in Solids, eds., L.M. Falicov, W. Hanke and M.B. Maple (NorthHolland, Amsterdam, 1981) p. 321.
168
J. Aarts et al. / “Si NMR
[ 1 l] M. Loewenhaupt and E. Holland-Moritz. J. Appl. Phys. so (1979) 7456. (121 E.V. Sampathkumaran, L.C. Gupta and R. Vijayaraghavan, J. Phys. Cl2 (1979) 4323. [13] From a calculation similar to that of J.E. Adams, B.F. Williams and R.R. Hewitt, Phys. Rev. 151 (1966) 238, we find that HL is to be measured at 85% of the peak
and relaxafion in CeCu&
height (on the outside of the peak). and Hii is to be measured at 50% of the shoulder height. These positions are indicated in fig. 3(a). [14] D.E. MacLaughlin and R.R. Hewitt, J. Appl. Phys. 49 (197X) 2121; see also ref. [S]. [IS] N.T. Hutchings, Solid State Phys. I6 (1964) 227.
%i NUCLEAR MAGNETIC STATE OF CeCu& J. AARTS
and F.R.
RESONANCE
AND RELAXATION
IN THE P ARAMAGNETIC
de BOER
Natuurkundig Laboratorium der Uniuersitei? van Amsterdam, 1018 XE Amsterdam, The Netherlands
D.E.
MacLAUGHLlN
Physics Department, University of California, Riverside, California 925.21, USA Received 17 September 1982 Revised IS November 1982 *‘Si nuclear magnetic resonance (NMR) and relaxation studies of the unstable-moment compound CeCuzSiz have be-n carried out to probe the electronic state of the nearly-trivalent Ce ions. Isotropic and anisotropic NMR shifts indicate effects of both crystalline electric fields (CEF) and low-temperature moment reduction on the Ce ionic states. A relatively large anisotropic shift was observed at low temperatures, and also obtained from a CEF-state calculation in the molecular-field approximation. The hyperfine coupling also appears to be anisotropic, although this is not manifested in the temperature dependence of the shift due to changing CEF-state populations. NMR estimates of the Ce-spin fluctuation time vary with temperature in a manner similar to the neutron quasielastic scattering linewidth at high temperatures, but suggest the onset of spatially coherent fluctuations.
The
compound
position
among
intermetallics
CeCu& the
[l].
occupies
unstable-moment
No magnetic
ved; there is almost
order
no anomaly
a unique
reported
Ce-based
[3].
is obser-
related
in the difference
will
static susceptibility
Nuclear
spin-lattice
data of Lieke relaxation
to the Ce ionic spin fluctuation
be
compared
to
the
width
r/2
quasielastic
would be indicative
The samples were prepared by arc stoichiometric quantities of the elements
and
at 0.6 K a transition
conducting to involve
occurs
valence into
(IV);
a super-
state which, most remarkably, seems Cooper pairing between 4f electrons
[ 1,3]. Further information on the microscopic behavior of this unusual compound is clearly of interest. In previous resonance
work
(NMR)
[4-61
nuclear
and relaxation
magnetic
measurements
have been used to probe the local static and dynamic magnetism of unstable-moment systems. This paper reports the results of 29Si NMR in CeCuzSiz and LaCuzSiz. The *‘Si resonance is well suited to NMR measurements, since I = 4 and there is no quadrupole interaction. Determination of spectrum centroids and saturation in pulsed spin-lattice relaxation measurements are thereby simplified. NMR paramagnetic shifts will be discussed
in connection
037%4363/83/000~000/$03.00
with the previously0
1983 North-Holland
trum as reported
are
time, and
between the thermal expansion of CeCu& and the non-magnetic isomorph LaCu2Si2 [2], which of intermediate
line in the neutron
et al.
rates of
scattering
the spec-
by Horn et al. [7]. melting Cu, Si,
and Ce or La. They were subsequently annealed at 1120°C for 100 h to improve sample quality [3]. As a result no indications of a second phase could be found in Guinier-De Wolff X-ray NMR absorption spectra and measurements. relaxation
rates
in the
300 K were obtained [S]. The
temperature
using spin-echo
shift was measured
range
I.5
techniques
with respect
to the
27Al resonance in a saturated AK& solution, assuming the ratio of gyromagnetic ratios -y(29Si)/y(27Al) = 8.458/l 1.094 [8]. Fig. 1 gives the temperature dependence of the isotropic static molar susceptibility ,Y,, of a polycrystalline specimen of CeCu$$, obtained after correcting the measured susceptibility for an impurity contribution as decribed previously [3]. Fig. 2 gives the dependence of the 29Si isotropic
J. Aarts et al. I “Si NMR
% t=. L. I
r
1 +I
LOO
xm l .
50[
10-g m3 mole1 .
200
tc*y
/y
//
,Y
100
T [Kl -
n I ,’
I
"0
n
I
200
100
300
”
Fig. 1. Temperature dependence of the impurity-corrected bulk molar susceptibility ,y,,, of CeCu&. Circles: measured susceptibility. Triangles: measured inverse susceptibility. Dash-dot curve: inverse susceptibility (,&JO calculated from eq. (3) in the presence of CEF splitting of the Ce3’ J = 5 manifold. Dashed lines are guides to the eye.
frequency shift Ki, on x,,,, with temperature as an implicit parameter. Above 77 K our results agree well with those of Sampathkumaran et al. [9]. Kisstim) is found to be linear from room temperature down to 7 K, as expected from the relation
(1)
Kiss = (HdNPB)Xm 0.91 0.8-
I
I
I
I 292
0.70.6-
I
I
I 78
,
I
I
TlKl -
I 1 107 ‘/
t K,sol%~
0.5-
0’
0.1 -
0.
I
I
**
_
P0
t**
03-
+4
Ce Cu2 Si2
4+*
1 -01I I I I I 1 1 1 1 X cofr [l”-g$e
0
50
--
100
Fig. 2. Dependence of the ‘%i isotropic frequency shift Ki, on bulk molar susceptibility x,,, in CeCu2Siz. Circles: this work. Crosses: ref. [9]. Triangle: Ki, and x,,, of LaCuzSi2 at 77 K. The line is a guide to the eye.
and relaxation in CeChSi2
163
for the shift due to a single, temperature-independent, transferred hyperfine field & [8]. Here N is Avogadro’s number and pa in the Bohr magneton. The linearity of Kimtim) in CeCu& is in contrast to the behavior of Kim in another unstable-moment system, CeAl*, [5], where crystalline electric field (CEF) splitting of the Ce3+ J = $ manifold, together with anisotropy in Hhf, leads to a pronounced departure from linearity. The present results seem to suggest that Hhf is sensibly isotropic in CeCu&, since appreciable CEF splitting has been established by inelastic neutron scattering [7]. (See, however, the discussion of anisotropic shift measurements below.) The value of Hhf obtained from the slope of Kiwhm) is 5.1 ? 0.3 kOe/pB. A small anomaly is discernible at low temperatures in fig. 2, where Kim lies above the extrapolated high-temperature line for the four points measured below 7 K. Such an increase is also observed in a number of well-characterized IV compounds [lo], where it is tentatively attributed to the onset of hyperfine-coupling enhancement in a correlated 4f state. In CeCu& this anomaly occurs at comparatively low temperatures, due perhaps to a low spin-fluctuation temperature: Td- 10 K from the low-temperature quasielastic neutron linewidth [4, 111. It should be noted, however, that the susceptibility correction [3] involves application of high fields ~BH - k,T,. The correction technique is invalid if these high fields significantly alter the state of the system. It should also be noted that the observed anomaly between 4 and 7 K (AKobs-0.04%) cannot be accounted for by the demagnetization correction [5,8] (AK,,,, - 0.008%) calculated using the measured (uncorrected) susceptibility [3]. But AKobs and AK,, are comparable between 2 and 4 K. The value of Kim extrapolated to x,, = XPauli(LaCU*SiZ) = 3 X 10d9 m3/mole is very small compared to the much larger shift in LaCu& [12], also shown in fig. 2. If the conduction bands of the two compounds were similar, one would expect these quantities to be comparable, in which case Kiwkm) would have to be curved above 300 K. This might indeed occur as an effect of CEF and an anisotropic Hhf [5], especi-
J. Aarts et al. / “Si NMR
164
ally since large CEF splittings (-300 K) are found from neutron scattering (71. Further shift and susceptibility measurements are under way to investigate this point; see also the shift data of ref. [c)]. At low temperatures the NMR line developed considerable anisotropy, as shown in fig. 3. The anisotropic shift K, was extracted from the Van Hove singularities in the powder-pattern spectrum, taking Gaussian broadening into account [ 131, and is given in fig. 3(c). At 4.2 K the observed values of K, = -0.2% are an order of magnitude larger in absolute value than the dipolar contribution (Ka)dip = -0.015%, calculated as previously described [14]. This suggests that anisotropy of the static susceptibility is important, if one assumes that Z&f is isotropic. We have calculated the ground-state susceptibility using a CEF scheme suggested by the neutronscattering data [7], and we indeed find considerable anisotropy. This might be expected, since the crystallographic unit cell is tetragonal. Our calculation is based on the following from of the CEF Hamiltonian: Y&F = z$o;
+ sllop
+ B$O$ ,
(2)
where the operators B:: and 0: are as defined by Hutchings [lS]. The values used for the B:: were taken from ref. [7], and the resulting level splittings and wave functions are given in table I. Our result is diflicult to compare directly with since the calculated powderK,, however, average (i.e. isotropic) susceptibility 2 Cvisohl
=
1
(3)
j XI + j XII
and relaxation
7L2
BUZ
-3.5 8.5
89
-0.40 0.37
11)=1*1/2), B%
-6.25 5.7
7L3
736
739
7L2
Fig. 3. (a) “Si spectrum in CeCu2Sil at 4.2 K. The Van Hove singularities, from which the anisotropic shift K, is obtained. are indicated. (b) %i spectrum at 77 K; the anisotropic shift is too small to be resolved. (c) Temperature dependence of K,.
considerably overestimates the measured susceptibility of a polycrystalline specimen (see fig. 1). Here xl and XII are the calculated CEF susceptibilities perpendicular and parallel to the tetragonal c axis, respectively. The reduction in the measured susceptibility presumably arises either from moment instability (Kondo-lattice formation or IV), or from antiferromagnetic correlations between uncompensatred Ce moments at high temperatures. Either of these mechanisms could give rise to a negative paramagnetic Curie-Weiss temperature as observed (0, = -140 K). In either case a phenomenological description of the resulting susceptibility might be attempted with the help of a molecular-field-like parameter A:
Table I CEF parameters, energy splittings, and wave functions (b) alternative CEF scheme (see text) 12) = cl\ f S/2) - c,I 5 3/2),
in CeCu&
IO) = c,l
for: (a) CEF scheme
”
from ref. [7];
S/2) + ~215 3/2)
Ei1,- Eli,, (W
EIZ)- ElII) (W
Cl
Q
144 144
360 360
0.83 -0.49
0.56 0.87
J. Aarts et al. / “Si NMR and relaxation
in CeCuL%
165
IIIIII~~~
I,,,III,I
-i _i
(4)
_I,
Note that A simply extends a Curie-Weiss-like description of the susceptibility to the case of non-zero CEF splittings, and does not necessarily signify an exchange interaction between spins. The values of A obtained by setting hi,)A given by eq. (4) equal to the experimental A,,, are shown in fig. 4. The temperature dependence of A below 60 K signifies a breakdown of CurieWeiss behavior. Nevertheless, we shall use A(T) below 60 K to obtain an estimate of the anisotropic susceptibility from the expression
(5) assuming that A is isotropic. The quantity xti is plotted in fig. 5, together with K, and xao= k&+ It can be seen that Ati, in contrast to ~~(1, has the same temperature dependence as K, [after subtraction of a constant term K,(T = 0) = -O.lS%], at least below -5OK. However, the slope (dKJdxaA) is an order of magnitude larger than found for the isotropic shift and susceptibility (dKi,/dXm) from the data of fig. 2, which is in conflict with the hypothesis of an isotropic Hhf. Obviously susceptibility measurements on single-crystal samples are needed for a direct determination of the anisotropy of Hhf. We have also checked the sensitivity of xan to the CEF parameters by calculating it in another CEF scheme, chosen as follows: Assuming that
I
I
I
I
t
0
100
200
I
I
300
Fig. 4. Temperature dependence of the molecular-field-like parameter A, obtained from fits of the experimental bulk susceptibility of CeCurSir to eq. (4). The dashed line is a guide to the eye.
50-
?,
\
/
\ \
-
0 -:
_
Ia1 Ibl
[,()-gd-1
/ ‘\
(dl
0
0
TIKI 50
l
t K,I%l
l
--01
0
t l
0
0
I I I I I 0
.
\ ,/--‘_M
IIIIIIII1
0 0
/’
-2 -1
1
-5-\
N-L \
/’
I I I I
ICI
1
r----.
I/ I’
‘... . .. . -.-._ _----__ : ; I I r7 :>
t x, bo-g * moe
t xalj”-g&j-
TIKI-
IIIIIIIII 50
Fig. 5. (a) Theoretical anisotropic susceptibility xa,, (dash-dot line) and xti (dashed line) of CeCurSir. The latter is calculated in the molecular-field approximation, eq. (5) of the text. The h’s used are those obtained with the CEF parameters of ref. 171. (b) x.*, as in (a) above, on an expanded scale. (c) x.~ from the alternative CEF scheme discussed in the text. (d) Experimental ?ji anisotropic shift in CeCurSir.
the level splittings are determined by the neutron scattering data [7], there are still a number of possibilities for B$!, II:, and B%. For constant Bj/BO, there are two sets of CEF parameters, which naturally yield quite different wave functions. These are also given in table I. The procedure described above was then used to calculate A(T) and xar_ It is interesting to note that A(T) was found to be insensitive to the choice of CEF parameters. The results for Aa,, obtained from both sets of CEF parameters are shown in fig. 5, and it can be seen that the second set gives a result which differs qualitatively from the observed K,(T). Although this result corroborates the original choice of CEF parameters [7], the caveats of the previous paragraph should be kept in mind. Turning now to spin-lattice relaxation measurements, fig. 6 gives the temperature dependence of the ?Gi spin-lattice relaxation rate T;‘. These data resemble T;‘(T) found in another unstable-moment compound, CeAI, [5]. Below 30 K, relaxation measurements were
J. Aarts et al. / 29SiNMR And relaxation in CeCu&
166
Ce Cu2G2
* I
505
_
LO{ . 30L 1 2o
IO0
1
T;lkl 3
0
I 50
I 100
I 5
I 10
3q
1 0
i-
TIKI I 150
TLKI I 15
I 200
20
Fig. 6. (a) Temperature dependence of the “Si nuclear spinlattice relaxation rate Ti’ in CeCurSir. (b) Anisotropic spinlattice relaxation rates observed at low temperatures. Triangles show Ti!, squares show Til{.
made at the powder-pattern singularities which correspond to Si-site tetragonal axes perpendicular and parallel to the applied field. These measurements yielded the relaxation rates T;: and T$, respectively. The spectrometer bandwidth was adjusted to be much smaller than the splitting. It can be seen from fig. 6 that anisotropy is also present in the relaxation. In analogy with the definitions of Kim and K, we define
duction-electron contributions to the observed Ki, and T;‘. NMR data obtained from LaCu& shown in table II, can be used as estimates of the corresponding values in CeCu&, and the 4f components (Ki,), and (T;‘)t can then be obtained by subtraction. Alternatively, the nearly zero Kiwhm) intercept of fig. 2 can be taken as evidence for negligible conductionelectron contributions to both Ki, and T;’ in CeCu&. Fig. 7 gives the temperature dependence of h/~,~ calculated on both of these hypotheses, as well as the width r/2 of the quasielastic neutron scattering line [7]. Several features emerge from this analysis: corrections, not sur(1) The conduction-electron prisingly, are most important at high temperatures. The NMR estimates of h/7,* lie above r/2, as is (2) also found for CeAI*. continue to depend on (3) The NMR estimates -10 K, and even lie temperature below somewhat below the quasielastic neutron linewidth r/2( T + 0) = 1 meV [7]. At high temperatures fluctuations of neighboring Ce spins should not be substantially correlated. In this case, the fact that each 2’Si Ce nucleus is coupled to several neighboring
and
An NMR estimate of the effective Ce-spin fluctuation rate T;A can be obtained from T;‘, Kis”, and x,,, as described previously [4, S]. The relation between these quantities is 7;; = 2Ny*ks[(K,,):lT,~TIxmrl
3
where the subscript f indicates the 4f component of the quantity involved. It is difficult, however, to determine the con-
Fig. 7. Temperature dependence of estimated Ce spinfluctuation rates (expressed in energy units) in CeCu&. Open circles: Estimates obtained from NMR data and eq. (7). Filled circles: Estimates obtained from NMR data, corrected for conduction-electron contributions to K, and Ti’ using Nh4R measurements in LaCu&. Triangles: neutron quasielastic linewidth r2. Drawn lines are guides to the eye.
J. Aarts et al. / 29Si NMR
Table I1 %i isotropic Knight shift Ki, and spin-lattice relaxation time-temperature product TIT in the nonmagnetic reference compound LaCu2Siz, measured for comparison with data from CeCuzSiz T (K) 4.2 71.3
Kim (%) 0.084 * 0.01 0.087 5 0.02
TIT (s K) 39.5 -t 49?8
1.3
and relaxation
in C&u&
167
from CEF effects. Around the latter temperature a small increase in transferred hyperfine interaction, as well as the changing ratio (h/~,&(r/Z), suggest the onset of spatial correlation between Ce spins. Further experiments will probe the effect of superconductivity on the magnetic environment of “3Cu nuclei, via nuclear quadrupole resonance in zero applied field.
Acknowledgements spins results in a ratio (h/~,&(r/2) which is greater than unity [4,5]. The experimental ratio is uncertain by at least the correction discussed above, but is comparable to the number of 5 nearest Ce neighbors to a Si site. The difference in temperature dependence between h/~,~ and r/2 at low temperatures is probably due to the onset of spatial correlation between Ce-spin fluctuations. The fact that h/~~~ continues to vary below -10 K suggests that the low-temperature coherent ground state is not yet fully formed at this temperature. As for the observed anisotropy in T;‘, from eqs. (1) and (7) we note that
We are grateful for several useful discussions with P.F. de Chitel, G.J. van het Hof, M.J. Lysak, and 0. Peiia. One of us (J.A.) would like to thank the staff of the Physics Department of the University of California, Riverside, for their hospitality and assistance during his stay there, which was made possible by a grant of the “Stichting voor Fundamenteel Onderzoek der Materie” (FOM). This work was supported by the U.S. National Science Foundation, Grant No. DMR-7810301, and by the FOM.
References that if Hhf and T,~ are isotropic the anisotropy in T;’ should be the same as that in x, hence in K. But the ratio (KJKi,) becomes more negative with decreasing temperature, whereas (T;pT;f) remains roughly constant. This may indicate the onset, below 10 K, of anisotropy in the fluctuation rate itself: fluctuations parallel to the tetragonal axis may live longer than fluctuations perpendicular to it. But anisotropy in h/~,~, like anisotropy in Hhf, can only be determined through susceptibility measurements in single crystals. In summary, considerable structure has been found in NMR shifts and relaxation rates in paramagnetic CeC@i. After taking the anomalously reduced susceptibility (for which no satisfactory explanation has been given) into account, the evidence points to an electronic state of the system which remains essentially unchanged from 300 K down to about 10 K, apart so
[l] F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz and H. Sch%fer, Phys. Rev. Letters 43 (1979) 1982. [2] W. Franz, A. Griessel, F. Steglich and D. Wohlleben, Z. Phys. 31 (1978) 7. [3] W. Lieke, U. Rauchschwalbe, C.D. Bredl, F. Steglich, J. Aarts and F.R. de Boer, J. Appl. Phys. 53 (1982) 2111. [4] D.E. MacLaughlin, F.R. de Boer, J. Bijvoet, P.F. de Chltel and W.C.M. Mattens, J. Appt. Phys. 50 (1979) 2094. [5] D.E. MacLaughlin, 0. PeRa and M. Lysak, Phys. Rev. B23 (1981) 1039. [6] 0. PeRa, M. Lysak, D.E. MacLaughlin and Z. Fisk, Solid State Commun. 40 (1981) 539. [7] S. Horn, E. Holland-Moritz, M. Loewenhaupt, F. Steglich, H. Scheuer, A. Benoit and J. Flouquet, Phys. Rev. B23 (1981) 3171. [8] G.C. Carter, L.H. Bennett and D.J. Kahan, Metallic Shifts in NMR, Progr. Mat. Sci. 20 (1977) 1. [9] E.V. Sampathkumaran, L.C. Gupta and R. Vijayaraghavan, Phys. Letters 70A (1979) 356. [lo] D.E. MacLaughlin, in: Valence Fluctuations in Solids, eds., L.M. Falicov, W. Hanke and M.B. Maple (NorthHolland, Amsterdam, 1981) p. 321.
168
J. Aarts et al. / “Si NMR
[ 1 l] M. Loewenhaupt and E. Holland-Moritz. J. Appl. Phys. so (1979) 7456. (121 E.V. Sampathkumaran, L.C. Gupta and R. Vijayaraghavan, J. Phys. Cl2 (1979) 4323. [13] From a calculation similar to that of J.E. Adams, B.F. Williams and R.R. Hewitt, Phys. Rev. 151 (1966) 238, we find that HL is to be measured at 85% of the peak
and relaxafion in CeCu&
height (on the outside of the peak). and Hii is to be measured at 50% of the shoulder height. These positions are indicated in fig. 3(a). [14] D.E. MacLaughlin and R.R. Hewitt, J. Appl. Phys. 49 (197X) 2121; see also ref. [S]. [IS] N.T. Hutchings, Solid State Phys. I6 (1964) 227.