Transition from Kondo to intermediate valence regime in (La1-xCex)Ni: An ESR study

Article abstract of DOI:10.1088/0953-8984/10/43/020

We report on electron spin resonance (ESR) results for the series of compounds (La_1-xCe_x)Ni doped with Gd. We show that from the Gd g-value and linewidth one can determine the concentration x_c where the system goes from Ko

Full text of DOI:10.1088/0953-8984/10/43/020

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: an ESR study
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1998 J. Phys.: Condens. Matter 10 9763
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J. Phys.: Condens. Matter 10 (1998) 9763–9768. Printed in the UK
PII: S0953-8984(98)94439-3
Transition from Kondo to intermediate valence regime in
(La1−xCex)Ni: an ESR study
A N Medina, F G Gandra†, W R Azanha and L P Cardoso
Universidade Estadual de Campinas, Instituto de Fisica, 13083-970, Campinas, SP, Brazil
Received 19 May 1998, in final form 14 July 1998
Abstract. We report on electron spin resonance (ESR) results for the series of compounds
(La1−xCex)Ni doped with Gd. We show that from the Gd g-value and linewidth one can
determine the concentration xc where the system goes from Kondo single impurity to Kondo
lattice (and intermediate valence) regimes. The observed behaviour in both the g-value and
the slope of the linewidth–T curves is explained using the indirect interaction between Gd and
Ce moments. The calculation leads to the determination of the Ce–Gd exchange parameter
JCe–Gd = 4.8 meV and the Ce–conduction electron exchange parameter |Jf –s| = 19 meV, for
x = 1.
1. Introduction
Intermetallic compounds based on Ce have attracted great attention due to their interesting
physical properties [1] related to the Ce 4f electron. It is known that the dilution of such
compounds with La promotes a tuning of the s–f interaction in analogy with the application
of external pressure on the undiluted sample. As a consequence it is possible to induce
different regimes on Kondo systems as function of the Ce concentration [2, 3]. It has
been shown particularly for the series (La1−xCex)Ni, using several techniques (resistivity,
susceptibility, specific heat etc) [4–6], that the system is characterized as a Kondo single
impurity for the low concentration side (x < 0.7), changing to a Kondo lattice behaviour
above this value. Furthermore, when x is very close to 1, the Ce ion presents intermediate
∼
valence ( 3.5) [7]. Among the quoted techniques, the electrical resistivity has been widely
=
used to characterize the different regimes, which have a − ln T or T 2 dependence in each
case. However it is not possible to determine a clear turning point between both regimes
using resistivity.
The ESR technique can be a useful tool to probe the density of states and exchange
parameter of rare-earth magnetic impurities diluted into a metallic host [8]. Therefore the
ESR technique is very sensitive to variations on the exchange parameter [9–13] and may be
an alternative tool to observe the turning point. Since the ESR of Ce3+ cannot be detected in
this kind of compound (the large exchange parameter broadens the line beyond detection),
Gd is used as a magnetic probe instead. We expect to observe a g-shift and changes in
the behaviour of the linewidth–temperature curves, which are proportional to the exchange
interaction between the Gd and Ce moments, when the Ce concentration is changed.
It is our purpose in this paper to show that ESR can be used as a sensitive technique
to observe the transition from Kondo single impurity to Kondo lattice regimes in the
(La1−xCex)Ni system.
† E-mail: gandra@ifi.unicamp.br.
c
0953-8984/98/439763+06$19.50 ꢀ 1998 IOP Publishing Ltd
9763

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A N Medina et al
2. Experiment
Polycrystalline samples with 0 6 x 6 1 in steps of 0.1 with 0.5% of Gd impurity were
prepared using an arc-furnace and high purity elements. The samples were treated at
600 ◦C for 14 days in argon. In general the samples are brittle, specially for the high
concentration side. X-ray diffraction patterns (θ : 2θ scans) of the samples were carried
out at 300 K in a Philips PW1710 diffractometer using Cu Kα radiation and a graphite
secondary monochromator. The electrical resistivity was measured using standard four-
probe dc method in the temperature range between 1.5 and 300 K. The ESR experiments
were carried out at 9.3 GHz with 2 mW power in a home-made spectrometer between 5.5
and 25 K.
2.1. X-rays
X-ray diffraction patterns were obtained for all samples of the (La1−xCex)Ni:Gd system. The
˚
compounds presented orthorhombic symmetry and lattice parameters a = (3.79 ± 0.01) A,
˚
˚
b = (10.51±0.03) A and c = (4.36±0.01) A for x = 1 which are in good agreement with
the literature reported values [14]. In figure 1 we show the relative variation of the lattice
parameters and the unit cell volume as a function of the Ce concentration. The results show
that the lattice parameters a and b vary almost by the same amount while c has a relative
variation about three times smaller. This can be related to the observation of magnetic
anisotropy in single crystals of CeNi [4, 15], with the easy magnetic axis coincident with
the c axis. The reduction of the unit cell volume as x increases is similar to the application
of external pressure and induces the change of Kondo impurity to Kondo lattice regimes.
The observed volume variation can be described by two lines intersecting around x = 0.7,
which is very close to the reported transition value. Above this concentration the volume
reduces faster due to the reduction of the Ce ionic radius as a consequence of the Ce valence
increase [4, 16].
Figure 1. Relative variation of the lattice parameters a, b and c (upper figure) and unit cell
volume variation (bottom figure) with Ce concentration.

ESR of (La1−xCex)Ni
2.2. Resistivity
9765
Our samples were doped with 0.5% Gd which was used as a probe for the ESR experiments.
It was then necessary to run resistivity experiments from 1.5 to 300 K to characterize the
samples with the Gd magnetic impurity. The results show that the addition of the Gd does
not change the resistivity behaviour which is in good agreement with the literature data
[4]. In figure 2 we plot the normalized resistivity for several concentrations where a clear
− ln T dependence is observed for x 6 0.5 (upper figure) and a T 2 dependence is found
for x > 0.9 (bottom figure). However, for the intermediate concentrations x = 0.6, 0.7
and 0.8, it is hard to consider one predominant regime. The fit for both dependencies on T
is quite poor for these concentrations. Consequently, the critical concentration (xc) can be
determined to be within the range from x = 0.5 to x = 0.8.
Figure 2. Behaviour of the resistivity for several Ce concentrations. In the upper figure we
show the − ln T behaviour for x < 0.6 characteristic of single impurity Kondo systems. In the
lower figure, the T 2 dependence for high concentration evidences the change of regime.
2.3. ESR
The ESR spectrum of Gd3+ in (La1−xCex)Ni is shown for several concentrations at 5.5 K
in figure 3. For the intermediate concentrations a second line is observed. This broad
line is due to Ni aggregates or other phases of the compound which are formed during
the sample preparation. This line is also observed for the non-doped samples. The Gd
spectra were fitted to a Dysonian [17] line and the best fit was obtained for g-values
∼
close to 2 and linewidths 1H
500 G. For each sample, the g-values are essentially
=
constant in the studied temperature range while the linewidth followed a linear dependence,
1H = a + beff T . However, the g-value increases from g = 2.00 for LaNi up to g ≈ 2.03
for x = 0.7. For higher concentrations, g decreases down to g ≈ 2.00, and its behaviour
can be described by two straight lines intersecting at xc, as shown in figure 4. Although the
relative variation of the g-value reaches 1.5%, the ESR lines are not narrow, giving rise to
error bars for the g-value around 0.5%. For this reason, xc can assume values between 0.5
and 0.7.

9766
A N Medina et al
Figure 3. ESR of Gd3+ at T = 5.5 K for several Ce concentrations. Dots are experiment and
the line is the fit to a Dysonian line. A second broad line was considered in the fit as explained
in the text.
Figure 4. Effective g-factor of Gd3+ and linewidth thermal broadening coefficient as function
of the Ce concentration showing the regime transition close to x = 0.6. The dotted lines are
just a guide to the eyes.
The effective slope beff of the linewidth with the temperature reduces from about
(17 ± 1) G K−1 at x = 0 to negative values at x = 0.7. Going further to higher
concentrations, the slope returns to beff ≈ 20 G K−1, which is close to the initial value.
This peculiar behaviour of the effective slope will define xc clearly as discussed below.
3. Discussion
It is well known that for a bottlenecked system the linewidth behaviour with the temperature
is strongly dependent on the concentration of the local moment ion (Gd). This regime can

ESR of (La1−xCex)Ni
9767
be destroyed with the addition of other magnetic ions and, consequently, the slope of
the linewidth should increase [18]. In our case, measurements of the thermal broadening
and g-shift for x = 0 and x = 1 show that these parameters are independent of the Gd
concentration (<1%), confirming that (La1−xCex)Ni:Gd is not bottlenecked.
Although we have described the linewidth varying linearly within the studied
temperature range, this is not necessarily true for all temperatures and concentrations. In
fact we observed a negative slope for x = 0.7, what is a clear indication of indirect magnetic
interaction between the Gd moment and other magnetic ion, Ce in our case. For x = 0
the usual Korringa behaviour is observed. When a small quantity of Ce replaces La in the
lattice an indirect interaction between Ce and Gd (RKKY interaction) takes place giving rise
to an extra channel for the relaxation process and also a different internal field. Jaccarino
[19] showed that the g-shift is given by
X
χCe
gGdµ2B
1g =
x
Jij
(1)
i
where χCe is the Ce molar susceptibility, Jij is the RKKY oscillatory function, µB is
the Bohr magneton and x is the Ce concentration. Altshuler et al showed that the extra
contribution to the linewidth is [11, 13]
−πz(JGdn(εF ))JCeHresχCe
1H1(x, T ) =
x
(2)
2Naµ2B
where J is the s–f exchange parameter, n(εF ) is the density of states, z is the number of
conduction electrons per formula unit and Hres is the resonance field. Both contributions
are proportional to the Ce susceptibility. For small x, χCe is essentially independent of
the concentration [4] and therefore, 1g is proportional to x. In the high concentration
region, the Ce effective moment is reduced when x increases and promotes the consequent
reduction of 1g, as observed in figure 4. To explain the linewidth behaviour, we must
consider the temperature dependence of 1H1. For each x, the linewidth can be assumed to
be 1H = a + bT + cχCe. For low concentrations the susceptibility is given by a Curie law
[4] such that a competition between a linear term and a 1/T term takes place. However,
within the limited temperature range used, 1H showed a linear behaviour with an effective
slope beff . For x = 0 the slope is b ≈ 17 G K−1. As x increases, the 1/T term becomes
predominant such that beff reaches negative values. On the other hand, when x is close
to 1, χCe presents just a weak dependence on the temperature in the range of interest and,
consequently, 1H has the same slope as the reference compound.
For x = 0, the slope is given by the Korringa relation [9–13]
ꢀ
ꢁ
2
4πKBg gj − 1
b =
(JGdn(εF ))
(3)
µB
gj
where gj is the Lande´ g-factor, leading to the determination of [JGdn(εF )] = 0.027.
This result should provide a g-value around 2.02, that is close to the observed value
g = 2.00(±0.015). Considering that γ = (2/3)π2k2n(εF ) = 5 mJ mol−1 K−2 [5], we
calculate n(εF ) = 1.06 states eV−1 and JGd = 25 meV. These values are of the same
magnitude as found for other materials [11, 20]. Assuming that [JGdn(εF )]x=1 = 0.027 and
taking χ = 2 × 10−3 emu mol−1 [4, 5] and b = 18 G K−1 for x = 1, we obtain from
equation (2) JCe–Gd = 4.8 meV and |JCe| = 19 meV.
In conclusion, we have shown that the ESR results can establish a critical concentration
which determines the transition from Kondo single impurity to Kondo lattice regimes.
This was clearly observed as a discontinuity in the effective slope of the temperature
dependence of the linewidth and on the g-value with the concentration (or unit cell volume).

9768
A N Medina et al
The behaviour of the ESR parameters was explained considering the magnetic interaction
between the Gd moment and the Ce ion. In addition, we determined the Ce exchange
parameter for CeNi.
Acknowledgments
This work was partially supported by the Brazilian agencies FAPESP, CNPq and FAEP-
UNICAMP.
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