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Mössbauer emission spectra and electronic properties of 170Yb 3+ in palladium
P. Bonville, F. Gonzalez-Jimenez, P. Imbert, G. Jehanno, L.C. Lopes, A.K.
Bhattacharjee, B. Coqblin
To cite this version:
P. Bonville, F. Gonzalez-Jimenez, P. Imbert, G. Jehanno, L.C. Lopes, et al.. Mössbauer emission
spectra and electronic properties of 170Yb 3+ in palladium. Journal de Physique, 1984, 45 (3),
pp.467-486. �10.1051/jphys:01984004503046700�. �jpa-00209778�
Mössbauer emission spectra and electronic properties of 170Yb3+ in palladium
P. Bonville, F. Gonzalez-Jimenez (*), P. Imbert, G. Jéhanno
Service de Physique du Solide et de Résonance Magnétique, CEN-Saclay, 91191 Gif-sur-Yvette Cedex, France
L. C. Lopes (**), A. K. Bhattacharjee and B. Coqblin
Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France
(Reçu le 22 juillet 1983, accepte le 7 novembre 1983)
Résumé. 2014 Cet article rend compte de l’étude à très basse température, des propriétés électroniques de l’ion Yb3 +
fortement dilué (100 ppm) dans le palladium, à l’aide de la spectroscopie Mössbauer d’émission sur 170Yb. Les spectres hyperfins à deux raies observés montrent que l’état fondamental de Yb3 + dans Pd est le doublet de champ
cristallin 03937, et que l’une des raies possède un élargissement statique important. Nous avons mesuré la fréquence
de relaxation paramagnétique de Yb3+ entre 0,11 K et 2 K; aux plus basses températures (T ~ 0,65 K), nous
avons calculé une forme de raie de relaxation dans l’approximation de relaxation lente ou « séculaire » bien
adaptée au cas où les deux raies ont des élargissements statiques différents. La variation thermique de la fréquence
de relaxation de Yb3 + révèle l’existence d’un état excité de champ cristallin quasi dégénéré avec l’état fondamental 03937 ; elle est interprétée en admettant que les électrons de conduction diffusés par l’impureté ont un fort caractère d.
L’analyse des élargissements statiques nous a permis de déterminer que le premier état excité de champ cristallin
est le quadruplet 03938.
Abstract.
2014We report here the study, at very low temperature, by means of emission Mössbauer spectroscopy
on 170Yb, of the electronic properties of the Yb3+ ion diluted (100 ppm) in palladium. The observed two-line
hyperfine spectra show that the ground state of Yb3 + in Pd is the crystal field doublet 03937, and that one of the lines has an important static broadening. The Yb3+ paramagnetic relaxation rate was measured between 0.11 K and 2 K; at the lowest temperatures (T ~ 0.65 K), we computed a relaxation lineshape within the slow-relaxation
or « secular » approximation, well suited to the case when the two lines have different static broadenings. The
obtained thermal variation of the relaxation rate evidences an excited crystal field state which is quasi-degenerate
with the ground state 03937; it is interpreted by assuming that the conduction electrons scattered by the impurity
have a strong d character. An analysis of the static broadenings allowed us to determine that the first excited crystal
field state is the 03938 quartet.
Classification
Physics Abstracts
76.80
1. Introduction.
As magnetic susceptibility (x) [1, 2] and resistivity [2]
measurements have shown, dilute rare earth impu-
rities in palladium appear as trivalent ions, except for Ce and Pr.
In contrast with the dilute alloys PdGd3 +, PdEr3 +
and PdDy3 + which have been the subject of several
E.P.R. studies [3, 4], the PdYb3 + system has not
(*) On leave from Universidad Central de Venezuela, Caracas, Venezuela.
(**) On leave of absence from Instituto de Fisica da U.F.R.J., Ilha do Fundao, Cidade Universitaria, 21944 Rio
de Janeiro, Brasil.
Work partially supported by CNPq Brasil.
JOURNAL DE PHYSIQUE.
-T. 45, No 3, MARS 1984
received much attention until now. A M6ssbauer emission spectrum with the 1’°Yb isotope has been
obtained by St6hr [5], at T
=1.4 K in a Pd (170Tm*
1 7ðYb3 +) alloy containing 1000 ppm of thulium : the observed spectrum is quite different from that
expected for an isolated Yb3 + impurity substituted in a non-magnetic fcc host lattice, and St6hr’s inter-
pretation assumes the formation of magnetically
ordered rare earth clusters.
We have reexamined the problem, with improved experimental conditions in order to try and observe the behaviour of the isolated Yb3 + impurity in palladium : we prepared a much more dilute alloy (100 ppm of Tm) and paid great attention to the
metallurgical problems during the preparation of
the radioactive alloy.
31
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01984004503046700
The 170 Yb isotope presents a 84.3 keV M6ssbauer transition between nuclear levels having spins Ig
=0
and Ie
=2. In emission spectrometry, it allows very dilute ytterbium impurity levels to be studied [6].
The spectra first of all provide the possibility of checking the valence of ytterbium and the local symmetry of the impurity site. In the case of the
Yb3+ ion, extra information may be obtained. Yb3+
is a Kramers ion with total angular momentum
J
=7/2 in its ground spin-orbit state; the decomposi-
tion of this multiplet in a cubic crystalline electric
field yields two doublets r 6 and r 7 and a quartet T 8.
At low temperature the paramagnetic hyperfine spectrum, which reflects the ion’s static crystalline
field properties, allows the nature of the ground
electronic level to be determined. At higher tempe- rature, the ionic paramagnetic relaxation rate may be obtained from the observed lineshape. For example,
in a previous work on Yb3 + in gold, we observed a
thermal dependence of the relaxation rate indicative of a Kondo behaviour [7-10].
We present here a study of the static and dynamic properties of the Yb3 + ion in palladium, based on
M6ssbauer emission spectra recorded between 0.11 and 2 K. This article is organized in the following
way : section 2 briefly describes the cryogenic and
thermometric experimental set-up; the metallurgical
difficulties encountered during the PdTm sample preparation are reported in section 3, which also contains a new interpretation of the spectrum obtain- ed by Stohr [5]. Section 4 deals with the parama-
gnetic slow relaxation spectrum observed at the lowest temperature (T
=0.11 K). Analysis of this
spectrum shows that the ground state of the Yb3+
ion is the r 7 doublet, and reveals the existence of distortions from cubic symmetry due to the random strains present in the alloy. Section 5 is devoted to
the study of the thermal variation of the Yb3 + para- magnetic relaxation rate between 0.11 and 2 K : this
gives information about the intensity and the nature
of the coupling between the impurity 4 f electrons and the palladium conduction band electrons, as well as about the position of the first excited crystal
field level of Yb3+ in this metal. It is worth pointing
out here that all our results concerning the static and dynamic properties of Yb3+ in palladium (sec-
tions 3, 4 and 5) are coherently interpreted by assum- ing that this first excited crystal field level lies very close to the ground state (roughly 2 cm - 1 ).
Finally, in section 6, we compute the relaxation rate of the Yb3 + ion, within the ground r 7 doublet, under
the influence of atomic d-f exchange : the data of section 5 indeed suggest that the Coulomb d-f interac- tion (direct and/or exchange) plays an important role
in the dynamic behaviour of the ytterbium impurity
in palladium.
Some preliminary results concerning this work have been published previously [10, l lJ.
2. Experimental set-up.
The experiments between 0.11 and 1.15 K have been performed in a 3He- 4He dilution refrigerator.
In this refrigerator, more thoroughly described in
references [11, 12], the sample is located outside the dilution chamber. The sample-holder is made up of
a copper half-cylinder, thermally connected to the mixing chamber. The radioactive alloy sample, which is ribbon-shaped, is cooled by contact with the flat
gold-plated side of the sample-holder, against which
it is pressed by means of an aluminium clamp, trans- parent to y-rays and tightened with two stainless steel
screws.
The sample temperature is measured with a carbon resistor embedded in a copper cylinder screwed on
the clamp. Superconducting aluminium (below - 1 K) being a bad heat conductor, the clamp is covered with
a thin sheet of copper, relatively transparent to y-rays, which ensures thermal contact between the resistor and the sample. The precision of the measurement of the sample temperature is estimated to be : + 0.005 K.
Experiments between 1.3 and 2 K have been per- formed in a 4He cryostat by pumping on the liquid
helium bath.
The M6ssbauer emission spectra were recorded with
a YbB6 single line moving absorber, 70 % enriched
with 1’°Yb, and containing about 33 mg of 17°Yb
per cm2. This absorber is cooled to a temperature close
to that of the liquid helium bath. The full linewidth obtained with this absorber and a standard TmAl2
source is : Go = 2.7 mm/s.
The 84.3 keV photons emitted by 17°Yb are detected by an intrinsic germanium diode. The Mossbauer drive is locked to a symmetrical triangular velocity signal, and the spectra were obtained by folding the
data.
3. Preparation and characterization of Pd : Tm alloys.
The 17°Tm isotope, radioactive parent of 17°Yb, is
obtained from 169Tm by neutron capture :
As palladium can give rise to long lived radioactive
isotopes, it is better not to submit it to neutron irra- diation. Therefore, to prepare the sample, we melted
a previously activated Tm grain (L-- 1 mg) together
with 5N purity palladium wires. Fusion was carried
out in a high frequency induction furnace; induction
takes place, through a silica tube, on a graphite sus-
ceptor in which is located a BeO (or Th02) crucible containing the alloy components, under argon atmo-
sphere. The alloys were not quenched.
An important difficulty in the preparation of these alloys arises from the high reactivity of thulium metal with oxygen, especially at high temperature. Indeed,
in our search for optimal preparation conditions, we
initially observed, in the M6ssbauer emission spectrum of the obtained alloys, the presence of a wide compo- nent, characteristic of Tm!03. Thus, we took precau- tions in order to eliminate most of the oxygen present in the system prior to melting : strong degassing of the graphite susceptor and of the crucible in a dynamic secondary vacuum for half-an-hour; use of oxygen free (U-grade) argon. In order to get rid of traces of oxide Tm203 that could have formed during melting,
we performed successive fusions, in order to take profit
of the fact that oxide particles tend to move towards
the sample surface during melting, and the alloy was
then etched in hot aqua regia.
The alloy is then cold-rolled to a thickness of 0.25 mm, then etched again with aqua regia; the ribbon homogeneity is checked by autoradiography. In spite
of the precautions taken, we sometimes detected small
zones of concentrated activity, probably due to clus-
ters of not thoroughly dissolved Tm*, or to Tm*03
inclusions. In this case, we carefully cut off these zones,
and kept for our study a ribbon of about 1 cm2 area, having an activity of a few mCi; this was annealed
in a sealed silica tube in a secondary vacuum (10-6 torr)
at 850°C for about 20 hrs, in order to eliminate defects created by cold-rolling.
With the aim of checking and optimizing the pre-
paration of our alloys, we recorded a M6ssbauer
spectrum at T
=1.4 K after each stage of the metal-
lurgical treatment : melting, rolling and annealing. Let
us mention, in anticipation of the discussion of sec-
tion 4, that we identified the ground state of the Yb3 +
ion in a cubic site in palladium as the r 7 doublet,
whose two-line Mossbauer spectrum at low tempe-
rature is easily recognizable (see Refs. [7 and 8]).
Our observations after each stage of the alloy pro-
cessing are as follows :
1) Initial as-melted ingot (after etching with aqua
regia to separate it from the crucible) : the M6ssbauer spectra of these alloys contain a variable percentage
(from 20 % to 50 %) of an extra emission superimposed
onto the two lines originating from the r 7 doublet.
We identified this emission pattern as that of Tm!03.
It may be possible that this partial oxidation of thu-
lium, in spite of the precautions taken to eliminate
oxygen, comes from the porosity of the silica tube that may arise when the latter is radiatively heated during alloy melting.
2) As-rolled ribbon, subsequently etched with aqua
regia : in every case the spectra of these samples show
that the two lines associated with the r 7 state in a
cubic site have practically disappeared and that
instead a dominant 4-line component is observed, analogous to the emission spectrum recorded by
St6hr at T
=1.4 K in PdTm* [5]. St6hr specifies that
his measurements were performed on cold-rolled
samples which were submitted to an annealing at
800 OC for about 5 hrs. Furthermore, he states that
a satisfactory fit is obtained with an effective field
hyperfine interaction :
where go un I is the nuclear moment of the l7°Yb nucleus excited state, Heff is a hyperfine field of a few MG, and aQ the constant of the quadrupolar hyper-
fine interaction. St6hr’s interpretation assumes the
formation of magnetically ordered rare earth clusters.
However this interpretation raises several difficulties :
first, the clusters cannot be metallic thulium particles
included in the palladium matrix, because the 1’°Yb
emission spectrum in Tm metal only presents a weak transferred hyperfine field (Hhf ~ 100 kG at 4.2 K [6]).
They could consist of a Mössbauer 1 7°Yb3 + ion and
some Tm3 + neighbours, with a magnetic coupling possibly enhanced by a local polarization of the pal-
ladium matrix : however, as mentioned by St6hr, it is not clearly understood why similar 166Er3+-Ho3+
clusters did not show up in his Pd 166 Er emission spectra, although Ho is less soluble in Pd than Tm.
We propose an alternative explanation of this
spectrum : it can be also fitted with an anisotropic hyperfine interaction characteristic of an isolated
impurity, in the slow paramagnetic relaxation regime :
where A II and A1 are the magnetic hyperfine tensor components and S the effective spin (S
=t) of the
Kramers doublet. The values obtained for A II
(23 mm/s), Ai/A j j (0.2 ) and (XQ ( - 4. 5 mm/s) correspond
to an anisotropic Kramers doublet, whose wave func-
tion contains a dominant contribution from the state
J = 7/2; J,, = + 7/2 ).
It thus seems that the 4-line spectrum comes from
an isolated ytterbium impurity, in a site distorted with respect to cubic symmetry; the analysis below
of spectra recorded after suitable annealing supports this assumption. The origin of the great sensitivity of
the Yb3 + spectrum in palladium to the distortions of the crystal lattice will be discussed in section 4.2.
3) Ribbon after annealing in a secondary vacuum
at 850°C for about 20 h : we observe that the « non-
cubic » component, discussed above, has now disap- peared, leaving only the two-line spectrum characte- ristic of the Yb3 + ion in a cubic site.
In view of these results, it seems clear that the spectra observed by St6hr in PdYb3 + come from isolated Yb3+ ions, in non-cubic sites, arising probably from
the fact that the heat treatment was not long enough
to anneal out all the defects. Indeed, our annealing procedures, of longer duration, restored the basic cubic symmetry of the rare earth environment in the
alloy.
In some of our samples, we observed an appreciable quantity of a component due to Tm*03 in the spectra after annealing, which indicates that oxide inclusions
are still present in the bulk of the ribbon.
In exchange-enhanced host materials such as Pd,
very low concentration levels of iron or other 3d
impurities are required; indeed, these impurities give
rise to giant moments, which are known to yield spin-glass behaviour for concentrations of about 150 ppm. For that reason, we used 5N-purity palla-
dium containing less than 1 ppm of iron, and cold- rolling of the samples was performed between crysocal
sheets in order to avoid iron contamination.
The results presented in sections 4 and 5 concern an alloy free from oxide, containing a nominal concen-
tration of 100 ppm of Tm, obtained by melting palladium with a fraction of a master-alloy containing
500 ppm of Tm in Pd. The M6ssbauer emission spectra, down to the lowest temperature (T
=0.11 K),
show a behaviour typical of an isolated Yb para-
magnetic impurity without any evidence of magnetic ordering or cross relaxation effects.
4. Crystal field levels of the Yb3+ ion in palladium : analysis of the T = 0.11 K spectrum.
4.1 EXPERIMENTAL RESULTS. - The M6ssbauer emis- sion spectrum of 17°Yb in palladium, recorded at
T
=0.11 K in the ’He-’He dilution refrigerator,
is represented on figure la.
This spectrum shows a two-line paramagnetic hyperfine structure, which reflects the existence of a
paramagnetic moment of the Yb impurity in a slow
relaxation regime. Such a pattern is characteristic of the valence state Yb3+(2F7/2) and rules out the
presence of the diamagnetic valence state Yb 2+(ISO)
as well as of an intermediate valence state without intrinsic magnetic moment.
The spectrum can be fitted in first approximation
with the isotropic hyperfine Hamiltonian :
with mm/s or
843 MHz.
This identifies the electronic ground state of Yb3 +
as to be close to the Kramers doublet r 7’ for which,
in the insulating compound CaF2, the hyperfine
constant of 170Yb (84.3 keV) is A
=+ 13.18 ±
0.07 mm/s [13]. The eigenstates of Jehf are two hyper-
fine multiplets corresponding to the values : F1
=3/2 (degeneracy 2 F1 + 1
=4) and F2 = 5/2 (degeneracy 2 FZ + 1 = 6) of the total spin : F = I + S, and
whose energies are respectively : nWl = - 1 A and : nW2
=+ A. The hyperfine separation is thus : db f
=2 A. Table I shows that the positions and the
relative intensities of the two lines of the spectra below 0.65 K, fitted with two Lorentzian shaped lines, are in rather good agreement with such a level scheme.
Our measurements are thus the first observation
of the Yb3 + impurity in a quasi-cubic site in palladium
and they clearly establish that its ground state is the F7
doublet.
Fig. 1.
-Emission spectra of 1’°Yb in palladium at
T
=0.11 l K (a) and T
=0.40 K (b), fitted by 2 Lorentzian-
shaped lines.
Table I.
-Characteristics of the 2 lines of the ’7oYb 3+
hyperfine spectrum in palladium at low temperatures
(fitted with two Lorentzian-shaped lines). G : full width
at half-height (minimal experimental width Go =
2.7 mm/s). co : position with respect to the point with
zero velocity v
=0. P : relative intensity.
The spectrum on figure la presents however
some differences with respect to the spectrum asso- ciated with a pure r 7 level in a perfect cubic site :
i) the two lines have very different widths. Taking
into account the fact that the experimental linewidth Go of our reference absorber is about 2.7 mm/s,
the ratio of the broadenings of the two emission lines is (see Table 1) :
ii) The r 7 hyperfine constant A extracted from the line positions is significantly smaller than the
value Ac observed in cubic sites in insulators.
iii) With the fitting procedure used the centre of gravity of the spectrum (about - 0.3 mm/s) does
not correspond to an isomer shift value characteristic for 1 7°Yb3 + ions in metallic hosts, namely about
+ 0.3 mm/s relatively to the YbB6 absorber [6].
We interpret these anomalies in terms of the presence of a low lying excited crystal field state in the
next paragraph.
4.2 CRYSTAL FIELD EXPERIENCED BY THE Yb 3 + ION IN PALLADIUM.
-If one compares the hyperfine
spectrum associated with the 17°Yb3+ r 7 doublet
in palladium with that of Yb3 + in gold [7, 8, 12],
one notices that the main difference lies in the conside- rable broadening of the line arising from the F2 hyperfine multiplet (right-hand line in the spectrum).
Broadening of the lines of the M6ssbauer spectrum may come from two main sources : the dynamic
interaction of the electronic moment with its environ- ment (« lifetime » or homogeneous broadening) and
the scatter of the crystal field parameters occurring
in the sample (static or inhomogeneous broadening).
The question of the homogeneous broadening of
the lines under the influence of paramagnetic relaxa-
tion of the Yb3+ ion will be dealt with in detail in section 5.2. Let us mention here that in a dilute
alloy at low temperature, the dynamics of the elec- tronic moment is mainly due to its exchange inter-
action with the conduction electrons. With this
hypothesis, we show in section 5.2 that around T
=0.1 K paramagnetic relaxation broadens each of the two lines by about the same amount ; further- more, the study of section 5. 3 indicates that the
broadening is near 0.1-0.2 mm/s at this temperature, and is thus much smaller than that experimentally
observed. Therefore, the important broadening of the
line associated with the F2 multiplet cannot be
attributed to dynamic causes.
W e conclude that this broadening is of a static
nature, and that it comes from local distortions of the Yb3 + ion site in palladium.
These distortions from cubic symmetry are randomly
distributed in the sample, and the observed spectrum is thus a superposition of static « non-cubic » hyperfine
spectra.
Such a great sensitivity of the M6ssbauer spectrum with respect to local strains is related to the presence
of a low energy excited crystal field level of" the Yb3+
ion in palladium : indeed the study of the thermal variation of the paramagnetic relaxation rate of the Yb3 + ion, which will be reported in detail in section 5, strongly suggests that the energy 4 of the first excited level is only about 2.5 K. The mixing coefficient of this excited state with the ground state induced by
non cubic crystal field terms, which is inversely proportional to L1, is therefore particularly large in
this case. Furthermore, the hyperfine interaction of the excited nuclear state is of the same order of
magnitude as the non-cubic random strain terms
(- 0.1 K), and thus must be included in the analysis.
A thorough investigation of the hyperfine and strain mixing of crystal field excited states into the ground
state r 7 will be performed in a separate publication [ 14].
We will simply give here a qualitative discussion of the main spectroscopic implications of these interactions.
If one examines the modifications of the isotropic hyperfine interaction due to the presence of a small non-cubic component of the crystal field, two effects
are observed. First, the magnetic hyperfine tensor A, proportional for 17°Yb3 + to the spectroscopic g-ten-
sor, becomes slightly anisotropic. Second, deviation
from cubic symmetry gives rise to a weak electric field gradient on the nucleus site.
The joint effects of the anisotropy of A and of the hyperfine quadrupolar interaction lead then to the
following spectroscopic features :
i) A degeneracy lifting of the lines arising from the
two hyperfine multiplets, the spectroscopic splitting
of the 3 lines arising from F 2 (nW2
=A ) being generally
more important than that of the 2 lines arising from
Ft(nwt = -! A ). The spectra of reference [13], which
are simulations in the presence of tetragonal and trigonal crystal field components, clearly illustrate
this phenomenon.
ii) The mean energy difference between the two groups of lines is reduced with respect to the cubic
value : 1 A,,. This can be described in terms of an
effective hyperfine constant Aeff ; the difference AA
=Aeff - Ac contains two terms [14] : a dominant magnetic term, proportional to Ac, and a much
smaller electric term proportional to the quadrupolar hyperfine constant. The magnetic part of AA is in fact proportional to the reduction Ag of the mean g , g = gx + gy gz . h respect to the cubic -value . - - 9 + 3 + with respect to the cubic
value gc. This reduction Ag has been calculated in the
case of a trigonal deformation [15] of the cubic site, and the calculation in the presence of a tetragonal
deformation is detailed in Appendix 1.
As to hyperfine mixing, it leads to the same qualita-
tive effects as deviation from cubic symmetry, i.e.
degeneracy lifting of the hyperfine multiplets and
reduction of the effective hyperfine constant, but also to a significant displacement of the apparent isomer shift value towards negative velocities.
The anomalous features of our T
=0.11 K spec- trum (§ 4.1, i, ii, iii) may thus be accounted for by the
presence of hyperfine and strain mixing of the ground r 7 doublet with a low lying excited state. It is to be
noticed that the reduction effect of the hyperfine
constant prevails, in the case of Yb3 + in Pd, over
its enhancement (with respect to the insulating compounds) coming from the dynamic polarization
of the metal s-type conduction bands [16].
These features provide further information about the crystal field level scheme of Yb3 + in palladium.
First, we note that for Yb3 +, a quasi-degeneracy
of the r 7 ground state with another crystal field
level may arise for only two values of the x parameter of the energy diagram of reference [17], corresponding
to a level crossing : namely x1
= -0.583 (crossing
with r 8) and X2 = 0.200 (crossing with T6). Our
spectrum simulations, in the presence of a Gaussian
distribution of axial distortions with respect to cubic symmetry clearly show that one can simulate the
experimentally observed differential broadening of
the two lines only in the vicinity of the crossing point x between r 7 and r 8’ Furthermore the crossing
value x 1
= -0.583 is close to the x value extrapolated
for Yb3 + from the x and W parameters [17] of the Er3+ ion in palladium [18], i.e. : x = - 0.85 and
W = - 3 K.
Second, our simulations also show that a strongly negative apparent isomer shift is obtained only in
the presence of a low lying T8 state.
For these reasons we can state that the first excited crystal field level, which lies close to the r 7 ground level, is the T8 quartet.
We present in figure 2 a lineshape simulation of the spectrum at 0.11 K, obtained in the presence of random strains. In the frame of this crude model,
we neglected the hyperfine mixing of the two lowest crystal field levels. We also neglected the effects of
paramagnetic relaxation and assumed that the broa-
dening of the lines is solely due to static crystal field
effects. This is justified, because, as we shall see in
section 5. 3, the dynamical broadenings at 0.11 K
amount to a few percent of the full width of the lines
arising from F1 and from F2. The simulated lineshape
was obtained with the following assumptions : i) existence of axial distortions, along a [111]
direction, with respect to cubic symmetry; the crystal
field Hamiltonian then writes :
where the z axis is chosen along [111] ;
ii) we keep for W the previously extrapolated
value : W
= -3 K, and choose : x
= -0.600,
so that the energy separation A(F7-F8) is 2.4 K, in accordance with the value obtained from the ther-
Fig. 2.
-Simulation of the experimental lineshape observed
at 0.11 K by means of a fitted Gaussian distribution of
trigonal local distortions. The curve is a superposition of
slow relaxation « axial » hyperfine spectra (see text).
mal variation of the relaxation rate of Yb3 + at higher
temperatures (see section 5 . 3 . b) ; then : A(F7-F6)
is about 70 K ;
iii) existence of a Gaussian distribution for the value of the axial component B.
The spectral shape depends in fact mainly on the
ratio : BIA(F7-F8); with the above quoted value
for A(F7-F8), we fitted the parameters of the distri- bution of B values, and obtained : Bo
= -0.05 K (mean value) and : J
=0.09 K (mean square devia-
tion). Such an order of magnitude is quite in agree- ment with what is usually assessed for crystal field
strains.
However, the non-vanishing value of the mean
axial component Bo is here an artifact of the calcula- tion, which disappears as one introduces hyperfine mixing [14].
In spite of this slight shortcoming, this model of static strains accounts for the overall shape of the
T
=0.11 K experimental spectrum. Furthermore, it allows a distribution of relaxational lineshapes to be performed in a simple way, as discussed in section 5. 3.
Let us also point out that, in the frame of the above described model, one can simulate the effect on the M6ssbauer lineshape of defects created by cold- working by assuming a value : B
=0.25 K for the
axial component : the ground state is then strongly
altered relative to a pure F7 state, and the associated
hyperfine spectrum is analogous to the 4-line spectrum obtained in as rolled samples.
A great sensitivity to random strains has already
been observed by E.P.R. studies in the case of cubic
alloys where the first crystal fields excited levels are close to the ground state (A - 10 K) : LaSbDy3+ [19],
AgDy" [20], AuEr3+ [21] and LaSEr3+ [22]. It must
also be pointed out that the existence of a weak axial
crystal field component along one of the 111 >
directions has been proposed, from an E.P.R. study
of the Er3 + ion in a palladium single crystal, to
account for the presence of « forbidden » lines in the
hyperfine spectrum associated with the ground quartet T8 [4]. However, an alternative interpretation of these
results in terms of a dynamic Jahn-Teller effect has also been put forward [23].
Knowing that palladium may accept great quan- tities of hydrogen in interstitial position, one may wonder whether the presence of occluded hydrogen
contributes to the local strains evidenced in the M6ssbauer spectra of Yb3 + . In order to check this
assumption we submitted a rolled and annealed sam-
ple to degassing in a secondary dynamical vacuum at
700°C during 8 h, then at room temperature during
64 hours. The sharpening of the line arising from the F2 multiplet after degassing, measured on the
T
=0.11 K spectrum, amounts to about 15 % of the
whole broadening. The presence of occluded hydrogen
thus does not seem to contribute strongly to the local
lattice distortions, but this is not definitively esta-
blished since the residual hydrogen content is not
known.
5. Paramagnetic relaxation of the Yb3 + ion in palla-
dium.
5.1 QUALITATIVE DESCRIPTION OF THE SPECTRA AND PROBLEMS RAISED BY THEIR INTERPRETATION.
-In addition to the 0.11 K spectrum described in the
preceding section, we recorded twelve spectra at temperatures ranging between 0.18 K and 4.2 K;
3 spectra were recorded at higher temperatures, respectively at T
=8, 12 and 75 K. The spectra obtained at 0.11 and 0.40 K are represented on figure 1
and the 1.3 K spectrum on figure 3. One can observe
the progressive line broadening due to the influence of paramagnetic relaxation when temperature increases. At higher temperature, the spectrum
collapses into a unique line whose full width, at first quite large (about 23 mm/s at 4.2 K) progressively
decreases to 4.1 mm/s at 75 K in the fast paramagnetic
relaxation regime.
Whereas the relaxation spectra of the 1 7°Yb3 + ion in cubic sites in gold, obtained between 0.6 and 26 K [9], could be analysed without any special difficulty with the so-called «high-temperature»
lineshape (k B T >> ’d hf = !A) 2 developped in refe-
rence [7], the fitting of the l7°Yb relaxation spectra in
palladium raises several problems :
i) inhomogeneous crystal field distortions give rise
to very different static linewidths for the two lines observed at low temperature, whereas the above mentioned high temperature theoretical lineshape
assumes the existence of a common static linewidth.
Furthermore the results obtained in the temperature
range below T
=0.65 K cannot be fitted using the high-temperature approximation;
Fig. 3.
-Fitted curves for the 1.3 K spectrum : a) using
the high-temperature « cubic » relaxation lineshape (3);
b) using the same distribution of trigonal distortions as in
figure 2. The curve is a superposition of high-temperature
«axial relaxation lineshapes (see text).
ii) the same lineshape is no longer valid at tempe-
ratures above about 2 K, as we shall see below, because the first excited crystal field level, which lies
at an energy a few Kelvin above the ground state,
becomes then appreciably populated.
Analysis of the Yb3 + spectra in palladium, as well
as of recently obtained Yb3 + spectra in gold at very low temperature [10, 12], led us therefore to reexa-
mine the problem of theoretical relaxation lineshapes
in Mossbauer emission spectroscopy in a cubic dilute
alloy, when the high temperature approximation (kB T >> 4hf) breaks down. In addition, as we make
use in this study of a certain number of relaxation formulas and lineshapes that may seem puzzling, we
feel it useful to give a review of the situation concerning
the analysis of relaxation in emission Mossbauer spectroscopy on 17°Yb in cubic symmetry. This is done in the next paragraph. The analysis of experimental
results will take place in paragraphs 5.3 and 5.4.
5 . 2 PARAMAGNETIC RELAXATION LINESHAPES IN CUBIC DILUTE ALLOYS IN M6SSBAUER EMISSION SPECTROSCOPY.
-
In a M6ssbauer emission experiment the lineshape
in the presence of relaxation writes [8a, 25] :
where :
In this expression, the trace must be performed over
the states of the electronuclear system, 0"( ’tn) is the density matrix of the electronuclear system associated with the excited nuclear level at the mean time T.
of emission of the Mossbauer photon, TM + (resp. Tf)
is the M component of the tensorial operator driving
the emission (resp. absorption) transitions of the y-ray, and ’1.L(p) is a Liouville operator [24] :
acting on mixed states I fg >, where I g > (resp. If») is
an electronuclear state associated with the ground (resp. excited) state of the nucleus. The operator X’
is the Liouville operator associated with the hyperfine Hamiltonian Jehf’
The matrix R is a function of the relaxation inter- action which couples the electronic spin with its
environment. Its matrix elements ( gf I R I g’ f ’ > are
of the order of magnitude of the transition probabilities
or electronic « relaxation rates », and are given in
reference [25].
In dilute alloys, the dynamics of the impurity magnetic moment is dominated at low temperature by the exchange interaction with conduction electrons.
It is generally assessed that the most important term
of this interaction is the scalar coupling between the
spin s of a conduction electron and the real spin S’
of the ion :
Within the rare earth J multiplet : S’ = (gj - 1) J.
Then :
If one considers only the ground doublet : gS
=g J J, and :
with
The matrix elements of R are then linear combina- tions of spectral densities I(w) [26] associated with the
scattering of conduction electrons between two impu- rity levels separated by an energy hw :
where n(EF) is the density of electronic states at the Fermi level per spin direction, and where OJ is positive (resp. negative) in the case of an energy loss (resp. gain)
of the scattered electron. The « detailed balance »
principle holds for the spectral densities :
[N.B. This definition of the spectral densities slightly
differs from that given in references [8, 12, 25], where
the opposite sign convention for m is used, and which
includes the parameters a and Jkf.]
Computation of the matrix R involves the spectral
densities for scattering of conduction electrons between the two degenerate ground electronuclear levels
I 19
=0, ms
=+ ’ >, as well as between the two
excited hyperfine multiplets F1 and F2, separated by
an energy : dhf =- I 2 A
=0.10 K (for "’Yb’+ in Pd),
and the matrix elements of R are thus functions of 1(0)
and I( ± Ahf). Consequently, one must consider two temperature ranges in the lineshape calculation :
kB T >> Ahf and kB T - Jhf Furthermore, we shall
see that the density matrix 0-(1"0) may depend on the
relaxation rates in the range : kB T - d h f.
In this so-called high temperature approximation,
the conduction electron exchange scattering on the impurity site does not depend on hyperfine energies : I( ± A hf) 2-- I(0). Relaxation within the electro-nuclear system may then be treated as a problem of elastic scattering of conduction electrons by an impurity
with spin S
=1/2. Besides this, the density matrix Q(in) is simply proportional to the unit matrix E :
Computation of the lineshape in this approximation,
which was performed in reference [7], involves only one dynamic parameter 1/7B, proportional to 1(0), i.e. to temperature (Korringa law) :
where
lIT 1 is the relaxation rate, and T 1 is identical to the longitudinal or transversal relaxation time as it is measured by E.P.R. on the impurity in a weak magnetic
field Ho ( g,uB Ho kB T). The high-temperature line- shape in cubic symmetry writes [25b] :
where p = - - jr im. [N.B. A more general high tempe-
rature relaxation lineshape valid in axial symmetry is
given in reference [7].]
When comparing this lineshape with the experi-
mental spectrum, the natural linewidth F of the emission process (T
=68.6 MHz for 1 7°Yb) must be replaced by an effective experimental linewidth
G (G > 2 r) which includes the absorber linewidth,
as well as the static line broadenings, assuming that they are identical for all the transitions in the spectrum (we have already mentioned that this is not true for
170Yb 3+ in Pd).
According to the relative values of I/Tl 1 and All,
one may distinguish between different relaxation
regimes. When : 1/T1 Alii (quasi-slow relaxation),
the spectrum is little different from that in the absence of relaxation; the lines are Lorentzian-shaped and do
not overlap, and they acquire a dynamic broadening
worth respectively 5 p y 5 T 1 and 3 5 -T 1 1 for the line arising g from F1 1 and from F2. For increasing values of the relaxation rate, the spectrum broadens and the hyper-
fine structure is smeared out (liT 1 "" Alii); then, in
the quasi-rapid relaxation regime (I/Tl > Alh), the spectrum is made up of a unique Lorentzian-shaped
line centred in oi
=0, and with a dynamic broadening :
In the presence of relaxation processes involving an
excited crystal field level i ), with energy d i, the exact
solution of the lineshape problem would require taking
into account the spectral contributions coming from
this level. One may however use an approximation,
which was shown to hold in the case of two extremely
anisotropic doublets (gl
=0) when : kB T di [27],
and which amounts to replacing 1/ T 1, in the lineshape
associated with the ground doublet, by :
where : Wit is the probability per second of a tran-
sition from r 7 towards the excited state ( i ). The T7 ground state depopulation rate Wit involves the spec- tral densities I (,J j) for inelastic scattering of conduction electrons between the crystal field levels, with loss of energy of the incoming electron. In the case of an
interaction Hamiltonian of the form (1), one can show, with the help of the Fermi golden rule, that :
The vector J having zero matrix elements between
I F7 > and I r 6 >, the only contribution to I/T’ comes
from the r 8 states, and one obtains :
where L1 is the energy separation between I r 8 ) and I r 7 >’ More generally, this type of thermal depen-
dence (Hirst-Orbach law [26]) can be written :
where : J’(x) = x/(e’ - 1) and fl is a constant depending
on the nature of the interaction between localized and conduction electrons (p
=1 in the above calculation
assuming the isotropic exchange interaction Xkf)-
We shall see, in section 5.3, that the experimental
results led us to think that the anisotropic d-f exchange
interaction between 4f and conduction electrons, plays a role in the paramagnetic relaxation of Yb3 + in palladium. The calculation of the f3 coefficient in this hypothesis is detailed in section 6.
It is to be noted that, in emission Mossbauer spec- troscopy on rare earths, it is theoretically possible to observe, under certain conditions, excited crystal
field states, populated out of thermal equilibrium by
the radioactive decay [28, 29]. The depopulation rate Wi, of an excited level, which is a function of :
I(- d i) N n(EF)’. Ai when : Ai >> kB T, is usually
much faster than 1/T.. So, it will be impossible to
observe these states in an emission spectrum, unless the relaxation transition between the ground state
and this excited level is forbidden, as is the case for the.
F6 -> r 7 transition in the hypothesis of the relaxation mechanism described by the Hamiltonian Jekf (expres-
sion (1)).
The observation (or non-observation) of excited crystal field levels in an emission spectrum may thus
yield informations about the nature of the relaxation interaction.
In this low-temperature region, not only is it
necessary to correctly handle the inelastic scattering
of conduction electrons between the two hyperfine multiplets F1 and F2, but the density matrix u(’t"n) of F1 and F2 at the average time of the emission of the y-ray may depend upon the relaxation rate. Indeed, during the average lifetime in of the nuclear excited state, relaxation driven by the scattering of conduction electrons will tend to restore Boltzmann equilibrium
between F1 and F2, populated out of thermal equi-
librium by the radioactive decay :
The value of O’(!n) then depends upon the relative values of T. and of the relaxation time Tihf between
the two multiplets [8], which is defined as :
where Wi and Wi are respectively the probabilities
of the transitions F, -> F2 and F2 -> F1.
If : T1hf > Tn’ the populations of the hyperfine
levels show little evolution till the moment of the emission of the y-ray, and Q(in) is little different from the initial density matrix Gin; if Tlhf in, Boltzmann equilibrium is reached at the moment of
the M6ssbauer emission, and :
In the intermediate regime, i.e. Tlhf - in, the
hyperfine populations have intermediate values bet-
ween the initial ones and those corresponding to
Boltzmann equilibrium, and the matrix a(rn) is a
function of the ratio Tlhf/T.. In this regime of quasi-
slow relaxation
....
