Electronic transport properties of compounds with temperature unstable intermediate valence of Ce
Results of a thermoelectric power component (Sf) and electrical resistivity (ρf) measurements connected with the temperature unstable intermediate valence of Ce are presented for CeNi, CeNi₂ and CeNi₂Si₂ compounds in the temperature range 4–800 K. It is shown that dependences Sf (T) and ρf (T) are...
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irk-123456789-1190082017-06-04T03:03:03Z Electronic transport properties of compounds with temperature unstable intermediate valence of Ce Koterlyn, M.D. Yasnitskii, R.I. Morokhivskii, B.S. Results of a thermoelectric power component (Sf) and electrical resistivity (ρf) measurements connected with the temperature unstable intermediate valence of Ce are presented for CeNi, CeNi₂ and CeNi₂Si₂ compounds in the temperature range 4–800 K. It is shown that dependences Sf (T) and ρf (T) are well described in a wide temperature range within the framework of a simple model of a narrow peak in the density of states gf (E) of Lorentzian shape near the Fermi level. The width of the peak depends on temperature and defines the characteristic single-ion Kondo temperature TK. Для cполук CeNi, CeNi₂ та CeNi₂Si₂ прeдcтавлeні рeзультати вимірювання в інтeрвалі тeмпeратур 4–800 K cкладових тeрмо-e.р.c. (Sf) та eлeктроопору (ρf), викликаних тeмпeратурно-нecтабільною проміжною валeнтніcтю Ce. Показано, щ о залeжноcті Sf T) та ρf (T) в широкому інтeрвалі тeмпeратур добрe опиcуютьcя на оcнові проcтої модeлі вузького піку гуcтини cтанів gf (E) лорeнцівcької форми біля рівня Фeрмі. Ширина піку залeжить від тeмпeратури і визначаєтьcя одно-іонною тeмпeратурою Kондо TK. 2004 Article Electronic transport properties of compounds with temperature unstable intermediate valence of Ce / M.D. Koterlyn, R.I. Yasnitskii, B.S. Morokhivskii // Condensed Matter Physics. — 2004. — Т. 7, № 2(38). — С. 265–274. — Бібліогр.: 28 назв. — англ. 1607-324X PACS: 72.20.Lp, 72.10. Fk, 72.15.Qm, 75.30.Mb DOI:10.5488/CMP.7.2.265 http://dspace.nbuv.gov.ua/handle/123456789/119008 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Results of a thermoelectric power component (Sf) and electrical resistivity (ρf) measurements connected with the temperature unstable intermediate valence of Ce are presented for CeNi, CeNi₂ and CeNi₂Si₂ compounds in the temperature range 4–800 K. It is shown that dependences Sf (T) and ρf (T) are well described in a wide temperature range within the framework of a simple model of a narrow peak in the density of states gf (E) of Lorentzian shape near the Fermi level. The width of the peak depends on temperature and defines the characteristic single-ion Kondo temperature TK. |
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Article |
| author |
Koterlyn, M.D. Yasnitskii, R.I. Morokhivskii, B.S. |
| spellingShingle |
Koterlyn, M.D. Yasnitskii, R.I. Morokhivskii, B.S. Electronic transport properties of compounds with temperature unstable intermediate valence of Ce Condensed Matter Physics |
| author_facet |
Koterlyn, M.D. Yasnitskii, R.I. Morokhivskii, B.S. |
| author_sort |
Koterlyn, M.D. |
| title |
Electronic transport properties of compounds with temperature unstable intermediate valence of Ce |
| title_short |
Electronic transport properties of compounds with temperature unstable intermediate valence of Ce |
| title_full |
Electronic transport properties of compounds with temperature unstable intermediate valence of Ce |
| title_fullStr |
Electronic transport properties of compounds with temperature unstable intermediate valence of Ce |
| title_full_unstemmed |
Electronic transport properties of compounds with temperature unstable intermediate valence of Ce |
| title_sort |
electronic transport properties of compounds with temperature unstable intermediate valence of ce |
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Інститут фізики конденсованих систем НАН України |
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2004 |
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http://dspace.nbuv.gov.ua/handle/123456789/119008 |
| citation_txt |
Electronic transport properties of compounds with temperature unstable intermediate valence of Ce / M.D. Koterlyn, R.I. Yasnitskii, B.S. Morokhivskii // Condensed Matter Physics. — 2004. — Т. 7, № 2(38). — С. 265–274. — Бібліогр.: 28 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT koterlynmd electronictransportpropertiesofcompoundswithtemperatureunstableintermediatevalenceofce AT yasnitskiiri electronictransportpropertiesofcompoundswithtemperatureunstableintermediatevalenceofce AT morokhivskiibs electronictransportpropertiesofcompoundswithtemperatureunstableintermediatevalenceofce |
| first_indexed |
2025-07-08T15:04:56Z |
| last_indexed |
2025-07-08T15:04:56Z |
| _version_ |
1837091624117600256 |
| fulltext |
Condensed Matter Physics, 2004, Vol. 7, No. 2(38), pp. 265–274
Electronic transport properties of
compounds with temperature unstable
intermediate valence of Ce
M.D.Koterlyn ∗1,2 , R.I.Yasnitskii 1 , B.S.Morokhivskii 1
1 Ivan Franko National University of Lviv,
Dragomanova Str. 50, 79005 Lviv, Ukraine
2 Academy of Bydgoszcz, Sq. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
Received March 12, 2004
Results of a thermoelectric power component (Sf ) and electrical resistivity
(ρf ) measurements connected with the temperature unstable intermediate
valence of Ce are presented for CeNi, CeNi2 and CeNi2Si2 compounds in
the temperature range 4–800 K. It is shown that dependences Sf (T ) and
ρf (T ) are well described in a wide temperature range within the frame-
work of a simple model of a narrow peak in the density of states gf(E)
of Lorentzian shape near the Fermi level. The width of the peak depends
on temperature and defines the characteristic single-ion Kondo tempera-
ture TK.
Key words: rare earth compounds, valence fluctuation, electrical
resistivity, thermoelectric power
PACS: 72.20.Lp, 72.10.Fk, 75.30.Mb
1. Introduction
Metallic systems containing rare-earth elements with unstable 4f -electronic states
have been very attractive for the last decades. A specific feature of this class of
compounds turns out to be the anomalously high values of certain physical charac-
teristics, e.g., the coefficient γ of the electronic-specific heat, magnetic susceptibility
χ, thermoelectric power S, that can exceed the values typical of simple metals by
10 − 103 times [1,2]. In the band energy representation, a formation of the reso-
nance peaks of the density of f -states, gf(E), near the Fermi level EF with a width
of the order of the characteristic single-ion Kondo temperature TK (the so-called
Abrikosov-Suhl resonance [2]) corresponds to this phenomenon. Despite the presence
of a large number of experimental and theoretical works devoted to the many-body
∗E-mail: koterlyn@mail.lviv.ua
c© M.D.Koterlyn E-mail: koterlyn@mail.lviv.ua , R.I.Yasnitskii, B.S.Morokhivskii 265
M.D.Koterlyn, R.I.Yasnitskii, B.S.Morokhivskii
effect studies when the conduction electrons interact with the 4f electrons in the
compounds of this class, the nature of the resonant structure of the gf(E) remains
the main issue to be discussed in future. Of special interest herein there are the in-
termetallic compounds showing the temperature unstable intermediate valence (IV)
of Ce. These are most suitable for a model description in a study of the formation
mechanism of the gf (E) structure.
Transport properties of metallic compounds containing Ce with unstable f -
electrons turn out to be most sensitive to the peculiarities of the near Fermi state
spectrum and can be used as a “fine instrument” while studying the nature of
the ground state. It is known that transport characteristics of such systems can
be described in the relaxation time approximation with allowing for the exchange
scattering of conduction electrons on local f -states [3–5]. However, with a detailed
consideration of a number of important factors, such as the f -state orbital degen-
eracy, crystal field-split f -states, the f -state hybridization with the band electrons,
many-body effects connected with f -electron correlation effects, one cannot succeed
in obtaining a general solution of the transport coefficient behavior problem in a
wide temperature range [6,7]. Moreover, one cannot succeed in coordinating the
results of description of the transport coefficients with the data of measurements
of other physical properties. All this contributed to the development of a number
of phenomenological approaches to the description of transport properties of such
systems [8–10]. However, detailed comparisons of calculation values of transport
properties within the limits of approximations [8–10] with experimental ones in a
wide temperature range have not been carried out yet. This caused an insufficient
study of the possible usage of such experimental data for the determined resonance
structure gf(E) parameters in a wide temperature range.
The given paper shows temperature dependences of the contribution of Ce f -
states to the total thermoelectric power (Sf ) and to the electrical resistivity (ρf )
for compounds CeNi, CeNi2 and CeNi2Si2 with different temperature stability IV of
Ce. Based on the phenomenological approach offered by us earlier [10–12] there was
carried out the analysis of Sf(T ), ρf(T ) dependences as well as of the transformation
of the resonance structure gf(E) near the Fermi level at temperature changes within
the largest limits (4–800 K).
2. Experimental data
Preparation of polycrystalline samples and methods of the performed measure-
ments were described in pervious papers [13,14]. Transport properties of the com-
pounds CeNi, CeNi2, CeNi2Si2 and the corresponding analogs with La were partially
analysed by us earlier [13–16]. The thermoelectric power of compounds with Ce is
positive and reveals a typical maximum. The electrical resistivity manifests essential
discrepancies from the Bloch-Grüneisen law characteristic of the systems with IV
of Ce. For compounds with La, the thermoelectric power and electrical resistivity
behavior is similar to that observed in non-magnetic transition metals.
Assuming that the resistivity of the lanthanum-based counterpart can be taken
266
Electronic transport properties of compounds . . .
as a good approximation of the phonon contribution to the total measured resistivity
of CeNi, CeNi2 and CeNi2Si2 we expressed ρCe(T ) for these compounds as follows:
ρCe(T ) = ρ0,Ce + ρLa(T ) − ρ0,La + ρf (T ),
where ρ0,Ce, ρ0,La and ρCe, ρLa denote temperature-independent residual resistivity
and total electrical resistivity of a compound with Ce and the corresponding isostruc-
tural analog with La. While analyzing the peculiarities of ρf(T ), the component ρ0
can be neglected and ρf (T ) ≈ ρCe(T ) − ρLa(T ) assumed.
When defining f -state contribution to the total thermoelectric power, the Gorter-
Nordheim relation [10,11] is usually used
Sf (T ) =
(SCeρCe − SLaρLa)
(ρCe − ρLa)
,
where SCe, SLa denote the total thermoelectric power of a compound with Ce and the
corresponding isostructural analog with La. In our case we assumed that Sf(T ) ≈
SCe(T ) − SLa(T ). Such a ratio appears to be more convenient since the presence of
the local structure gf(E) near the level EF is the domineering factor in forming the
total thermoelectric power (SCe) and frequently it is not domineering in the case of
the total electrical resistivity (ρCe). It is particularly characteristic of Ce compounds
with transition 3d-elements [13].
3. Theoretical details
Theoretically, the transport properties of the systems with the IV of Ce have
been most logically studied by means of the Anderson model (AM) [5–7]. However,
it has not been possible so far to derive analytical relationships allowing for a de-
scription of the behavior of the systems with transport properties using the Ce IV
in a wide temperature range. This urged the development of various phenomenolog-
ical approaches [8–13], based on a two-band model. According to [8–13], the main
contribution to the transport properties was caused by scattering the electrons from
a broad s(d)-band to a narrow f -band of Lorentzian shape. The scattering process
can be described by the relaxation time in the form of
τsf(E, T )−1 ∝ gf(E)Rph(T ).
The function Rph(T ) takes into account the possible phonon-induced interband
s-f transition.
From the linearized Boltzmann transport equation, the following expressions for
electrical resistivity component and thermoelectric power connected with the IV of
Ce have been
ρf (T ) =
1
e2
1
L0
, Sf(T ) = − 1
|e|
L1
L0
,
Ln =
∞∫
−∞
Enτsf(E, T )
(
− ∂f
∂E
)
dE, n = 0, 1,
267
M.D.Koterlyn, R.I.Yasnitskii, B.S.Morokhivskii
where f(E) is the Fermi-Dirac distribution function. The contribution of such s-f
transitions to thermoelectric power in the approximation of an independent scatter-
ing on f -centers can be written as [13,17]
Sf(T ) =
2
3
π2kB
|e|
Tεf
(π2/3)T 2 + ε2
f + Γ2
f
, (1)
where εf and Γf are the position of the gf(E) peak relative to the Fermi level EF
and its width, respectively. Parameter kB is the Boltzmann constant. Equation (1)
satisfactorily describes the temperature dependences of thermoelectric power of the
majority of systems with IV of Ce even without taking into account the possible
temperature dependences of the parameters εf and Γf . However, the parameters
of the gf(E) peak determined from equation (1) do not quite agree with those de-
termined based on the measurements of thermodynamic and spectroscopic charac-
teristics [2,18,19]. The relationship between the parameters εf and Γf considerably
deviates from that assumed in the AM [6] or in the local Fermi-liquid model [20]
(by the thermopower data εf/Γf < 1 [8,9,13,17] when theoretical εf/Γf > 1). In the
case of strong orbital degeneracy of f -states (Nf � 1), which occurs in systems with
intermediate Ce valence, it is appropriate to use the well-known relation connecting
the parameters εf , Γf and TK (εf ≈ TK and Γf ≈ πTK/Nf [6]). Then, in place of
equation (1), we obtain a more convenient expression,
Sf(T ) =
2
3
π2kB
|e|
T · TK
(π2/3)T 2 + (1 + π2/N2
f )T 2
K
, (2)
with only one fitting parameter TK.
Recently we have shown [12] that a good agreement of the thermoelectric pow-
er curves calculated by equation (2) with the experimental data can be obtained
only when the temperature dependence of the parameter TK is taken into account.
This especially holds true for systems with the IV states of Ce, which are sensi-
tive to temperature. There arises an important problem of realistic estimations of
the temperature behavior of TK and their possible usage when describing electrical
resistivity within the framework of the accepted model.
With the aim of getting some idea of the behavior of the calculation ρf (T ), in
order to describe the contribution of phonon-induced interband s-f transition to the
resistance we use the simplest two-band spherical Mott–Wilson model [21] widely
employed in nonmagnetic transition metals with an incomplete d shell. Taking into
consideration only the N -process and temperature independent values of a matrix
element for phonon induced s-f transition, we receive
ρf(T ) =
R0 · Rph(T )
(π2/3)T 2 + (1 + π2/N2
f )T 2
K
, (3)
Rph(T ) = ns(T )−1
(
T
θD
)3
J3
(
θD
T
)
, (4)
268
Electronic transport properties of compounds . . .
where θD is the Debye temperature, R0 is the coefficient taking into account a
number of characteristic parameters of the model [21], ns(T ) is the effective number
of s electrons per atom depending on the temperature caused by the changes of f -
state occupation. The functions J3(x) are the well-known transport integrals defined
by
J3(x) =
∫ x
0
y3dy
(ey − 1)(1 − e−y)
.
Due to the special sensitivity of thermoelectric power to the parameters of the
fine structure density of states, a detailed concordance of the calculation with the
experiment was carried out only for the Sf(T ) component. The values of Sf cal-
culated by equation (2) were normalized by the coefficient p = Sfmax,exp/Sfmax,calc,
where Sfmax,exp and Sfmax,calc denote the maximal values of the experimental ther-
moelectric power and the calculated one. The parameter p takes into account the
discrepancy between the experimental values of Sf (T ) and those calculated without
allowing in (2) for the concentration of scattering f -centers and the presence of other
scattering mechanisms in the compound under study [22]. The dependences TK(T ),
obtained due to such a concordance, were used for the estimation of ρf (T ) and some
other crystal physical characteristics.
4. Results and analysis
According to spectroscopic measurements [23], transition of Ce from a state
with strongly mixed valence (Ce3.2+) to almost magnetic one (Ce3+) is observed
in CeNi in the temperature range T < 300 K. The similar decrease of the Ce
valence (≈ 0.1 − 0.2) takes place in the case of CeNi2 and CeNi2Si2 reaching the
state of Ce3.1+ [23,24]. Temperature dependences of the f -states of Ce contribution
to the total thermoelectric power (Sf) for compounds CeNi, CeNi2 and CeNi2Si2
are presented in figure 1. Apparently, typical features of the Sf(T ) dependence for
the compounds in question appear to be the presence of asymmetric maximum
(qualitatively Sf ∼ T at T < TSfmax
and Sf ∼ T−1 at T > TSfmax
) and a certain
deviation from linear behavior Sf ∼ T at low T with the occurrence of positive
curvature. A good agreement of the calculated thermoelectric power (figure 1, solid
curve) with the experiment is reached when the temperature dependence of the
parameter TK is considered (figure 2). In the low temperature range (T < TSfmax
),
the parameter TK sharply increases until values TK ≈ (2 − 5)TSfmax
. Linearity of
the dependence Sf (T ) at T < TSfmax
frequently observed in such systems [2,8,13] is
achieved only at TK = const according to equation (2). Such a dependence is shown
for CeNi2Si2 (figure 1, dotted curve calculated at TK = 680 K). The appearance of
the positive curvature on the dependence of Sf (T ) in the low temperature range
and the corresponding increase of TK (figure 2) makes it possible to coordinate the
parameters of the resonant structure gf(E) with the main thermodynamic properties
of crystals.
269
M.D.Koterlyn, R.I.Yasnitskii, B.S.Morokhivskii
Figure 1. Temperature dependences of the contribution of Ce f -states to the
total thermopower of CeNi (1), CeNi2 (2) and CeNi2Si2 (3). Solid lines plot ther-
mopower calculated from equation (2) in the suggested temperature dependence
of parameter TK and TK = const (dotted curve).
Figure 2. Temperature dependences of the parameter TK of CeNi (1), CeNi2 (2)
and CeNi2Si2 (3), obtained based on the agreement of experimental thermoelec-
tric power with that calculated by equation (2).
270
Electronic transport properties of compounds . . .
It is well known [6,25] that the majority of thermodynamic properties of the
systems with the IV of Ce are satisfactorily described within the framework of a
single impurity Anderson model with allowing for strong orbital degeneration
χ(0) =
µ2nf(0)
3TK(0)
(5)
and
γ(0) =
π2k2
Bnf (0)
3TK(0)
, (6)
where µ2 = g2
JJ(J + 1)µ2
B is the effective magnetic moment of the cerium 4f 1-
state, nf(0) and TK(0) is the electronic occupation of f -states of Ce and single-
ion Kondo temperature, respectively, at low temperatures. To assess the values of
TK(0) we use the known data [23] for the occupation of f -states of Ce in CeNi
(nf(0) = 0.88) determined at T = 80 K. To deduct the contributions of d-states of
Ni to the values of coefficients γ(0) and χ(0), it is possible to use the similar data for
LaNi. According to the data [26,27], γ(0) = 65 mJ·mol−1(CeNi), 5 mJ·mol−1(LaNi);
χ(0) = 2.2 · 10−3 emu·mol−1(CeNi), 0.2 · 10−3 emu·mol−1(LaNi). After substitution
of the data presented in equations (5) and (6), we obtain TK(0) = 350 and 390 K,
correspondingly. Results of the estimation of TK(0) are in a good agreement with
those determined by means of the thermoelectric power at low temperatures (we
obtain TK(0) = 360 K at T = 15 K). A similar assessment carried out for CeNi2 in
[19] gives TK(0) = 1500 K, which is also in a fair agreement with our calculations
(we obtain TK(0) = 1450 K by the thermoelectric power data at T = 15 K).
Figure 3. Temperature dependences of the contribution of Ce f -states to the
total electrical resistivity of CeNi (1) and CeNi2Si2 (2). Lines plot calculated
dependences according to equation (3).
271
M.D.Koterlyn, R.I.Yasnitskii, B.S.Morokhivskii
The experimental and calculated (solid curves) dependences of the component
ρf(T ) are shown in figure 3. The component for CeNi2 is not given, LaNi2 being
an unsuitable analogue for singling out a phonon component of electrical resistivity.
Calculation of normalized resistivity ρf(T )/R0 was carried out by equation (3) with
the use of the found dependence TK(T ) and additionally taking into account the
residual electrical resistivity ρf (0), taken from the experiment. The coefficient R0 is
chosen such that the numerical value of ρfmax/R0 agrees with the experimental data.
In the case of CeNi, the best agreement between the calculation and the experiment
is reached when the function Rph(T ) in equation (3) has the form of equation (4)
with θD = 110 K and dependence ns(T ) = ns(0) + 0.7 · 10−4T − 0.5 · 10−2T 1/2,
found with the spectroscopic data [23]. In case of CeNi2Si2, the best concordance
with the experiment is achieved only assuming Rph(T ) = const. The necessity of
taking into account the temperature dependence of the time relaxation testifies
to a considerable effect of electron-phonon interaction in CeNi on ρf (T ) behavior.
This fact agrees with an anomalously strong interaction of the electron system with
lattice vibrations revealed previously [28]. In the case of CeNi2Si2, the behavior type
of ρf (T )corresponds to the Mott scattering on s-f -transitions with allowing for the
temperature narrowing of the peak density of states gf(E). Some discrepancy of the
calculation with the experiment for CeNi2Si2 in the low temperature range can be
caused by partial display of coherent effects.
5. Conclusions
By the set of the data presented one can conclude that the transport properties
of the compounds with the temperature unstable IV of Ce can be satisfactorily
described in a wide temperature range within the framework of a simple model of a
narrow peak of the density of states gf(E) of Lorentzian shape with allowing for its
narrowing caused by stabilization of the Ce3+ states as the temperature increases.
The values of TK obtained at a low temperature are completely realistic and in a
good agreement with the assessments made by other methods. The differences in the
character of temperature dependences of electrical resistivity for CeNi and CeNi2Si2
are probably caused by different roles of band states played at forming IV of Ce.
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273
M.D.Koterlyn, R.I.Yasnitskii, B.S.Morokhivskii
Eлeктронні транcпортні влаcтивоcті cполук з
тeмпeратурно-нecтабільною проміжною
валeнтніcтю Ce
М.Д.Kотeрлин 1,2 , Р.Й.Яcницький 1 , Б.C.Морохівcький 1
1 Львівcький національний унівeрcитeт імeні Івана Франка,
вул. Драгоманова 50, 79-005, Львів, Україна
2 Акадeмія Бидгощcка, пл. Вeйcceнгоффа 11, 85-072 Бидгощ, Польща
Отримано 12 бeрeзня 2004 р.
Для cполук CeNi, CeNi2 та CeNi2Si2 прeдcтавлeні рeзультати вимі-
рювання в інтeрвалі тeмпeратур 4–800 K cкладових тeрмо-e.р.c. (Sf )
та eлeктроопору (ρf ), викликаних тeмпeратурно-нecтабільною про-
міжною валeнтніcтю Ce. Показано, що залeжноcті Sf (T ) та ρf (T ) в
широкому інтeрвалі тeмпeратур добрe опиcуютьcя на оcнові проcтої
модeлі вузького піку гуcтини cтанів gf (E) лорeнцівcької форми біля
рівня Фeрмі. Ширина піку залeжить від тeмпeратури і визначаєтьcя
одно-іонною тeмпeратурою Kондо TK.
Ключові слова: рідкіcнозeмeльні cполуки, валeнтні флуктуації,
eлeктроопір, тeрмоeлeктрорушійна cила
PACS: 72.20.Lp, 72.10. Fk, 72.15.Qm, 75.30.Mb
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