Anomalous expansion and phonon damping due to the Co spin-state transition in RCoO_ {3}(R= La, Pr, Nd, and Eu)

Abstract

We present a combined study of the thermal expansion and the thermal conductivity of the perovskite series RCoO3 with R=La, Nd, Pr, and Eu. The well-known spin-state transition in LaCoO3 is strongly affected by the exchange of the R ions due to their different ionic radii, i.e., chemical pressure. This can be monitored in detail by measurements of the thermal expansion, which is a highly sensitive probe for detecting spin-state transitions. The Co ions in the higher spin state act as additional scattering centers for phonons, therefore suppressing the phonon thermal conductivity. Based on the analysis of the interplay between spin-state transition and heat transport, we present a quantitative model of the thermal conductivity for the entire series. In PrCoO3, an additional scattering effect is active at low temperatures. This effect arises from the crystal-field splitting of the 4f multiplet, which allows for resonant scattering of phonons between the various 4f levels.

Full text

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arXiv:0803.1957v1 [cond-mat.str-el] 13 Mar 2008
Anomalous expansion and phonon damping due to the Co
spin-state transition in RCoO3with R=La, Pr, Nd and Eu
K Berggold1, M Kriener1‡, P Becker2, M Benomar1, M Reuther1,
C Zobel1and T Lorenz1
1II. Physikalisches Institut, Universit¨ at zu K¨ oln, Z¨ ulpicher Str. 77, 50937 K¨ oln, Germany
2Institut f¨ ur Kristallographie, Universit¨ at zu K¨ oln, Z¨ ulpicher Str. 49b, 50674 K¨ oln, Germany
E-mail: tl@ph2.uni-koeln.de
Abstract.
conductivity of the perovskite series RCoO3 with R = La, Nd, Pr and Eu.
known spin-state transition in LaCoO3 is strongly affected by the exchange of the R ions
due to their different ionic radii, i.e. chemical pressure. This can be monitored in detail by
measurements of the thermal expansion, which is a highly sensitive probe for detecting spin-
state transitions. The Co ions in the higher spin state act as additional scattering centers for
phonons, therefore suppressing the phonon thermal conductivity. Based on the analysis of
the interplay between spin-state transition and heat transport, we present a quantitative model
of the thermal conductivity for the entire series. In PrCoO3, an additional scattering effect is
active at low temperatures. This effect arises fromthe crystal field splitting of the 4f multiplet,
which allows for resonant scattering of phonons between the various 4f levels.
We present a combined study of the thermal expansion and the thermal
The well-
PACS numbers: 65.40.-b, 65.40.De, 65.40.G-, 72.20.-i
‡ current address: Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502,
Japan

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Anomalous thermal expansion and damping of the phonon heat transport of RCoO3
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1. Introduction
Cobalt compounds are of particular interest due to the possibility that Co ions can exhibit
differentspinstates andhencetheoccurrence oftemperature-drivenspin-statetransitions. The
most prominent example is LaCoO3, which has been intensively studied and controversially
debated for more than fifty years, see e.g. [1, 2, 3, 4, 5, 6, 7, 8, 9]. The Co3+ions in LaCoO3
feature a 3d6configuration which in principle can occur in three different spin states: a
nonmagnetic low-spin (LS) (t6
high-spin (HS) state (t4
realize the LS state at low temperatures. Above approximately 25K a higher spin state,
either IS or HS, becomes thermally populated affecting various physical properties, e.g. the
magnetic susceptibility χ or the thermal expansion α, which both exhibit pronounced maxima
in their temperature dependencies [10, 11]. The susceptibility is obviously affected because
the excited spin state, either IS or HS, induces a strong increase of the magnetization above
25K. The thermal expansion is affected due to the different ionic radii of the smaller LS-Co3+
with empty and the larger IS- or HS-Co3+ions with partially filled egorbitals. The spin-state
transition can be well described in a LS–IS scenario, i.e. the excited spin state is the IS state,
with a constant energy gap of ∆Co = 185K [10, 11]. However, more recent investigations
show, that a LS/HS model including spin-orbit coupling is more reasonable [12, 13, 14]. A
consequenceofthelattermodelisatemperature-dependentenergy gap∆Co(T),whichstrongly
increases with increasing temperature [13].
The spin-state transition in LaCoO3 is strongly affected by both, heterovalent and
isovalent doping on the La site. The former possibility causes hole doping and chemical
pressure and suppresses the spin-state transition due to the implementation of Co4+ions
[15, 16]. The latter one, i.e. chemical pressure without changing the Co valence, is usually
realized by introducing trivalent rare-earth ions R3+. In RCoO3the spin-state transition is not
suppressed but its onset is shifted to higher temperature. The energy gap between the LS and
the excited spin state increases from about ∆Co= 185K for R = La to ? 2000K for R = Eu
[11]. Moreover, due to the decreasing ionic radius of the lanthanide series, the structure
changes from rhombohedral in LaCoO3to orthorhombic for R = Pr, Nd and Eu. Recently,
it has been reported, that the low-temperature thermal conductivity of LaCoO3is also very
anomalous [17, 18]. This behaviour has been qualitatively attributed to the onset of the spin-
state transition. However, a quantitative analysis of the anomalous thermal conductivity of
LaCoO3has not been presented yet.
The aim of this paper is to develop a consistent picture of the influence of the spin-state
transition on the thermal conductivity. Therefore, we measured the thermal conductivity κ(T)
of the series RCoO3with R = La, Pr, Nd and Eu. Moreover, we studied the thermal expansion
α(T), which is a very sensitive probe to investigate spin-state and also crystal-field transitions
and their coupling to the lattice. In the quantitative analysis of our data, we will consider
both models of the spin-state transition, which are favoured for LaCoO3in the literature, i.e.
we will consider the LS–IS scenario with a constant ∆Coand the more recently proposed
spin-orbit coupled HS (SOcHS) model with a temperature dependent energy gap ∆Co(T).
2ge0
g, S = 0), an intermediate-spin (IS) (t5
g, S = 2). It is generally agreed that the Co3+ions in LaCoO3
2ge1
g, S = 1) and a
2ge2

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Anomalous thermal expansion and damping of the phonon heat transport of RCoO3
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Table 1. Characteristic properties of the investigated crystals. Here, Tondenotes the onset
temperature of the spin-state transition, ∆Cothe energy gap between the LS ground state and
the excited spin state (either IS or HS) and γ is related to their ionic radii difference (see text).
Due to the large Tonof EuCoO3we can only give lower limits for the values of γ and ∆Co, as
it was also the case in the related analysis of the magnetic susceptibility [11]. The last three
columns give the room-temperature values of the thermopower SRT, which for the LaCoO3
crystals have been taken from [18], and the crystal dimensions (sample cross section A and
sample length L) which are important for the measurements of κ (the cross section of S5 is an
approximate value, since it is not of rectangular shape).
Sample
Ton(K)
∆Co(K)
γ (%)
SRT(µV/K)
A(mm2)
L(mm)
LaCoO3(S1)
LaCoO3(S2)
LaCoO3(S3)
LaCoO3(S4)
LaCoO3(S5)
PrCoO3
NdCoO3
EuCoO3
251850.7 -700
1000
-600
1000
-300
-400
-400
-500
0.8 × 1.5
1.1 × 0.8
1.4 × 0.8
0.8 × 1.4
≃ 2.3
1.0 × 3.8
1.7 × 2.0
0.3 × 0.85
3.7
2.3
3.4
2.6
4.7
2.5
2.8
2.0
175
230
400
1200
1700
? 2000
2.8
4.8
? 10
2. Experiment
All RCoO3crystals have been grown in a floating-zone image furnace. We examine five
different LaCoO3 crystals identical to those used in [18], where details of the sample
preparation and characterization are given. For EuCoO3this information can be found in
[11]. The NdCoO3and PrCoO3single crystals have been grown in the same way as those
of LaCoO3and EuCoO3. Characteristic properties of all crystals are listed in table 1. The
thermal conductivity measurements have been performed by a standard steady-state method
using a differential Chromel-Au+0.07%Fe-thermocouple[19]. The thermal expansion below
≈ 200K was measured using a home-built high-resolution capacitance dilatometer [20],
whereas the high-temperature measurements 135K ? T ? 670K were performed using
commercial inductive dilatometer (TMA 7, Perkin-Elmer).
3. Results and Discussion
3.1. Thermal Expansion
In figure 1(a) we show the thermal-expansion coefficients α(T) = 1/L·∂L/∂T of RCoO3. The
low-temperature results of LaCoO3and EuCoO3were already discussed in detail in [10, 11].
The thermal expansion consists of a phononic part and a Schottky contribution, caused by
the thermal population of the egorbitals of the Co3+ions, i.e. α = αPh+ αSch. The latter
contribution causes the large maximum at ≃ 50K in LaCoO3. To further analyze the data
we subtract αPh, which we estimate using a Debye function with the Debye temperature
ΘD = 600K of LaCoO3 [21]. Here, we used the same ΘD for the various cobaltates,
but sample-dependent prefactors determined by scaling the Debye function to the low-

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Anomalous thermal expansion and damping of the phonon heat transport of RCoO3
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0200 400600
0
10
20
30
40
T (K)
αPh(Nd)
La
RCoO3
Eu
Pr
Nd
α (10
-6 / K)
(a)
0200400600
0
20
40
60
80
α−αPh (10
-6 / K)
400 K
TMI
(b)
Pr
Eu
Nd
T (K)
La
230 K
175 K
25 K
Figure 1. (a) Thermal expansion of RCoO3with R = La, Pr, Nd and Eu. The solid line is
the estimated phonon contribution of NdCoO3(see text). (b) Anomalous part of the thermal
expansion obtained by subtracting the phononic background. For clarity the different data
sets are offset by 10−5/K with respect to each other. The arrows signal the approximate
onset temperature of the spin-state transition and the solid circles denote the metal-insulator
transition temperature estimated from resistivity measurements for each compound. The solid
lines are fits of the respective Schottky anomalies, see equations(1) and (2), assuming a
constantenergygap∆Cobetweenthe differentspinstates ofCo3+. ThedashedlineforLaCoO3
is a similar fit using ∆Co(T) obtained from the magnetic susceptibility (see text).
temperature data of each compound. As an example, we show αPhfor NdCoO3in figure 1(a);
αPhof EuCoO3(PrCoO3; not shown) is slightly larger (smaller). Since a clear separation of
αPhand αSchis not possible for the low-temperature data of LaCoO3, we used αPhof EuCoO3
also for LaCoO3. The resulting αSchof all crystals are shown in figure 1(b). We note that, in
particular for PrCoO3and NdCoO3the spin-statetransitionis seen much better in the thermal-
expansion data than in the magnetic susceptibility. The reason is that αPhis rather small
compared to the total thermal expansion, whereas χ is dominated by the large contribution of
the 4f moments of the Pr3+and Nd3+ions, respectively, which makes a further analysis rather
uncertain. The insulator-metal transitions occurring above about 500K, see e.g. [11, 22] also
cause anomalies in α(T). The solid circles in figure 1(b) signal the transition temperatures
TMI, which have been determined from resistivity measurements on our crystals (not shown).
Within the LS/IS scenario with a constant ∆Co, αSch(T) is given by [10]
νexp(−∆Co/T)
?1 + νexp(−∆Co/T)?2,
where ν = 3 is the degeneracy of the excited spin state and γ is a measure of the ionic radii
difference of the Co3+in the LS and the excited spin state. Moreover, γ is related to the
uniaxial pressure dependence of ∆Covia γ = kB/Vfu· ∂∆Co/∂pα, where kBis Boltzmann’s
constant, Vfu≃ 56Å3the volume per formula unit and pαmeans uniaxial pressure along the
direction of which α is measured [23, 24]. To get the hydrostaticpressure dependence one has
to use the volume expansion which in the case of the twinned RCoO3single crystals is given
by 3α. The corresponding fit of α of LaCoO3(already presented in [10]) is shown by the solid
αSch(T) = γ∆Co
T2
(1)

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Anomalous thermal expansion and damping of the phonon heat transport of RCoO3
5
line in figure 1(b). The fit parameters are ∆Co= 185K and γ = 0.007 giving a hydrostatic
pressure dependence ∂(ln∆Co)/∂phydr≃ 45%/GPa, in agreement with the increase of ∆Coof
≃ 42% obtained from measurements of χ under ≃ 1.1GPa [25].
FortheSOcHS modelonehas toconsiderthetemperaturedependenceof∆Co[13], which
can be calculated from the measured χ(T) [11]. For LaCoO3, this yields a linear increase
∆HS
the MI transition. Using this ∆HS
Co(T) = ∆0
Co+ a · T with ∆0
Co= 135K and a = 1.66 in the temperature range almost up to
Co(T) in the partition sum, equation(1) modifies to
αSch(T) = γHS∆0
T2
?
The corresponding fit of αSchwith γHSas the only free parameter gives the dashed line in
figure 1(b). Obviously, both fits hardly differ because the modified ∆HS
larger value of γHS= 0.02. We note, however, that this does not necessarily correspond to a
larger pressure dependence of ∆0
dependencies of ∆0
of the small differences between both fits for LaCoO3, and since there are no indications for a
temperature-dependent ∆Cofrom other physical quantities, the fits of αSchof the other RCoO3
crystalshavebeen doneforconstantenergygapsonly. Sinceequations(1)and(2)areidentical
for a = 0, this analysis is not able to distinguish between both models. The obtained values of
∆Coand γ are given in table 1. As expected, ∆Costrongly increases with decreasing radius of
the R3+ions and therefore the spin-state transition monotonically shifts to higher temperature.
The onset temperature Tonof the spin-state transition for each compound, Ton≃ 25, 175, 230
and 400K for R = La, Pr, Nd and Eu, respectively, are marked by arrows in figure 1(b).
Co
νexp(−(∆0
Co+ aT)/T)
1 + νexp(−(∆0
Co+ aT)/T)
?2.
(2)
Cois compensated by a
Co, because αSchof equation(2) is determined by the pressure
Coand that of the slope a; see e.g. the discussions in [23, 26, 27]. In view
3.2. Thermal conductivity
Figure 2(a) displays the thermal-conductivity data of RCoO3. As has been already found in
previous studies on LaCoO3[17, 18], the overall shape and qualitative behaviour of κ(T) is
rather unusual. First of all, κ is rather low in the whole temperature range and its temperature
dependence clearly deviates from the typical behaviour expected for a conventional phononic
heat conductor. The thermal conductivity of LaCoO3exhibits a maximum around 20–30K.
Towards higher temperatures κ rapidly drops and features a minimum around 150K instead
of the expected 1/T-decrease (see also [18]). Qualitatively, this minimum can be traced back
to the spin-state transition of LaCoO3, which sets in close to the maximum of κ. The thermal
population of the Co eglevels induces a certain fraction of Co3+ions with a larger ionic radius
compared to the LS Co3+ions. These randomly distributed larger Co3+ions do not only cause
the huge anomaly in α(T), but also lead to additional disorder in the lattice and therefore act
as additional scattering centers for phonons. Hence, the thermal conductivity is additionally
suppressed. A quantitative description will be given below.
Since the spin-state transition shifts to higher temperature when La3+is replaced by
smaller R3+ions, the above scenario suggests that the onset of the suppression of κ(T) of
RCoO3systematically shifts towards higher temperature with decreasing radius of the R3+