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Ground-state properties of the mixed-valence cobaltites Nd0.7Sr0.3CoO3, Nd0.7Ca0.3CoO3and Pr0.7Ca0.3CoO3This content has been downloaded from IOPscience. Please scroll down to see the full text.
2013 J. Phys.: Condens. Matter 25 216006(http://iopscience.iop.org/0953-8984/25/21/216006)
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IOP PUBLISHING

JOURNAL OF PHYSICS: CONDENSED MATTER

J. Phys.: Condens. Matter 25 (2013) 216006 (12pp)

doi:10.1088/0953-8984/25/21/216006

Ground-state properties of themixed-valence cobaltites Nd0.7Sr0.3CoO3,
Nd0.7Ca0.3CoO3 and Pr0.7Ca0.3CoO3
Z Jirák1 , J Hejtmánek1 , K Knı́žek1 , M Maryško1 , P Novák1 , E Šantavá1 ,T Naito2 and H Fujishiro2
1
2

Institute of Physics ASCR, Cukrovarnická 10, 162 00 Prague 6, Czech Republic
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan

E-mail: jirak@fzu.cz

Received 15 January 2013, in final form 9 April 2013
Published 3 May 2013
Online at stacks.iop.org/JPhysCM/25/216006
Abstract
The electric, magnetic, and thermal properties of three perovskite cobaltites with the same
30% hole doping and ferromagnetic ground state were investigated down to very low
temperatures. With decreasing size of large cations, the ferromagnetic Curie temperature andspontaneous moments of cobalt are gradually suppressed: TC = 130 K, 55 K and 25 K andm = 0.68 µB , 0.34 µB and 0.23 µB for Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 andNd0.7 Ca0.3 CoO3 , respectively. The moment reduction with respect to the moment of theconventional ferromagnet La0.7 Sr0.3 CoO3 (TC = 230 K, m = 1.71 µB ) in the so-called low
spin/intermediate spin (IS/LS) state for Co3+ /Co4+ was originally interpreted using aphase-separation scenario. Based on the present results, mainly the analysis of the Schottky
peak originating from Zeeman splitting of the ground-state Kramers doublet of Nd3+ , we find,however, that the ferromagnetic phase in Nd0.7 Ca0.3 CoO3 and likely also in Pr0.7 Ca0.3 CoO3 is
uniformly distributed over the whole sample volume, despite the severe drop of moments. The
ground state of these compounds is identified with the LS/LS-related phase derived
theoretically by Sboychakov et al (2009 Phys. Rev. B 80 024423). The ground state of
Nd0.7 Sr0.3 CoO3 with an intermediate cobalt moment is inhomogeneous due to competition
between the LS/LS and IS/LS phases. In the theoretical part of the study, the crystal field split
levels for 4f3 (Nd3+ ), 4f2 (Pr3+ ) and 4f1 (Ce3+ or Pr4+ ) are calculated and their magnetic
characteristics are presented.
(Some figures may appear in colour only in the online journal)

1. Introduction

temperature increasing above ∼40 K the energetically close
HS (high spin, t42g e2g ) species start to be populated by thermal
excitation. The process is readily seen in the course ofmagnetic susceptibility or in anomalous terms of the lattice
expansion due to the ionic size of HS being notably larger
than that of LS (see e.g. [4]). These experiments show thatthe HS population increases gradually with the steepest rate at∼80 K, and is practically saturated above 150 K, comprising
about 40–50%. Strong HS/LS nearest neighbor correlations oreven short-range ordering are anticipated in this phase [5–7].
At still higher temperature the ordering melts, which isaccompanied by a drop of the electrical resistivity andIn the perovskite cobaltites, two prototypical behaviors can be
distinguished. The first one is associated with spin transition,or spin-state crossover of Co3+ ions in LaCoO3 and its rareearth analogs, while the second one is manifested by a robust
ferromagnetic metallic ground state that is observed in themixed-valence La1−x Srx CoO3 systems above a critical doping
value of x = 0.22 and exists up to the formally pure Co4+ end
compound SrCoO3 [1–3].
It is well established that the ground state of LaCoO3
is based on non-magnetic low spin (LS, t62g ) states. With0953-8984/13/216006+12$33.00

1

c 2013 IOP Publishing Ltd Printed in the UK & the USA

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

thermopower values at about 530 K, reminiscent of the I–M
transition. The character of the high-temperature phase is not
yet recognized. Intermediate spin (IS) Co3+ states (t52g e1g )have been tentatively suggested [8, 9, 7], but very recent
LDA + DMFT calculations did not reveal any significant
amount of IS Co3+ in the fluctuating mixture of spin states
in LaCoO3 at high temperatures [10].
The metallic conductivity in La1−x Srx CoO3 systems
with stable ferromagnetic ground state is related to fastvalence fluctuations that involve various 3dN (N = 5–7) states
on cobalt sites [11]. In particular, for La0.7 Sr0.3 CoO3 , thedominant population is the IS/LS states for Co3+ /Co4+ , sothat the electronic structure can be approximated as t52g σ ∗0.7 ,where σ ∗ is an antibonding band of the eg parentage. This
yields a spontaneous moment of 1.70 µB , in agreementwith 1.71(2) µB determined by neutron diffraction (Curie
temperature TC = 230 K) [1, 2]. The spontaneous moment
increases with further hole doping, but most of the publisheddata for x > 0.5 are influenced by severe oxygen deficiencyof the samples. Nevertheless, the nearly pure Co4+ system
SrCoO3 has been prepared under very high pressures, yielding
a moment of 2.5 µB (TC = 305 K) [3]. This means thatelectrons are not depopulated from the eg -derived σ ∗ band
but from the more localized t2g levels, so that, in gross
simplification, the final electronic structure of SrCoO3 can bepresented as t42g σ ∗1 (see [11] for a more detailed description).
As far as the transition range between LaCoO3 andLa0.7 Sr0.3 CoO3 is concerned, significant data have beenobtained in the single crystal studies of He et al [12, 13].
The La1−x Srx CoO3 systems above x = 0.22 show characteristics of conventional ferromagnets. The ferromagnetic–paramagnetic (FM–PM) transition is manifested by a large
λ peak in the specific heat and by the presence of a sharp
critical scattering peak in small-angle neutron scattering
at TC . As shown in recent re-investigation of the criticalexponents β, γ and δ by Khan et al, the transition isunambiguously of second order, characterized by scaling
behavior that belongs to the universality class of the 3D
Heisenberg model [14]. In contrast, in single crystal samples
below x = 0.22 the anomalies at TC are absent or smearedout, pointing to a much more complex temperature behavior
including magnetic/electronic phase separation. The magnetic
inhomogeneity of low-doped La1−x Srx CoO3 has also been
proved in inelastic neutron diffraction by Phelan et al [15] orin NMR study by Smith et al [16].
The two regimes of behavior in La1−x Srx CoO3 , separated
by the critical doping x = 0.22, have been interpreted
theoretically by Sboychakov et al [17]. Based on a fermionicmodel of Hubbard type, two possible FM ground statesthat may coexist on a nanoscopic scale are found. One isderived from the phase characterized by an LS/LS state forCo3+ /Co4+ , in which only a few Co3+ t2g electrons arepromoted to itinerant eg levels with increasing strontium
doping. The second phase is an IS/LS state for Co3+ /Co4+ ,i.e. the already mentioned t52g σ ∗ phase, which becomesdominant above the critical composition xc ∼ 0.20. The model
phase diagram presented in [17] thus reproduces remarkably
well the features actually observed in the La1−x Srx CoO3
system.

The properties of mixed-valence cobaltites can be further
modified by control of the ionic size on perovskite A sites.
Many studies have been carried out on the Pr1−x Cax CoO3
system that exists in a limited range up to x ∼ 0.55 [18, 19].
The substitution of smaller Pr3+ and Ca2+ ions for La3+and Sr2+ ions causes larger size misfit between the A andB sites of the perovskite structure (Goldschmidt’s tolerance
factor is reduced), which results in larger deviation of the
Co–O–Co bond angles from the ideal 180◦ and, subsequently,
in narrowing of the eg -derived band. The reduced bandwidth isdetrimental not only for macroscopic conductivity but also forferromagnetic interactions mediated by itinerant eg electrons(the double exchange). Ferromagnetism is thus suppressed
and, at the same time, the LS Co3+ states are promoted due tothe larger t2g –eg gap. As an ultimate effect we may mention
the peculiar behavior of Pr1−x Cax CoO3 systems within
the range x = 0.50–0.55; these exhibit a sharp first-ordertransition to a low-temperature highly resistive and weakly
magnetic state. It is of interest that the transition is associatedwith a charge transfer between the cobalt and praseodymiumsites, resulting in a stabilization of formally Pr4+ states;
see e.g. [20, 21] and references therein. In the region of
30% electron hole doping, on which our study is focused,pronounced effects of competing ground states were reported
for Pr0.7 Ca0.3 CoO3 , as well as for Nd0.7 Ca0.3 CoO3 , and thephase-separated nature of these compounds was guessed also
from the magnetization values, which are severely reduced
compared to La0.7 Sr0.3 CoO3 ones [22–25].
More direct information on the temperature dependenceof magnetic/electronic phase separation was recently provided
by the neutron diffraction, small-angle scattering, and magnetometry study of Pr0.7 Ca0.3 CoO3 by El-Khatib et al [25].
The study showed that FM clusters (presumably hole-rich
objects) were formed at a well-defined temperature T ∗ ∼250 K, while the hole-poor PM matrix was transformed tolong-range FM order at a much lower temperature TC =70 K. It is of interest that the preformed clusters did notdissolve immediately, but were preserved well below 70 K.
This unusual coexistence of short- and long-range ordered FMphases possessing different coercivities was further supported
by observation of exchange-spring behavior, which is known
for artificial hard–soft magnetic composites [25]. It should
be noted that such a behavior refers to a temperature rangeof 50–70 K only. The aim of this study is to resolve thefinal magnetic composition in Pr0.7 Ca0.3 CoO3 and related
compounds at the lowest temperatures.
Our paper reports on an electric, magnetic, and heat
capacity investigation of selected 30% doped systems,
in decreasing order of tolerance factors Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 . The respective spontaneous moments are determined as 0.68 µB , 0.34 µB
and 0.23 µB (TC = 130, 55 and 25 K). Such a dropof magnetization compared to 1.71 µB in La0.7 Sr0.3 CoO3
possessing a robust IS/LS phase was previously interpreted
within the phase-separation scenario, supposing that FM
ordered regions of higher hole doping are embedded in
the non-magnetic matrix of low hole doping [22–25]. The
present results contradict this conjecture. Based on detailed2

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et alcharacterization and novel application of Kramers ions Nd3+
as a local probe of the magnetic ground state, we showthat the internal field formed by cobalt spins is uniformly
distributed over the sample volume. The presence of grossmagnetic/electronic phase separation in Nd0.7 Ca0.3 CoO3 or
Pr0.7 Ca0.3 CoO3 at the lowest temperatures is thus questioned.
We argue that the ground state of these samples is in fact the
FM saturated LS/LS-derived phase suggested by Sboychakov
et al [17].

2. Experimental details
Polycrystalline samples of Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3
CoO3 and Nd0.7 Ca0.3 CoO3 were prepared using a solid-state
reaction. Raw powders of Pr6 O11 , Nd2 O3 , Y2 O3 , Co3 O4 ,CaCO3 and SrCO3 were weighted with proper molar ratios
and ground using an agate mortar and pestle for 1 h. The
mixed powders were calcinated at 1000 ◦ C for 24 h in air.
They were subsequently pulverized and ground. Then they
were pressed into pellets of 20 mm diameter and 4 mm
thickness. The pellets were sintered at 1200 ◦ C for 24 h
in 0.1 MPa flowing oxygen gas. The measured density ofeach sample was greater than 90% of the ideal density.
Powder x-ray diffraction patterns were taken for each sample
using Cu Kα radiation; the samples were confirmed tohave a single phase orthoperovskite (Pbnm) structure. The
lattice parameters and volumes per f.u. actually obtained
were a = 5.364 Å, b = 5.409 Å, c = 7.599 Å, V/Z =3
55.11 Å for Nd0.7 Sr0.3 CoO3 , a = 5.363 Å, b = 5.351 Å, c =37.570 Å, V/Z = 54.32 Å for Pr0.7 Ca0.3 CoO3 and a =35.344 Å, b = 5.342 Å, c = 7.549 Å, V/Z = 53.87 Å for
Nd0.7 Ca0.3 CoO3 . The present values are in agreement with theliterature data for the same compounds [22, 26]. As far as theimportant question of the oxygen stoichiometry is concerned,
practically ideal oxygen content of 2.99 ± 0.01 was evidenced
for the Pr0.7 Ca0.3 CoO3 specimen by Rietveld refinement of
the high resolution neutron diffraction data [27]. The same
seems to be valid for other two compounds based on indirect
arguments, which follow from thermopower data presented
below.
The electrical resistivity and thermoelectric power were
measured using a four-probe method with a parallelepipedsample cut from the sintered pellet. The electrical current
density varied in dependence on the sample resistivity
between 10−1 A cm−2 (metallic state) and 10−7 A cm−2
(insulating state). The measurements were made duringcooling and warming of the sample. In the low-temperature
range, a closed-cycle cryostat working down to 2–3 K
was used. For the high-temperature experiments up to
1000 K the sample was placed on a ceramic sample holder
centered in a small tubular furnace with precisely controlledtemperature. Standard chromel–alumel thermocouples wereused to monitor of the temperature gradient around 5 K,
imposed across the sample by means of an additional small
furnace.
The magnetic measurements were carried out using a
SQUID magnetometer MPMS-XL (Quantum Design) in the

Figure 1. Resistivity of the Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 andNd0.7 Ca0.3 CoO3 ceramic samples. Results for La0.7 Sr0.3 CoO3
ceramics are added for comparison. The inset shows that, except for
Nd0.7 Ca0.3 CoO3 , the apparent activation energy, defined as
EA = kd(ln ρ)/d(1/T), is below the thermal energy in the wholetemperature range (the full line refers to kT).

temperature range 2–400 K. The zero-field-cooled (ZFC)
and field-cooled (FC) susceptibilities were measured under
different applied fields. The initial AC susceptibility (H = 0)
was studied in the frequency region 0.12–87.4 Hz using adriving AC field of 3.9 Oe. The virgin magnetization curves
and hysteresis loops (−70 kOe, 70 kOe) in the ZFC regimes
were recorded for selected temperatures starting from T =2 K. In addition to this, the FC hysteresis loops were measured
after cooling the sample from T = 300 to 2 K under an appliedfield of 70 kOe.
The specific heat was measured by a PPMS device(Quantum Design) using the two-τ model. The data werecollected during sample cooling. The experiments at very low
temperatures (down to 0.4 K) were performed using the 3 He
option.

3. Results
3.1. Electric transport
Resistivity data obtained on ceramic samples of
Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 arepresented in the log–log plot in figure 1. As far as theimportant question on metallic or insulating character of thesesystems is concerned, we argue that the bulk properties are
generally influenced by the sample granularity, which also
seems to be so in the present case. Namely, the measured
resistivity steadily increases with decreasing temperaturebut, instead of divergence at the lowest temperatures, it
extrapolates to finite values of about 1–10 m cm atzero K, satisfying the criterion for metallic ground state,d(ln ρ)/d(ln T) → 0 [28]. Another signature for intrinsic
metallicity is the apparent activation energy, defined as EA =kd(ln ρ)/d(1/T). It does not exceed the thermal energy kB T,
except for slightly enlarged EA values for Nd0.7 Ca0.3 CoO3
3

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

Figure 3. The zero-field-cooled (full symbols) and field-cooled(open symbols) curves of DC susceptibility in Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 , measured at a field of1000 Oe. The effect of an additional disorder is demonstrated by thedata for (Nd1−y Yy )0.7 Ca0.3 CoO3 (y = 0.10).

Figure 2. The thermopower data for Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 , Nd0.7 Ca0.3 CoO3 and La0.7 Sr0.3 CoO3 .

above TC (see the inset of figure 1). On the other hand, thethermopower data are rather insensitive to the presence ofgrain boundaries. The Seebeck coefficient is positive over
the whole temperature range, pointing to a hole character ofthe carriers (figure 2). The low-temperature dependence isof linear (metallic-like) type, but soon tends to a maximum
at about 150 K, which reaches ∼25, 40 and 55 µV K−1
for Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 ,respectively. Then the thermopower slowly decreases towarda plateau of 20 µV K−1 at high temperatures. Let us notethat the maximum values of thermopower are indirect butvery sensitive indicators of the hole doping level and, basedon close agreement with data on samples oxygenated under
60 atm pressure in the work of Masuda et al [26], they attest
to an oxygen stoichiometry close to the ideal one for ourcompounds.
The
electric
properties
of
Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 differ substantiallyfrom the behavior of analogously prepared La0.7 Sr0.3 CoO3
ceramics, for which the data have been added to figures 1
and 2. First, the resistivity in the La0.7 Sr0.3 CoO3 sample
shows a typical metallic dependence with a resistivity drop
below TC ∼ 220 K. This becomes still more evident in thegraph of the apparent activation energy. A more importantsignature of a different ground state is, however, the changeof thermopower to negative values at low temperatures, inthe case of La0.7 Sr0.3 CoO3 pointing to a dominant role ofthe electron carriers of eg parentage. On the other hand,the above mentioned hole character of the thermopowerin Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3
suggests that the transport of eg carriers is impeded due tothe band narrowing and/or depopulation, and the t2g band
becomes the prevalent conducting channel.

susceptibility with effective moments that agree very wellwith free-ion values at intermediate and high temperatures,µeff ∼ 3.5 µB for both Nd3+ and Pr3+ . However, asignificant deviation from this behavior is observed below∼50 K, where the effects of crystal field splitting on the
4f shell become important. The low-temperature properties
then depend critically on the character of the rare-earth
ground state, which is a Kramers doublet for Nd3+ in the
low-symmetry crystal field of perovskite A sites, while thenon-Kramers ions Pr3+ possess a singlet state. This issue isdiscussed in detail below in section 3.3 and the appendix.
The basic magnetic characterization of Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 is represented by the
ZFC and FC susceptibilities χZFC and χFC measured in a fieldof 1000 Oe (figure 3). Starting from room temperature, bothsusceptibilities increase with decreasing temperature, and theonset of FM phase (Curie temperature) can be specified fromthe inflection point of the χFC (T) dependence. This yields
TC = 130, 55 and 25 K for Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3
and Nd0.7 Ca0.3 CoO3 , respectively. With further decreaseof temperature, the χZFC curves exhibit a maximum at atemperature decreasing with the increasing applied field.
The χFC data for Pr0.7 Ca0.3 CoO3 increase steadily toward
zero temperature, while those for Nd0.7 Sr0.3 CoO3 andNd0.7 Ca0.3 CoO3 show a sudden decrease at the lowest
temperatures. Such a drop is caused by Nd3+ moments thatare induced by the FM order in the cobalt subsystem andorient antiparallel to the Co3+ /Co4+ spins. See, e.g., themagnetic and neutron diffraction study of a Nd1−x Srx CoO3
sample with x = 0.33 by Krimmel et al [29]. This effect is notseen in the Pr0.7 Ca0.3 CoO3 sample since the singlet groundstate of Pr3+ lacks an intrinsic moment and shows only weakmagnetic polarization that arises due to mixing with excitedstates.
The inverse susceptibility data are presented in a broader
range of temperature in figure 4. The curvature above TC ,which is marked for Nd0.7 Ca0.3 CoO3 and Pr0.7 Ca0.3 CoO3 but

3.2. Magnetic properties
The magnetism in the presently studied systems is governedby the cobalt spins and their exchange interactions. The
contribution of rare earths is manifested by Curie-like
4

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

Figure 4. The inverse susceptibility for Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 , Nd0.7 Ca0.3 CoO3 and (Nd1−y Yy )0.7 Ca0.3 CoO3
(y = 0.10), based on FC data.

hardly visible for Nd0.7 Sr0.3 CoO3 , represents a characteristic
behavior for samples with ferrimagnetic ground state. Thissuggests that not only the Co–Nd but also the Co–Pr exchange
are of antiferromagnetic (AFM) kind.
Taking into account the complexity of exchange interactions and crystal field effects, no definite conclusions on thecobalt spin states and their temperature dependence can be
drawn from the low-temperature susceptibility data. A simpler
situation occurs close to room temperature, where the inverse
susceptibility approaches a linear Curie–Weiss behavior. The
slope for Nd0.7 Sr0.3 CoO3 gives, after subtraction of thefree-ion value for the Nd3+ contribution, an effective momentof µ2eff ∼ 10 µ2B per Co. This is exactly the theoreticalvalue for an IS/IS Co3+ /Co4+ mixture, which corroborates
the results for La1−x Srx CoO3 in the 300–600 K range
reported by Wu and Leighton [2]. On the other hand,the asymptotic behavior of the high-temperature inverse
susceptibility data for Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3
gives notably larger effective moments of µ2eff ∼ 15 and19 µ2B per Co, respectively, which may suggest that the Co3+
occur partially in the HS state as is the case for LaCoO3
at room temperature. This conjecture seems to be supportedby the observed Weiss temperature θ that changes frompositive (FM, case of Nd0.7 Sr0.3 CoO3 ) to negative (AFM,
case of Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 ) values. Withlarger disorder, the AFM interactions strengthen, as clearlyseen for the Nd0.7 Ca0.3 CoO3 sample with yttrium doping,
added to figures 3 and 4. Although the AFM interactions
between cobalt and rare earths may play some role, we
relate such drastic change of the magnetic interactions at hightemperature mainly to the presence of excited HS Co3+ statesin the matrix of dominant LS or IS Co3+ character.
The behavior of Nd0.7 Ca0.3 CoO3 and Nd0.7 Sr0.3 CoO3
in the vicinity of the FM transition has been further probed
by AC susceptibility, for which the real and imaginary parts
both culminate near TC . For Nd0.7 Ca0.3 CoO3 it is clearlyseen that the characteristic temperature Tf , at which thereal part χ 0 passes through a maximum, exhibits an upward

Figure 5. The real part of the AC susceptibility for Nd0.7 Ca0.3 CoO3
and Nd0.7 Sr0.3 CoO3 . The experimental data are marked by thesymbols; the full lines represent the least-squares fit of the peakform. The inset shows the frequency dependence of the freezing
temperature Tf , corresponding to the susceptibility maximum.

shift with increasing frequency ν of the applied AC field(figure 5). In analogy to freezing processes in spin-glass
systems, this shift can be quantified by a semiempiricaldimensionless parameter K = 1Tf /[Tf 1(log ν)]. The value of
this parameter was evaluated from the linear approximation of
the dependence Tf (log ν) (see the inset of figure 5) using theleast-squares method, which yields K = 0.0095 ± 0.0005. For
Nd0.7 Sr0.3 CoO3 , where the frequency shift is less obvious,
the analysis gives K = 0.0017 ± 0.0003. The existence of afinite frequency shift means that some glassiness or ‘glassy
ferromagnetism’ is involved in a broad range below TC , andthis refers not only to weakly magnetic Nd0.7 Ca0.3 CoO3 but
also to Nd0.7 Sr0.3 CoO3 with a stronger FM ground state.
The virgin magnetization curves and ZFC hysteresis
loops in fields up to 70 kOe are presented in figure 6.
The results at the lowest temperatures show a superpositionof a nearly rectangular hysteresis loop with a linear
component that is mostly due to the rare-earth contribution.
As expected for the magnetic ground state of Kramers
ions Nd3+ , this additional term (paraprocess) is especiallylarge for Nd0.7 Sr0.3 CoO3 and Nd0.7 Ca0.3 CoO3 , while it ismuch smaller and apparently temperature independent for
Pr0.7 Ca0.3 CoO3 . The spontaneous magnetization values for5

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

Figure 7. The heat capacity of Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3
and Nd0.7 Ca0.3 CoO3 at intermediate temperatures. The arrow marksa weak anomaly at TC for Nd0.7 Sr0.3 CoO3 .

signify that, unlike in Nd0.7 Ca0.3 CoO3 , the cobalt moment
in Nd0.7 Sr0.3 CoO3 increases notably under application ofan external field, namely from 0.67 µB /Co at zero field toabout 1.3 µB /Co at 140 kOe. The different behavior andinhomogeneous character of the Nd0.7 Sr0.3 CoO3 sample has
also been manifested in a shift of the center of the FC
hysteresis loop toward negative fields (the exchange bias is
actually 230 Oe at T = 2 K—not shown in figure 6(a)).
3.3. The low-temperature specific heat
The specific heat data for all studied samples are presented
in a broad temperature range in figure 7. The main
contribution comes from lattice dynamics, characterized by
the Debye temperature θD ∼ 350–400 K for Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 . In addition, there are
two contributions that may affect the specific heat values
at intermediate temperatures. One is the magnetic term due
to cobalt ions, which is manifested by a very weak λlike anomaly at TC in Nd0.7 Sr0.3 CoO3 , but is supposedly
spread over a larger temperature range in Pr0.7 Ca0.3 CoO3
and Nd0.7 Ca0.3 CoO3 . The second contribution is due tothermal excitation among the rare-earth 4f electronic levels.
In the Pr0.7 Ca0.3 CoO3 system with perovskite structureof the orthorhombic Pbnm symmetry, the 3 H4 electronic
multiplet of Pr3+ is split by crystal field effects to nine
singlet levels that are displaced over a large energy range of
100 meV [30]. The thermal population of the first excitationlevel at about 5 meV is manifested in the specific heat as abroad Schottky-type contribution, the onset of which is readily
seen as a hump in the Pr0.7 Ca0.3 CoO3 data at about 20 K. A
more interesting situation is encountered in Nd0.7 Sr0.3 CoO3
and Nd0.7 Ca0.3 CoO3 , where the 4 I9/2 multiplet of Nd3+ is
split to five Kramers doublet levels [31]. Firstly, the energy
gap between the ground doublet and the first excited doublet islarger, 12 meV, so that the relevant Schottky-type contribution
is shifted to higher temperatures and becomes more diffusive.
Secondly, the presence of an internal field due to FM orderingin the cobalt subsystem is responsible for lifting of the

Figure 6. The virgin magnetization curves and ZFC hysteresis
loops for Nd0.7 Sr0.3 CoO3 (a), Nd0.7 Ca0.3 CoO3 (b) andPr0.7 Ca0.3 CoO3 (c), taken at selected temperatures between TC and2 K.

the Co subsystem, estimated by linear extrapolation to zero
field, are 0.68, 0.34 and 0.23 µB /Co for Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 , respectively. (In order
to eliminate the contribution of Nd3+ moments in antiparallelalignment, the extrapolation was made using hysteresis curves
at higher temperatures, 40 K for Nd0.7 Sr0.3 CoO3 and 10 K for
Nd0.7 Ca0.3 CoO3 , and a small temperature correction of about
5% was applied, based rather arbitrarily on the S = 2 Brillouinfunction.) Concerning the rare-earth contribution, we note thatthe magnetization curve for Nd0.7 Ca0.3 CoO3 at 2 K tends
in high fields to a saturation of about 1.3 µB /f.u., whichshould be interpreted as a sum of µ(Co) + 0.7µ(Nd). Since
our Brillouin analysis of magnetization curves in a broader
temperature range did not reveal any observable paraprocessof the Co subsystem in the Nd0.7 Ca0.3 CoO3 sample, we may
conclude that the contribution of neodymium moments isabout 1.0 µB , or equivalently 1.4 µB per Nd3+ ion.
The same Nd3+ moment can be anticipated also for the
Nd0.7 Sr0.3 CoO3 sample. Here, much higher fields are needed
to approach magnetic saturation, because of the stronger
AFM coupling between the Co and Nd subsystems. Basedon a trial measurement at 2 K up to 140 kOe, we haveestimated a saturated moment of 2.3 µB /f.u.. This may
6

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

Figure 8. The low-temperature heat capacity of Nd0.7 Ca0.3 CoO3
and Nd0.7 Sr0.3 CoO3 . The background line corresponding to acontribution of the hyperfine, lattice and linear terms is estimatedwith a relative uncertainty of about 5%, which reflects someambiguity in the α, β and γ parameters.

Figure 9. The heat capacity divided by the temperature for
Nd0.7 Ca0.3 CoO3 and Nd0.7 Sr0.3 CoO3 , after subtraction of the latticeand nuclear terms. The full lines present the theoretical fit based on
the broadening due to anisotropic Zeeman splitting.

Kramers degeneracy of Nd3+ electronic states by Zeeman
effects. In particular, a ground level split by an internal field isa realization of the standard two-level system for pseudospins
J 0 = ±1/2 relevant to two eigenstates of the ground doublet.
Their thermal redistribution is reflected by the appearance ofa characteristic Schottky peak in the low-temperature specificheat, see e.g. [32, 33]. For the present samples, these Schottky
peaks and their shift with applied magnetic field are seen
in more detail in figure 8. In the subKelvin range there isanother field-dependent Schottky anomaly of nuclear (141 Pr,
143/145 Nd, 59 Co) origin. This T −2 term is especially strong forPr0.7 Ca0.3 CoO3 (not shown) because of the large Van Vleck
susceptibility of praseodymium in the ground singlet state andthe strong hyperfine coupling constant.
The profile of the Nd3+ related Schottky peaks and thelocation on the temperature scale ∼1–10 K are controlled by
Zeeman splitting of the ground doublet −1E = gJ 0 µB Heff ,where Heff is the vector sum of internal and external fields
experienced by pseudospins J 0 = ±1/2 in the solid-statematerial. The relevant data, i.e. after subtraction of thehyperfine, lattice and linear terms, are displayed as cSchottky /Tversus T in figure 9. Although the observed curves arebroadened with respect to the ideal Schottky peak as
exemplified in figure 10, no dual distribution of effective

fields is found. Macroscopic phase segregation is thus
ruled out. Moreover, the observed broadening does notnecessarily mean inhomogeneous distribution of effective
fields as it can be completely ascribed to anisotropy of
the gJ 0 -factor and averaging in polycrystalline samples. The
analysis has actually been made supposing an axial symmetryof the g-tensor for the Nd3+ ground doublet, so that itis described by two components gk and g⊥ only. Thismodel leads to a modified Schottky form, where the energy
splitting 1E for a particular site is given by the angle
θ corresponding to the deviation of the local gJ 0 -factor
axis from the direction of the magnetic field. The partial
contribution to the overall Schottky-like anomaly is calculated
as [(1Ek cos θ )2 + (1E⊥ sin θ )2 ]1/2 , and the contribution
to specific heat is weighted by sin θ , which corresponds
to the random orientation of crystallites in the sample.
The fit, represented by solid lines in figures 9 and 10,
gives for Nd0.7 Ca0.3 CoO3 the ratio 1Ek /1E⊥ = gk /g⊥ ∼3.0, irrespective of the strength of the applied field. The
Nd0.7 Sr0.3 CoO3 sample shows at Hext = 0 and 10 kOe an
excessive broadening and lower height of the Schottky peaks.
At higher fields, the curves acquire a similar form and thefit gives a ratio 1Ek /1E⊥ = gk /g⊥ ∼ 4.5. For the absolute
7

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

Figure 11. Average Zeeman splitting of the Nd3+ ground doublet
for Nd0.7 Ca0.3 CoO3 and Nd0.7 Sr0.3 CoO3 . The linear behavior for
Nd0.7 Ca0.3 CoO3 above Hext = 50 kOe gives hgJ 0 i = 1.85. Similar
dependence is observed also for the nuclear term αT −2 in
Pr0.7 Ca0.3 CoO3 . The parameter α, which is proportional to thehyperfine field induced by the Van Vleck susceptibility of the Pr3+
electronic singlet, reaches the values 0.0034 J K mol−1 and
0.0220 J K mol−1 for Hext = 0 and 90 kOe, respectively.

field to 3.65 ± 0.07 J mol−1 K−1 . These values correspondto 85% and 90% of the theoretical value, respectively. The
increase with applied field indicates an increasing numberof Nd3+ pseudospins contributing to the Schottky peak. The
reduced entropy value at zero field, the large width of the
Schottky peak showing a gradual narrowing with the appliedfield, and the magnetic characteristics mentioned above(paraprocess of the Co subsystem, finite exchange bias) aresignatures of an inhomogeneous FM state in Nd0.7 Sr0.3 CoO3 .

Figure 10. The cSchottky contribution to the low-temperature heat
capacity of Nd0.7 Ca0.3 CoO3 and Nd0.7 Sr0.3 CoO3 at Hext = 50 kOe.
The experimental peaks and their fitted profiles in the model ofanisotropic 1E are compared with the theoretical form for an ideal
Schottky peak (dashed line), which would correspond to an
isotropic model with the same entropy change and splitting h1Ei.

4. Discussion
Our structural and electric transport data indicate that
the Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3
samples are single phase highly homogeneous polycrystalline
systems of the perovskite Pbnm structure with oxygenstoichiometry close to the ideal one. As far as the magnetic
characteristics are concerned, a comparison with available
literature data on the same cobaltites is worthwhile. Boththe saturated magnetic moment 0.67 µB /Co and TC =130 K found for the Nd0.7 Sr0.3 CoO3 sample are definitely
lower compared to 1.55 µB /Co and 200 K, data whichwere reported for a chemically most similar Nd1−x Srx CoO3
sample, nonetheless with declared slightly higher Sr content
x = 0.33 [29]. Noting that this latter moment value is close
to 1.71 µB achieved for La0.7 Sr0.3 CoO3 , we presume that
the Nd1−x Srx CoO3 samples with x ∼ 0.3 are close to thecompositional transition from the LS/LS ground state to the
IS/LS one. This can explain the large difference in magnetic
response between these two samples, despite their very similar
chemical compositions. Considering the two above mentioned
possible ground states, the low critical temperature TC = 25 K
found for our Nd0.7 Ca0.3 CoO3 sample can be understoodas a fingerprint of a single phase sample with LS/LS FM
ground state, while a spin-glass freezing anomaly at a muchvalues of the Zeeman splitting and g-factors, the relevant data
are plotted in figure 11. It is seen that the average values of 1E
increase with external field in a gradual rate, and only at higher
fields is a linear dependence approached. Since the cobalt
moments are practically saturated in the Schottky peak range,
the final slope seems to be a sole effect of the applied fieldand can thus be used to determine the gJ 0 -factor. The averagevalue actually obtained for Nd0.7 Ca0.3 CoO3 is hgJ 0 i = 1.85.
A similar field dependence is observed also in the plot of thenuclear contribution αT −2 for Pr0.7 Ca0.3 CoO3 , which probes
the Van Vleck polarization of the Pr3+ ground singlet.
Turning back to the zero field values of 1E = gJ 0 µB Heff
for Nd0.7 Ca0.3 CoO3 and Nd0.7 Sr0.3 CoO3 (see figure 11), thespontaneous internal fields acting on the pseudospins can be
determined, using the value hgJ 0 i = 1.85, to be ∼25 kOe
and 80 kOe, respectively. The last quantity reported here is
the entropy change over the Schottky peak, calculated byintegration of cSchottky /T. A value of 3.95 ± 0.08 J mol−1 K−1
is obtained for Nd0.7 Ca0.3 CoO3 , which is 98% of thetheoretical value of 0.7NkB ln 2 = 4.04 J mol−1 K−1 . For
Nd0.7 Sr0.3 CoO3 , the value obtained from zero field data is
3.45±0.07 J mol−1 K−1 and increases with increasing applied
8

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

approximation, gk /g⊥ ∼ 4.2 (see table A.3 in the appendix).
To enable a comparison with our experiments, a numericalintegration over a random orientation of the crystallites has
been made, yielding an average value of hgJ 0 i = 2.51. This
corresponds to a pseudospin moment of 1.255 µB , which isin reasonable agreement with the above mentioned saturated
magnetization in Nd0.7 Ca0.3 CoO3 , giving an estimate of
1.4 µB per Nd3+ ion. On the other hand, the value hgJ 0 i = 1.85
deduced from the high-field shift of the Schottky peaks ismuch lower. An opposite discrepancy has been observed foranother Kramers ion Pr4+ in the low-temperature phase of(Pr1−y Yy )0.7 Ca0.3 CoO3 with y = 0.15, where the shift of the
Schottky peaks gives an unexpectedly large hgJ 0 i = 3.30 [33],while the calculations in table A.2 in the appendix give hgJ 0 i =2.07, and a still lower value would be obtained if a correction
for large Pr4+ covalency were made. These findings may
suggest that apart from the bare interaction of the external
field with the 4f moments, there is an indirect interaction
through a spin polarizable electronic cloud. The samemechanism probably also mediates the exchange interaction
between the FM ordered cobalt subsystem and the Kramers
pseudospins for rare earths, which is of AFM type for Nd3+
and FM type for Pr4+ .3

higher temperature of about 55 K reported for single crystal
samples of same composition by Kundu et al can reflect the
admixture of the IS/LS ground state with significantly higher
TC [23]. Simultaneously, we rule out a drop of the criticaltemperature due to oxygen deficiency in our sample (seee.g. [22]), since in spite of lower TC we observe a ‘stronger’
FM state with a spontaneous moment of 0.23 µB /Co andsignificant coercivity of ∼10 kOe at 2 K.
More extensive data are available for the Pr0.7 Ca0.3 CoO3
system. Our sample, for which oxygen stoichiometry
has been proved directly by neutron diffraction, exhibits
an FM transition at TC = 55 K and the spontaneous
moment reaches 0.34 µB /Co. Identical values and similar
hysteresis loops were also reported for Pr0.7 Ca0.3 CoO3
by Tsubouchi et al [19], while other literature datacluster around higher TC = 70 K and the magnitude of
the bulk FM moment is generally lower. A moment of
0.15 µB /Co for Pr0.7 Ca0.3 CoO3 is reported in the above
mentioned work of Kundu et al. The values found on
Pr0.7 Ca0.3 CoO3 by El-Khatib et al are 0.20 µB as deduced
from magnetization measurements and a long-range orderedmoment of 0.30 µB /f.u. determined by neutron diffraction(this latter value is not explicitly mentioned in the paper,
but can be deduced from the graph of magnetic intensities).
Cobalt moments of analogous value, ∼0.20 µB , are also
obtained by Kalinov et al [24] on Pr0.7 Ca0.3 CoO3 -related
systems with small A-site substitution by Eu3+ ions.
Importantly, the magnetization curves have been measured
up to high fields of 140 kOe, and the data evidence, after
subtraction of the Pr contribution, a saturation of cobalt
magnetization of ∼0.35 µB /f.u.. This value is close to a solecontribution of Co4+ ions and evidences thus a dominanceof LS/LS phase in Pr0.7 Ca0.3 CoO3 systems and consequently
also Nd0.7 Ca0.3 CoO3 .
The most significant results of the present study
refer to the heat capacity experiments, namely the study
and interpretation of the low-temperature Schottky peakassociated with the Nd3+ ground-state doublet. Using thisapproach we have demonstrated that the presence of rare-earth
ions with Kramers degeneracy can be used as a local magnetic
probe in mixed-valence cobaltites. Beyond the quantitative
information on entropy and level splitting, it is also possible
to analyze the intrinsic or inhomogeneous broadening of
the corresponding low-temperature Schottky peaks. For thispurpose we have performed theoretical calculations basedon the parameters of the crystal field, which have been
recently deduced from extensive study of terbium aluminate,
TbAlO3 , possessing the same Pbnm perovskite structure [34].
This procedure, described in detail in the appendix, provides
not only the necessary characteristic energies of the energy
level splitting but also the actual form of the respective
doublet or singlet states. In addition to the 4f3 electronic
configuration of Nd3+ and 4f2 for Pr3+ , calculations are
made also for the 4f1 electronic configuration, which isrelevant for the cases of Ce3+ and Pr4+ . Turning back to the4I3+
9/2 multiplet of Nd , the ground doublet is characterized
by a highly anisotropic g-tensor with principal components
gx = 4.472, gy = 1.185 and gz = 0.928 or, in pseudoaxial

5. Summary
The studied mixed-valence cobaltites are systems withcomplex behavior. These compounds possess an intrinsic
inhomogeneity that relates to chemical and size disorderat the perovskite A sites, the possibility of various spinstates at the cobalt sites, and macroscopic distortion
associated with cooperative tilt of the CoO6 octahedra. With
increasing octahedral tilt (decreasing Goldschmidt tolerance
factor) the FM interactions are suppressed. In particular,
for La0.7 Sr0.3 CoO3 , Nd0.7 Sr0.3 CoO3 , Pr0.7 Ca0.3 CoO3 , andNd0.7 Ca0.3 CoO3 with the same 30% doping level, themagnetic Curie temperature gradually decreases, TC =230, 130, 55 and 25 K, and the spontaneous FM momenton cobalt sites drops, 1.71, 0.68, 0.34 and 0.23 µB . Thereis also a difference in the critical behavior around themagnetic transitions. The La0.7 Sr0.3 CoO3 system behaves
as a conventional ferromagnet. The systems with reduced
magnetization show frequency-dependent AC susceptibility
peaks, pointing to a presence of larger FM clusters for
Nd0.7 Sr0.3 CoO3 and smaller clusters for Nd0.7 Ca0.3 CoO3
and Pr0.7 Ca0.3 CoO3 in a certain temperature range below
TC . (More direct evidence of unusual behavior in thelatter systems comes from small-angle neutron scattering on
Pr0.7 Ca0.3 CoO3 , which shows a presence of preformed FM
entities of 10 Å size, which only well below TC grow tomacroscopic size [25].)The
magnetization
dataon
Nd0.7 Sr0.3 CoO3 ,Pr0.7 Ca0.3 CoO3 , and Nd0.7 Ca0.3 CoO3 at low temperatures
exhibit standard FM hysteresis loops combined with
3 The exchange interaction couples the cobalt spins with the spin componentof the rare earth moments, which is oppositely oriented to the total momentum
in the J = L − S multiplet. The antiparallel orientation is valid also for
projection of spin momentum in the Kramers pseudospin J 0 .
9J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et ala paraprocess caused by rare-earth paramagnetism. The
long-range character of magnetic ordering is reported also
in a few neutron diffraction experiments; these, however,cannot decide whether the severely suppressed moment inPr0.7 Ca0.3 CoO3 and Nd0.7 Ca0.3 CoO3 is a manifestation ofa uniform phase of weakly magnetic character or refers to
two phase coexistence of macroscopic FM and non-magnetic
regions4 . Using low-temperature heat capacity experiments
as an efficient tool for analysis of internal magnetic fields,
we decide in favor of an essentially homogeneous phasein the calcium based compounds down to nanoscopic oreven atomic scale. Firstly, we note that the magnitude of
the cobalt moments is remarkably close to 0.3 µB , which isexactly the theoretical value for a mixture of non-magnetic
S = 0 ions of LS Co3+ and S = 1/2 ions of LS Co4+ .
No metamagnetic increase of cobalt magnetization has been
detected on application of fields up to 140 kOe. This strongly
supports our conclusion that the ground state is the LS/LS
phase with only minor promotion of t2g electrons to itinerant
eg levels. This promotion is necessarily associated with a riseof cobalt moments, but the increased magnetization might becompensated by the presence of oppositely oriented impurity
moments due to isolated S = 2 ions of HS Co3+ . Secondly,
the form and intensity of the Schottky peaks originating in
Zeeman splitting of the ground-state Kramers doublet of Nd3+
show unambiguously that all rare-earth sites experience thesame effective field. The uniform distribution of hole carriers(formally LS Co4+ ) in the main LS/LS phase is thus firmly
established for Nd0.7 Ca0.3 CoO3 and can be anticipated forPr0.7 Ca0.3 CoO3 as well, in order to account for the similarly
reduced magnetization of the Co subsystem, ∼0.3 µB .
For the remaining compound Nd0.7 Sr0.3 CoO3 , the observed
magnetization is intermediate between those for LS/LS in
Nd0.7 Ca0.3 CoO3 and IS/LS in La0.7 Sr0.3 CoO3 . Based on a
reduced intensity of the Nd3+ -related Schottky peak, weinfer that some rare-earth sites are located in magneticallydisordered regions or, to account for the exchange bias in
Nd0.7 Sr0.3 CoO3 , in AFM ordered regions. Such a finding isdirect evidence of the inhomogeneous state of this sample.
As a final remark, let us note that the present results
are closely related to the general problem of the 3d–4f
exchange in perovskite oxides, mediated presumably by
spin polarization of extended orbitals of rare-earth 5dparentage—see the Campbell’s indirect exchange mechanism
treated in [35] and references therein. It is not yet clear how
the mixed-valence character of cobaltites, i.e. the presenceof itinerant carriers, affects the strength and eventually also
the sign of the exchange interaction. To elucidate all theseissues, magnetic and heat capacity studies on twin-free single
crystals are desirable. Single crystal experiments may also
give a better test of the homogeneity of FM phases, probedby analysis of the actual form of the Schottky peaks, since
excessive broadening due to anisotropic g-factors will beeliminated.

Acknowledgment
This work was supported by Project No. 204/11/0713 of theGrant Agency of the Czech Republic.

Appendix. Electron states and magnetism oflanthanide ions in orthorhombic perovskites
To describe the 4f states of lanthanide ions, a Hamiltonianthat consists of the free-ion (atomic) and crystal field terms
is routinely used,Ĥ = Ĥa + ĤCF .

(A.1)

The free-ion Hamiltonian is spherically symmetrical andin a standard notation (see, for example, [36]) it can be writtenasXĤa = Eavg +F k f̂k + ζ4fNXŝi l̂i + α L̂2

i=1

k=2,4,6X+ β Ĝ(G2 ) + γ Ĝ(R2 ) +M j m̂jj=0,2,4+X

Pk p̂k +k=2,4,6X

T r t̂(r),(A.2)

r=2,3,4,6,7,8

where Eavg is the energy in the central field, terms proportional
to F k , α, β, γ and T r describe the electron–electron interaction, and terms with ζ4f , M j , Pk parameters represent thespin–orbit, spin–other-orbit and electrostatically correlated
spin–orbit interactions. N is the number of 4f electrons.
Within single electron crystal field theory the crystal field
Hamiltonian may be written as [37]X(k)ĤCF =B(k)(A.3)
q Ĉq (i),
k,q,i
(k)
where Ĉq (i) is a spherical tensor operator of rank k acting

on the ith electron and the summation involving i is over(k)
the f electrons of the lanthanide ion. Bq are crystal fieldparameters; the values of q and k for which they are nonzero
depend on the site symmetry and also on the choice of thelocal coordinate system. The local symmetry of the lanthanidesite in orthorhombic perovskites is Cs and choosing the crystal
field coordinate axes along the orthorhombic axes a, b, c(k)results in three nonzero, real B0 parameters (k = 2, 4, 6)(k)and six nonzero complex Bq parameters (k = 2, 4, 6; q =2, 4, 6; q 5 k). Rotation of the crystal field coordinate system
around the c axis allows elimination of the imaginary part of(2)
the B2 parameter (for detailed discussion of the crystal fieldin orthorhombic perovskites see [34]). The crystal field axes
x, y, z, (z k c) obtained in this way are used, in what follows,
also as the reference system for lanthanide susceptibility and gtensor. Low symmetry of the crystal field leads to a complete
lift of the orbital degeneracy of the 4f levels, so that the states
are either singlets (N even) or Kramers doublets (N odd).

4 In the theoretical case of FM–non-FM phase coexistence, the average valueof the ordered moment deduced from neutron diffraction is higher than the
average value deduced from magnetization data (this follows from the factthat the magnetic diffraction intensities give a root-square-mean value of the
moments). This situation seems to occur for the Pr0.7 Ca0.3 CoO3 sample
probed by El-Khatib et al, but the value of 0.3 µB (compared to 0.2 µB
obtained by the magnetization method) is close to the resolution limit ofneutron diffraction and is thus subject to large uncertainty.
10

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al

Table A.1. States of the ground 3 H4 multiplet of the Pr3+ ion splitby the crystal field. The energy, relative to the ground state, at zeroexternal magnetic field, and the magnetic moments mx , my , mz ,induced by a field of 10 kOe.
State

E (meV)mx (µB )my (µB )mz (µB )

1
2
3
4
5
6
7
8
9

0.00
8.29
9.94
11.57
27.57
29.98
52.92
63.61
74.20

0.04690.2765−0.2484−0.0667
0.0620−0.06240.0073−0.0052−0.00810.03080.0536−0.0182−0.0302
0.0321−0.04070.0041−0.0250−0.00430.0139−0.00210.0514−0.04310.0144−0.0038−0.02160.0743−0.0811For the free lanthanide ions the total angular momenta
L, S, and J are good quantum numbers. The ground states
are in accord with the Hund’s rules and for Ce3+ (f1 ), Pr3+(f2 ), and Nd3+ (f3 ) they are 2 F5/2 (S = 1/2, L = 3, J =5/2), 3 H4 (S = 1, L = 5, J = 4), and 4 I9/2 (S = 3/2, L =6, J = 9/2), respectively. For a given lanthanide ion the valuesof the parameters of the atomic Hamiltonian (A.2) depend tosome extent on the host compound. This dependence has little
significance for the results given below, however. The crystal
field is thus decisive for the low-temperature behavior of thelanthanide ions.
In order to calculate the electron states of trivalentlanthanides in orthorhombic perovskites we used the program‘lanthanide’ [38], which makes it possible to determine
energy levels and eigenfunctions of Hamiltonian (A.1) withan external magnetic field added. For the atomic parameters,
values given by Carnall et al [36] were adopted. The crystal(k)parameters Bq were taken to be the same as those determinedrecently by Gruber et al [34] for the non-Kramers Tb3+
ion in terbium aluminate. The eigenenergies and magnetic
moments we calculated for the 4f8 electron configuration
practically coincide with those obtained by Gruber et al [34].
In particular, the energy difference between the lowest two
Tb3+ singlets is only 0.026 meV; the very large magnetic
moment (8.8 µB at a magnetic field of 50 kOe) has an
Ising-like character with the Ising axis parallel to the x axis of
the crystal field. There are two crystallographically equivalentsites of Tb3+ ions in the unit cell related by reflection in the acplane. The x axis for these two sites makes an angle of ±36◦with the orthorhombic axis a.
Compared to Tb3+ , the Pr3+ ion is less anisotropic. Theenergies and magnetic moments of the states originating fromthe lowest 3 H4 multiplet of Pr3+ are given in table A.1. The
dependence of the magnetic moments on the magnetic field is
to a good approximation linear; only for the first and second
excited states and the field parallel to the x axis is there atendency to saturation in high magnetic fields. The induced
magnetic moments are small with the exception of the first andsecond excited states that may be classified as an Ising-like
pseudodoublet. The susceptibility χ is anisotropic and its
temperature dependence is displayed in figure A.1.
Ce3+ and Nd3+ are Kramers ions with 4f1 and 4f3
electron configurations respectively. The magnetic moments

Figure A.1. The theoretical dependence of the inverse
susceptibility of the Pr3+ ion, based on the singlet state energies intable A.1 and the calculated shifts in a field of 10 kOe. The full line
corresponds to the average over random orientations; the linear
Curie behavior at higher temperatures gives an effective moment ofµeff = 3.68 µB , in agreement with the experimental value of∼3.5 µB .
Table A.2. Three Kramers doublets of the ground 2 F5/2 multiplet of
the Ce3+ ion split by the crystal field. The energy, relative to theground state, at zero external magnetic field, and the g factors.
State

E (meV)

gx

gy

gz

1
2
3

0.00
33.46
56.36

3.757
1.298
0.945

0.935
2.298
1.212

0.606
1.458
3.451

Table A.3. Five Kramers doublets of the ground 4 I9/2 multiplet of
the Nd3+ ion split by the crystal field. The energy, relative to theground state, at zero external magnetic field, and the g factors.
State

E (meV)

gx

gy

gz

1
2
3
4
5

0.00
11.83
22.87
53.52
65.33

4.472
0.942
2.034
2.978
1.788

1.185
3.925
1.257
3.063
1.435

0.928
1.077
3.540
1.052
4.204

of all Kramers doublets are almost field independent: they
increase by 1–5% when the field changes between 10 and
100 kOe. There is considerable anisotropy of the moment,
the x axis being the easy axis of the ground doublet for both
Ce3+ and Nd3+ . The g factors of the Kramers doublets may be
determined by multiplying the magnetic moments by a factorof two, corresponding to a pseudospin of 1/2. The calculated
energies and the g factors are summarized in tables A.2 andA.3.

References[1] Caciuffo R, Rinaldi D, Barucca G, Mira J, Rivas J,
Señarı́s-Rodrı́guez M A, Radaelli P G, Fiorani D andGoodenough J B 1999 Phys. Rev. B 59 1068
[2] Wu J and Leighton C 2003 Phys. Rev. B 67 174408
11

J. Phys.: Condens. Matter 25 (2013) 216006

Z Jirák et al[21] Fujishiro H, Naito T, Ogawa S, Yoshida N, Nitta K,
Hejtmánek J, Knı́žek K and Jirák Z 2012 J. Phys. Soc.
Japan 81 064709[22] Kundu A K, Sampathkumaran E V, Gopalakrishnan K V and
Rao C N R 2004 J. Magn. Magn. Mater. 281 261[23] Kundu A K, Nordblad P and Rao C N R 2006 J. Solid State
Chem. 179 923[24] Kalinov A V et al 2010 Phys. Rev. B 81 134427[25] El-Khatib S, Bose S, He C, Kuplic J, Laver M, Borchers J A,
Huang Q, Lynn J W, Mitchell J F and Leighton C 2010
Phys. Rev. B 82 100411[26] Masuda H, Fujita T, Miyashita T, Soda M, Yasui Y,
Kobayashi Y and Sato M 2003 J. Phys. Soc. Japan 72 873[27] ORNL experiment, unpublished[28] Möbius A and Adkins C J 2000 Physica B 284 1669
[29] Krimmel A, Reehuis M, Paraskevopoulos M, Hemberger J andLoidl A 2001 Phys. Rev. B 64 224404[30] Podlesnyak A, Rosenkranz S, Fauth F, Marti W,
Scheel H J and Furrer A 1994 J. Phys.: Condens. Matter
6 4099[31] Podlesnyak A, Rosenkranz S, Fauth F, Marti W, Furrer A,
Mirmelstein A and Scheel H J 1993 J. Phys.: Condens.
Matter 5 8973
[32] Gordon J E, Fisher R A, Jia Y X, Phillips N E, Reklis S F,
Wright D A and Zettl A 1999 Phys. Rev. B 59 127[33] Hejtmánek J, Šantavá E, Knı́žek K, Maryško M, Jirák Z,
Naito T, Sasaki H and Fujishiro H 2010 Phys. Rev. B
82 165107[34] Gruber J B, Nash K L, Yow R M, Sardar D K, Valiev U V,
Uzokov A A and Burdick G W 2008 J. Lumin. 128 1271
[35] Richter M 1998 J. Phys. D: Appl. Phys. 31 1017
[36] Carnall W T, Goodman G L, Rajnak K and Rana R S 1989
J. Chem. Phys. 90 3443
[37] Wybourne B G 1965 Spectroscopic Properties of Rare Earths(New York: Wiley)[38] Edvardsson S and Aberg D 2001 Comput. Phys. Comm.
133 396[3] Long Y W, Kaneko Y, Ishiwata S, Taguchi Y andTokura Y 2011 J. Phys.: Condens. Matter 23 245601[4] Knı́žek K, Jirák Z, Hejtmánek J and Novák P 2006 J. Phys.:
Condens. Matter 18 3285
[5] Goodenough J B 1958 J. Phys. Chem. Solids 6 287[6] Bari R A and Sivardiére J 1972 Phys. Rev. B 5 4466
[7] Knı́žek K, Jirák Z, Hejtmánek J, Novák P and Ku W 2009
Phys. Rev. B 79 014430[8] Kyômen T, Asaka Y and Itoh M 2005 Phys. Rev. B 71 024418[9] Jirák Z, Hejtmánek J, Knı́žek K and Veverka M 2008 Phys.
Rev. B 78 014432[10] Křápek V, Novák P, Kuneš J, Novoselov D, Korotin D M andAnisimov V I 2012 Phys. Rev. B 86 195104[11] Kuneš J, Křápek V, Parragh N, Sangiovanni G, Toschi A and
Kozhevnikov A V 2012 Phys. Rev. Lett. 109 117206[12] He C, El-Khatib S, Wu J, Lynn J W, Zheng H, Mitchell J F andLeighton C 2009 Europhys. Lett. 87 027006[13] He C, Eisenberg S, Jan C, Zheng H, Mitchell J F andLeighton C 2009 Phys. Rev. B 80 214411[14] Khan N, Midya A, Mydeen K, Mandal P, Loidl A and
Prabhakaran D 2010 Phys. Rev. B 82 064422[15] Phelan D, Louca D, Kamazawa K, Lee S H, Ancona S N,
Rosenkranz S, Motome Y, Hundley M F, Mitchell J F andMoritomo Y 2006 Phys. Rev. Lett. 97 235501[16] Smith R X, Hoch M J R, Kuhns P L, Moulton W G,
Reyes A P, Boebinger G S, Mitchell J and Leighton C 2008
Phys. Rev. B 78 092201[17] Sboychakov A O, Kugel K I, Rakhmanov A L and
Khomskii D I 2009 Phys. Rev. B 80 024423[18] Tsubouchi S, Kyômen T, Itoh M, Ganguly P, Oguni M,
Shimojo Y, Morii Y and Ishii Y 2002 Phys. Rev. B
66 052418[19] Tsubouchi S, Kyômen T, Itoh M and Oguni M 2004 Phys.
Rev. B 69 144406[20] Herrero-Martin J, Garcı́a-Muñoz J L, Kvashnina K, Gallo E,
Subias G, Alonso J A and Barón-González A J 2012 Phys.
Rev. B 86 125106

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