# Phase diagram of the ( Pr 1 – y Sm y ) 0.7 Ca 0.3 Co O 3 system: Valence and spin state transition versus ferromagnetism

Yohann Breard, Francis Veillon, Laurence Hervé, Vincent Hardy, François Guillou, Kurt Kummer, Fabrice Wilhelm, Andrei Rogalev, Ronald Smith

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Yohann Breard, Francis Veillon, Laurence Hervé, Vincent Hardy, François Guillou, et al.. Phase diagram of the ( Pr 1 – y Sm y ) 0.7 Ca 0.3 Co O 3 system: Valence and spin state transition versus ferromagnetism. Physical Review Materials, 2022, 6 (1), pp.014401. 10.1103/PhysRevMateri- als.6.014401. hal-03874623

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# Phase diagram of the (Pr$_{1-y}$Sm$_y$)$_{0.7}$Ca$_{0.3}$CoO$_3$ system: Valence and spin state transition versus ferromagnetism

Y. Bréard, F. Veillon, L. Hervé, and V. Hardy

Normandie Univ, ENSICAEN, UNICAEN, CNRS, CRISMAT, 14000 Caen, France.

F. Guillou

Inner Mongolia Key Laboratory for Physics and Chemistry of Functional Materials, Inner Mongolia Normal University, 81 Zhaowuda Road, Hohhot 010022, Inner Mongolia, People's Republic of China

K. Kummer, F. Wilhelm, and A. Rogalev

ESRF European Synchrotron, 71 Avenue des Martyrs, F-38000 Grenoble, France

R.I. Smith

Rutherford Appleton Lab, ISIS Pulsed Neutron & Muon Source, Harwell Campus, Didcot OX11 0QX, Oxon, England

The “valence and spin state transition” is a very specific transition found in some cobalt oxides, which involves a coupled modification in the Co valence and the Co³⁺ spin state. In the phase diagram of these compounds, one can thus expect a competition of this transition with the ferromagnetism associated to Co⁴⁺ low spin - Co³⁺ high spin double-exchange. Here we study the phase diagram of (Pr₁_ySm_y)₀.₇Ca₃CoO₃ and Pr₁_xCaₓCoO₃ in order to shed some light on the competition between these two phenomena. To this end, we combine results obtained with a wide variety of techniques: magnetization, heat capacity, resistivity, neutron diffraction, x-ray absorption spectroscopy and x-ray magnetic circular dichroism. The origin of the various transition lines in the phase diagram of (Pr₁_ySm_y)₀.₇Ca₃CoO₃ as well as that of the “critical” value ycrit ~ 0.18 are discussed. Particular attention is paid to the nature of the groundstate magnetism which is an issue strongly debated so far in this type of cobaltates.

## I. INTRODUCTION

A very peculiar type of transition is observed in some cobalt oxides, showing a concomitant change in the valence (Co³⁺/Co⁴⁺) and in the spin state (Co³⁺ low-spin / Co³⁺ high-spin) degrees of freedom. Originally discovered in well oxygenated Pr₀.₅Ca₀.₅CoO₃ [1-5] (for an overview, see for instance [6] and references therein) the field of such a « valence and spin state transition » (VSST) was progressively extended to a broader range of compositions, namely (Pr₁_yRE_y)₁_xCaₓCoO₃ with RE = Sm, Eu, Gd, Tb, Y, and 0.2 ≤ x ≤ 0.5 as well as 0.0 ≤ y ≤ 0.3 [7-12].

In the first study on Pr₀.₅Ca₀.₅CoO₃ in 2002, Tsubouchi et al. [1] reported a metal-insulator transition accompanied with an abrupt drop in magnetization, a sharp peak in specific heat, and a decrease in the unit-cell volume, when cooling below the transition at T* ~ 90 K. Originally, this transition was regarded as a peculiar instance of a first-order spin-state transition among the Co³⁺ (from intermediate- to low-spin state), an interpretation that remained commonly accepted for several years. Starting from 2010 however, an accumulation of data pointed to a more complex scenario. First, in a neutron powder diffraction study of Pr₀.₅Ca₀.₅CoO₃, Barón-González et al. [2] observed that the Co-O bonds are almost unaltered at T*, whereas the Pr-O ones change a lot, a result leading them to suggest the possibility of a charge transfer between Co and Pr. Soon after, in their study of the heat capacity in (Pr₁_yY_y)₀.₇Ca₀.₃CoO₃ compounds, Hejtmánek et al. [10] found a Schottky-like anomaly at T < T*, a feature suggesting the presence of the Kramers ion Pr⁴⁺. Then, several experiments of x-ray
absorption spectroscopy provided direct evidences of the presence of Pr⁴⁺ below T* in different compounds. In Pr₀.₅Ca₀.₅CoO₃ for instance, García-Muñoz et al. [3] and Herrero-Martín et al. [4] both demonstrated a partial oxidation of Pr³⁺ into Pr⁴⁺ when crossing T* upon cooling.

The fact that the VSST requires the stabilization of a certain amount of Pr⁴⁺ at low temperatures is now widely accepted [2,3,10,13]. However, the very origin of such a mixed valence Pr³⁺ / Pr⁴⁺ is still a matter of debate. On the experimental side, the data on the value of this ratio is scarce and rather scattered. The only point that emerges clearly is that for a given (RE, x) couple, the ratio Pr⁴⁺ / Pr³⁺ increases with y [10,12,14]. Experimentally, another basic issue is the competition between the VSST and the ferromagnetic (FM) ordering. In (Pr₁-yRey)₁-xCaxCoO₃, one expects a “critical” y value (ycrit) below which ferromagnetism (related to that of Pr₁-xCaₓCoO₃) dominates and above which the VSST takes place. Even though one can expect a link between ycrit and the Pr⁴⁺ content in the ground state, a precise description of the crossover FM/VSST is still missing.

These various issues are addressed in the present paper. Our study was carried out in the (Pr₁-ySmy)₀.₇Ca₃CoO₃ system which is well suited for an experimental investigation of the VSST. Indeed, owing to its size —slightly smaller than that of Pr³⁺— Sm³⁺ offers the best fine control of the VSST, even though its magnetic response has to be taken into account in the analysis. A series of measurements have been conducted as a function of y: magnetic susceptibility, heat capacity, resistivity, as well as isothermal magnetoresistance and magnetization curves. From these data, the y dependencies of several characteristic temperatures have been derived: Curie temperature (T*C*), temperature of VSST (T*), and temperature of short-range ordering (SRO) of ferromagnetic clusters (T*SRO*). The exploration of physical properties was complemented by experiments of x-ray absorption spectroscopy (XAS) to characterize the Pr⁴⁺ / Pr ratio (at 5 K), and magnetic circular dichroism (XMCD) to address the spin state of Co³⁺. On this basis, we discuss an overall description of the phase diagram, with special attention paid to the boundary between the FM and VSST regimes.

## II. EXPERIMENTAL DETAILS

Polycrystalline samples of (Pr₁-ySmy)₀.₇Ca₀.₃CoO₃, with twelve compositions in the range 0 ≤ y ≤ 0.5 were prepared by solid-state reaction, in a way similar to that previously used for y = 0.3 [15-18]. Starting from stoichiometric proportions of Pr₆O₁₁, Sm₂O₃, CaO and Co₃O₄ precursors, the powders were intimately ground and the mixture was pelletized in form of 2x2x10 mm bars. These bars were first sintered at 1200 °C in flowing oxygen for 30 h, and then annealed in high-pressure (130 bar) O₂ atmosphere for 80 h at 650 °C with the aim of ensuring good oxygenation of the samples.

By nature, the VSST samples entangle steric and doping effects: the former originates from the size difference between Pr³⁺ and Sm³⁺, while the latter results from the impact of a Pr⁴⁺ / Pr³⁺ fraction on the Co⁴⁺ / Co³⁺ ratio (via charge balance). Accordingly, a second series Pr₁-xCaₓCoO₃ (x < 0.4) was investigated in order to isolate the role of the doping *per se* (there is no VSST for this x range). Using stoichiometric mixtures of the same precursors, the bars were first sintered at 1000 °C in air for 24 h, and then annealed in flowing oxygen for 24 h at 1200 °C, before being cooled down to room temperature in 40 h. The procedure was repeated twice, after grinding and re-pelletization of the samples. Lastly, we prepared the compound Pr₀.₇Ca₀.₃Ga₀.₇Ti₀.₃O₃ to get a direct estimate of the Pr³⁺ magnetism in the (Pr₁-ySmy)₀.₇Ca₀.₃CoO₃ series. With Ga³⁺ and Ti⁴⁺ at the B sites, the only magnetic cation is Pr³⁺ at the A sites, and by keeping the same x=0.3 Ca²⁺ content on the A site the Pr³⁺ environment will be similar to that in our Co-containing compounds. The synthesis procedure was previously described in [18].
To check the purity of the samples, X-ray diffraction was performed on a X'pert Pro PANalytical diffractometer (K<sub>α</sub> Cu = 1.549 Å), equipped with an X'Celerator detector. For a more detailed structure investigation, time-of-flight powder neutron diffraction (tofPND) data were collected at room temperature on the medium resolution, high count rate Polaris diffractometer [19] at the ISIS facility, Rutherford Appleton Laboratory, UK.

6g of each sample were loaded into an 8mm diameter thin-walled cylindrical vanadium sample can and mounted on the beamline's automated sample changer. Neutron diffraction data were collected simultaneously in all 5 Polaris detector banks for a total proton beam charge to the ISIS target of 150µAh (y = 0) or 400 µAh (y ≠ 0) - where 180µAh is equivalent to ~1 hour exposure in the neutron beam. Data reduction used the Mantid software [20], with normalised diffraction patterns from banks 1,2,3 used in structure refinement (average 2θ scattering angles approx. 10°, 26°, 52° respectively).

Crystal structure refinement by Rietveld profile analysis used the Fullprof suite of programs [21]. The neutron scattering lengths used were those included in the software, and a cylindrical sample absorption correction was applied during the refinements to account for the large wavelength-dependent neutron absorption cross-section of Sm in samples with y ≠ 0 (σa ~5900 barns at λ =1.8Å).

The magnetic data were collected using a superconducting quantum interference device magnetometer (MPMS, Quantum Design), while the heat capacity and resistivity measurements were carried out by means of a multi-purposes instrument (PPMS, Quantum Design). In addition to the temperature dependencies (2 - 400 K) of all these quantities, the field dependence of magnetization and resistivity was investigated in the ground state (T = 5 K).

X-ray absorption experiments at the Pr L<sub>3</sub> and Co K edges were carried out at the ID12 beamline of the European Synchrotron (ESRF) in a multi-purpose end-station [22]. The sample was mounted on a cold finger cryostat allowing the temperature of the sample to vary in the range 2.1-320 K. Partial fluorescence yield was collected in backscattering geometry using a Silicon Drift Detector mounted at 20° with respect to the incident beam.

X-ray absorption (XAS) and magnetic circular dichroism (XMCD) experiments at the Co L<sub>2,3</sub> edges presented in Supplemental Material [23] were carried out at the ID32 beamline of the ESRF. The experimental end-station allowed us to reach magnetic fields up to 9 T and temperature on the sample down to 5 K [24]. Bulk polycrystalline samples (~ 2 × 2 × 5 mm<sup>3</sup>) were cleaved in an ultra-high vacuum chamber before being transferred to the superconducting magnet. XMCD spectra were recorded by flipping both the helicity of the incoming beam and the magnetic field direction.

### III. RESULTS

#### A. Structural features

TofPND experiments in (Pr<sub>1-y</sub>Sm<sub>y</sub>)<sub>0.7</sub>Ca<sub>0.3</sub>CoO<sub>3</sub> have been carried out at room temperature for y = 0, 0.075, 0.15, 0.25 and 0.4. All the Rietveld refinements were successfully conducted with the *Pnma* space group that is expected for distorted perovskites. The Pr, Sm and Ca atoms were found to be statistically distributed over the same crystallographic site, without any indication of ordering phenomena. In agreement with previous studies, Figure 1(a) shows that the unit-cell parameters decrease continuously when y increases, as expected from the smaller size of Sm<sup>3+</sup> (1.132 Å) compared to that of Pr<sup>3+</sup> (1.179 Å) [8,25]. Due to the differences in relative atomic scattering powers between neutrons and x-rays, neutron diffraction allows us to determine much more precisely the oxygen atoms positions and therefore the Co-O-Co angles, which directly reflect the degree of distortion of
the perovskite (See details in [23]). The angle $\theta_1$ refers to the Co-O1-Co angle involving the apical oxygen atoms, while $\theta_2$ refers to the Co-O2-Co angle involving the basal oxygen atoms. Figure 1(b) shows that both angles decrease linearly with the increase of Sm content.

<figure><img src="image_3.png" /><figcaption>FIG. 1. Results of tofPND investigations of (Pr$_{1-y}$Sm$_y$)$_{0.7}$Ca$_{0.3}$CoO$_3$ at room temperature. (a) Unit-cell parameters as a function of y (Pnma space group); (b) Apical and basal Co-O-Co angles as a function of y.</figcaption></figure>

## B. Physical properties

Figure 2 shows magnetization curves divided by the applied field (5 T) for all values of y [26]. A crossover from the FM to the VSST regime for 0.175 < y < 0.19 is evident. In such a high field, the signature of $T^*$ remains well defined, whereas the ferromagnetic transition is broadened (a much smaller field will be used to define the $T_C$, as detailed hereafter). The inset of Fig. 2 displays an enlargement of the reciprocal susceptibility around room temperature, which shows a Curie-Weiss like form. One also notes a substantial decrease of susceptibility as y is increased.
<figure><img src="image_4.png" /><figcaption>FIG. 2. Ratio of the magnetization to the applied field (5 T) as a function of the temperature, for all the investigated y values. The inset shows the reciprocal within the high-T range.</figcaption></figure>

Figure 3 shows the heat capacity curves for selected values of y. A clear peak attributed to the VSST is visible for the largest y values (> 0.15). In contrast, no clear feature emerges on the $C(T)$ of the compositions (≤ 0.15) situated in the ferromagnetic regime (see enlargements in [23]). It can be noted that the peak at $T^*$ exhibits a maximum of sharpness at y ~ 0.3, a feature previously observed by Fujita *et al*. in this ($Pr_{1-y}Sm_y)_{0.7}Ca_{0.3}CoO_3$ system [8]. It also deserves to be noted that, for small y values, the low-$T$ part of the curves appears as a smooth extrapolation of the high-$T$ regime (following a Debye like shape), whereas the high-y curves exhibit a downward shift below $T^*$. This can be ascribed to the fact that the VSST is accompanied by a decrease in the unit cell volume upon cooling [1,7,2,27]. This induces an increase in Debye temperature when cooling below $T^*$, and thus a negative step in the lattice contribution (which is the greatest part of the baseline onto which the VSST peak is superimposed). The inset of Fig. 3 displays a $C/T$ vs. $T^2$ plot of the data within the low-$T$ range. For y = 0, one observes a straight line which indicates a response essentially made of a lattice term and an electronic one. A strong change takes place when increasing y, especially at the crossover FM/VSST: in addition to a decrease in the lattice term, the most prominent effect is the emergence of a Schottky peak (actually only its high-$T$ wing is visible in our $T$ range) that is ascribable to $Sm^{3+}$ (y = 0.15), as well as to the VSST-induced $Pr^{4+}$ (for y > 0.15), which are both Kramers ions.
<figure><img src="image_5.png" /><figcaption>FIG. 3. Heat capacity as a function of temperature, for selected y values. The inset shows the ratio C/T vs. T² at T ≤ 10 K. See [23] for details in the C(T) curves for y ≤ 0.15 and T ≤ 120 K.</figcaption></figure>

Figure 4 shows the resistivity of selected y values in a semi-logarithmic plot. The most salient feature is a sudden increase in resistivity upon cooling for the highest y values (those in the VSST regime). This transition corresponds to T* and these compounds reach at low-T a resistivity at least four orders of magnitude higher than in low-y compounds. The latter exhibit a weak resistivity over the whole temperature range, and which can even be regarded as a metallic-like one [28]. One can also note that these curves exhibit a flat maximum within the low-T range, i.e., there is a regime of decreasing resistivity upon cooling (see inset). Such a feature can be related to a FM transition based on a double-exchange (DE) mechanism [29].

<figure><img src="image_6.png" /><figcaption>FIG. 4. Resistivity (log scale) as a function of temperature, for selected values of y. The inset is an enlargement (linear scale) for the two lowest y values, whose curve exhibit a broad hump (marked by arrows).</figcaption></figure>
In Figure 5, we gather data about the field dependence of the ground state. Figure 5 (a) shows the central part of $M(B$: 5 T → -5 T → 5 T) recorded at 5 K for the whole y series. In the FM regime, one observes hysteresis loops with sizeable values of remanence and coercive field. The high-$B$ part keeps a positive slope till 5 T, while its height is slightly shifted downwards as y is increased. For $y > 0.175$, the crossover to VSST regime is quite clear, leading to $M(B)$ curves virtually reversible (e.g. for $y = 0.3$, a remanent magnetization of 0.003 µ$_B$/f.u. and a coercive field of 80 Oe). In other respects, these curves still exhibit a marked, monotonous increase with the field. In Fig. 5(a), one of the most striking features is the absence of saturation in the FM regime, which persists up to at least 14 T (see [23]). This behavior is in line with previous studies and it can be at least partly ascribed to the rare-earths magnetism.

Figure 5(b) shows the field dependence of the magnetoresistance, ($MR = [\rho(B) - \rho(0)]/\rho(0)$) recorded at 5 K within the y series (measuring path +9 T → -9 T). The crossover FM/VSST has a very visible impact, inducing changes in both the shape and sign of the $MR(B)$ curves. The negative $MR$ of the samples in the VSST regime is consistent with previous reports in related systems [30]; in contrast, the positive $MR$ found at the FM side is much more unusual. Curiously, we were unable to find in the literature previous results on the $MR$ at low-$T$ for $y = 0$ (Pr$_{0.7}$Ca$_{0.3}$CoO$_{3}$), despite the many studies carried out on this compound. For the y values of Fig. 5(b), $\rho(B)$ curves were recorded at regularly spaced temperature up to 140 K. The curves $MR(T)$ extracted from these data exhibit peaks located either at $T_C$ or at $T^*$, depending on the y value (see [23]).

From Figs 5(a) and (b), we derived the y dependencies of the remanent magnetization [Fig. 5(c)] and of the magnetoresistance [Fig. 5(d)] at 5 K. In both cases, a sharp crossover takes place at a critical value $y_{crit} \sim 0.18$, separating the FM and VSST regimes.

<figure><img src="image_7.png" /></figure>
FIG. 5. (a) Magnetic hysteresis loops at 5 K for all the y values. (b) Magnetoresistance [MR=100 {ρ(B)- ρ(0)}/ρ(0)] at 5 K for selected values of y. (c) Remanent magnetization derived from (a) as a function of y. (d) Magnetoresistance at 9 T derived from (b), and plotted as a function of y.

C. Phase Diagram

The characteristic temperatures of the (Pr₁-ySm)yCa₀.₇CoO₃ system were primarily derived from magnetic measurements, which led us to address the impact of the following three issues: value of the measuring field, hysteresis, and training effect (see [23]). The latter stems from the first-order nature of the VSST, which requires the sample to accommodate the structural distortion at the transition. In such a case, several crossings of the transition can be necessary before finding a reproducible “transition path”. In our compounds, this effect was found to be limited to the first cooling, which was thus systematically discarded from our analysis. The hysteresis across the VSST is still an active subject of debate. It is now admitted that it is not as high as initially reported, and that it is actually very dependent on the sweep rate [31]. It remains that a small hysteresis seems to persist even for quasi-static measurements, especially in case of the lowest T*, i.e., for the lowest y values [31,32]. To avoid related scattering, we considered the field cooled warming (FCW) mode at a rate of 0.5 K/min. The value of the measuring field impacts only weakly the T*, whereas it is mandatory to use a low field to get a reliable value of Tc. For this purpose, we used either 10 Oe in FCW mode, or preferably, the inspection of the spontaneous magnetization (Mspont), i.e., when cooling in the residual field of the superconducting coil after demagnetization (~ 1.5 Oe).

<figure><img src="image_8.png" /></figure>

FIG. 6. Phase diagram of the system (Pr₁-ySm)yCa₀.₇CoO₃. See [23] for illustrations of the criteria used to determine the characteristic temperatures. The T* line is derived both from the position of the inflection point on the M(T) curves and that of the peak on the C(T) ones. The thin red line is a fitting function of the form (y-ycrit)ⁿ (see text). The FM SRO line is derived from the kink on dMspont/dT (where Mspont is the spontaneous magnetization measured upon cooling in a field of ~1.5 Oe). The
squares are ascribed to the predominant Curie temperature of the distribution of FM clusters. These
characteristic temperatures are derived from the presence of a minimum in $[dM_{spont}/dT](T)$. On the
low-y side, it simply reflects the midpoint of the ferromagnetic ordering [absolute minimum in
$dM_{spont}/dT$], whereas it rather corresponds to a local minimum for larger y values. The dashed line
shows the expected $dT_C/dy$ calculated from data of the literature on cobaltates (see Section IV.A.2).

In our phase diagram, the characteristic temperatures are based on the derivative of $M_{spont}$ (see [23]). A negative maximum of $dM_{spont}/dT$ was ascribed to $T_C$; this definition is akin to the usual “midpoint” criterion applied to the rise of magnetization upon cooling. Since this feature is considerably weaker above $y_{crit}$ than below it, the $T_C(y)$ line will be divided into two parts. A positive maximum of $dM_{spont}/dT$ is ascribed to $T^*$; this reflects the positive step in (paramagnetic) magnetism that is associated with a change from (Pr$^{4+}$,Co$^{3+}$LS) to (Pr$^{3+}$, Co$^{4+}$ LS,Co$^{3+}$HS) when crossing $T^*$ upon warming [16]. Finally, the $T_{SRO}$ is connected to the takeoff of $dM_{spont}/dT$ upon cooling; we found it also corresponds to the start of a non-linear magnetic response.

The phase diagram resulting from these $T_C(y)$, $T^*(y)$ and $T_{SRO}(y)$ lines is shown on Fig. 6. We added to this plot the position of the maxima in $C(T)$, which can be regarded as another signature of $T^*$. The inflection points on the resistivity curves are also found to be well consistent with these lines (see [23])

<figure><img src="image_9.png" /><figcaption>FIG. 7. Curves of dc susceptibility ($M/B$) versus temperature: (a) Zero-field-cooled and field-cooled-cooling curves recorded in 0.1 T for $y = 0.19$; (b) Field-cooled-cooling curves recorded in 0.1 and 5 T for $y = 0.175$. The inset is an enlargement of the high-$B$ curve revealing a signature of $T^*$.</figcaption></figure>

D. Boundary FM/VSST

The $T^*(y)$ data is fitted to a function of the form $(y-y_{crit})^n$, leading to $y_{crit}=0.177$ and $n = 0.38$. Hereafter, we will keep the rounded value $y_{crit} \sim 0.18$. Let us emphasize that this $y_{crit}$ marks a *change in the hierarchy* between the FM and VSST regimes, but the two transitions can coexist. This is evident on Fig. 7(a) in the case of $y = 0.19$ ($> y_{crit}$), where one can observe below $T^*$ the signature of $T_C$, that is here clearly highlighted by the bifurcation between the ZFC and FCC branches. Very similar features were observed for $y = 0.0625$ in the $(Pr_1)$
$_yY_y$)$_{0.7}$Ca$_3$CoO$_3$ system [32]. On the other side, Fig. 7(b) shows that a signature of $T^*$ can be observed for $y = 0.175$ ($< y_{crit} $), when applying a magnetic field large enough to spread out the FM transition.

In mixed valent cobaltates, the FM response is intimately related to the Co<sup>3+</sup>/Co<sup>4+</sup> ratio.
Since the y<sub>crit</sub> value involves the strength of the FM response, it must be indirectly connected
to the Pr<sup>4+</sup>/Pr<sup>3+</sup> ratio. A basic question is thus to tackle the intrinsic y dependence of this Pr<sup>4+</sup>
content at low-T. To do so, XAS experiments is undoubtedly the most suited tool.

E. Pr valence at low T

Let us first summarize the literature on this issue. In the archetypical VSST compound Pr$_{0.5}$Ca$_{0.5}$CoO$_{3}$, a large range of values are reported (Pr$^{4+}$/Pr values at low-$T$ are between 0.15 [4] and 0.26 in [3]). In (Pr$_{1-y}$RE$_y$)$_{1-x}$Ca$_x$CoO$_3$ systems, the Pr$^{4+}$/Pr ratio was shown to increase with $y$; this was studied in detail in the case $x = 0.3$ for both Y and Tb: For RE = Y, when $y$ is doubled from 0.075 to 0.15, Pr$^{4+}$/Pr goes from 0.15 to 0.27 [14]; For RE = Tb, when $y$ is doubled from 0.1 to 0.2, Pr$^{4+}$/Pr goes from 0.19 to 0.25 [12].

The present work addresses the case RE = Sm, with nine y values between 0 and 0.43.
The Pr valence was determined from Pr L₃ spectra using a method similar to that previously
employed for VSST materials [3,4,6,14,18]. The Pr L₃ edge was fitted by a combination of 1
arctangent (accounting for the edge jump), 1 lorentzian forming the main white line
representative of Pr³⁺, and 2 lorentzian functions representative of Pr⁴⁺ (about 5 eV and 12 eV
above the main white line), see spectral decomposition in Ref. [18]. The Pr⁴⁺ fraction is then
calculated from the ratio of the integrated intensity of the lorentzian functions. The results of
Pr⁴⁺/Pr vs. y at T = 5 K are shown in Fig. 8. As y is increased, the increase in Pr⁴⁺/Pr exhibits a
S-like shape with an inflection point around y = 0.18, i.e., a value close to y crit .

<figure><img src="image_10.png" /><figcaption>FIG. 8. Average Pr valence at 5 K, derived from the analysis of XAS measurements at the Pr $L_3$ edge. The dashed line is a guide to the eye. Note the presence of a weak but undeniable jump between $y \sim 0.175$ and $y \sim 0.20$ (thick solid line).</figcaption></figure>
F. Doping effect

The interest in the series Pr<sub>1-x</sub>Ca<sub>x</sub>CoO<sub>3</sub> is to deconvolute the doping effect from the others in the analysis of the VSST transition. In this series, the doping corresponds to the ratio Co<sup>4+</sup>/Co that is directly given by x. For sufficient level of doping, FM related to a double-exchange mechanism between Co<sup>4+</sup> and Co<sup>3+</sup> takes place. In other respects, the Co<sup>3+</sup> can undergo a spin-state transition (SST) from LS to HS as the temperature is increased.

Susceptibility curves were recorded for eight values of x in the range 0-0.4 (raw data in [23]). To remove the Pr contribution, we employed a direct subtraction method [33,34] using the susceptibility of Pr<sup>3+</sup> proposed by Tsubouchi *et al.* [35]: χ<sup>Pr3+</sup>(T) = 1.6/(T + 54) emu/mol. Figure 9(a) displays the resulting curves reflecting the cobalt susceptibility χ<sup>Co</sup>, for selected values of x. The T<sub>SST</sub> and T<sub>C</sub> temperatures were derived from a rise in χ<sup>Co</sup>(T) and a negative maximum in dχ<sup>Co</sup>/dT as T is increased, respectively (see details in [23]). The x dependencies of these characteristic temperatures is reported in the phase diagram of Fig. 9(c). These lines are well consistent with those previously reported by El-Khatib *et al.* [36], except that we did not find evidence of a short-range ordering line around 250 K (see [23]).

<figure><img src="image_11.png" /></figure>

FIG. 9. Magnetic investigation of the Pr<sub>1-x</sub>Ca<sub>x</sub>CoO<sub>3</sub> series. Panels (a,b) shows susceptibility curves recorded in 0.1 T for selected x values. The contribution from the Pr<sup>3+</sup> ions has been removed to isolate the Co response (see text). Panel (a) refers to the low-x range, in which the rise in χ<sup>Co</sup>(T) is associated with the spin-state transition (SST) of Co<sup>3+</sup> from LS to HS. The characteristic T<sub>SST</sub> is associated with the midpoint of the transition (circles) while the beginning of the SST is derived from the crossing point between two linear extrapolations of χ<sup>Co</sup>(T). Robust signature of these features is no longer discernable for x > 0.05. Panel (b) corresponds to the high-x regime where a clear FM response takes place. The T<sub>C</sub> is derived from the point of maximum slope in χ<sup>Co</sup>(T) (circles). Panel (c) displays these temperatures as a function of x, which represents the fraction of tetravalent cobalt. Also shown are the beginning of the SST (open circles) and maxima in ∂<sup>2</sup>(χ<sup>Co</sup>)/∂T<sup>2</sup> on the FM side (dotted green lines).
which reflect the width of the Curie transition. The blue dashed line is an extrapolation of the $T_{SST}(y)$ line, aimed to materialize the interplay with the FM regime.

# IV. DISCUSSION

## A. Phase Diagram

Apart from the SRO lines, the most salient features of the phase diagram of Fig. 6 are: (i) existence of a $y_{crit}$ separating two regimes, dominated either by FM or VSST; (ii) below $y_{crit}$, the $T_C$ decreases as $y$ increases; (iii) above $y_{crit}$, the $T^*$ increases as $y$ increases. These features are in line with previous results of the literature on VSST. In $(Pr_{1-y}Sm_y)_{0.7}Ca_3CoO_3$, Fujita *et al.* [8] showed that the spin-state transition (SST, the “valence” character of the transition being unknown at that time) takes place at a temperature that increases as $y$ is increased, from $y \sim 0.2$ till $\sim 0.8$; the lower boundary was ill defined, but there was no SST for $y = 0.1$. Soon after, Wang *et al.* explored the same system with increased resolution in $y$, and they found a FM/SST boundary at $y_{crit} \sim 0.175$ [37]. Investigation of the closely related $(Pr_{1-y}Eu_y)_{0.7}Ca_3CoO_3$ showed the same qualitative behavior, with $y_{crit} \sim 0.19$ [11]. Actually, the most studied system in VSST literature is $(Pr_{1-y}Y_y)_{0.7}Ca_3CoO_3$, owing to the fact that $Y^{3+}$ is non-magnetic, which facilitates the analysis [10,14,27,30,32,38-40]. However, the size difference with $Pr^{3+}$ is quite strong, [41] which makes it difficult to follow the emergence of the VSST. In this system, Hejtmanek *et al.* [6] found that the lowest $y$ value of their series ($y = 0.0625$) is enough to switch the system into the VSST regime. In a later study, [30] it was shown that $y_{crit}$ is still lower, i.e. $< 0.05$. In practice, no compound characteristic of the FM regime was reported in $(Pr_{1-y}Y_y)_{0.7}Ca_3CoO_3$ for $y \neq 0$. The present study on the $(Pr_{1-y}Sm_y)_{0.7}Ca_3CoO_3$ system has the advantage to provide us with a quite complete phase diagram, encompassing the FM and VSST regimes, and allowing a fine inspection of the crossover between them.

### 1. Crossover FM/VSST: $y_{crit}$

Phelan *et al.* emphasized that the emergence of a $Pr^{4+}$ fraction in VSST compounds can shift the $Co^{4+}/Co^{3+}$ ratio below the threshold for ferromagnetism [30]. To investigate this issue in detail, let us consider the phase diagram established for $Pr_{1-x}Ca_xCoO_3$ [Fig. 9(c)] and the $Pr^{4+}$ ($y$) plot of Fig. 8. The $Pr^{4+}$ content exhibits a jump around $y_{crit} = 0.18$. The low $y$ side of this jump corresponds to $y = 0.175$ (with an average Pr valence of 3.06), a composition for which the main transition is a $T_C$ (see Fig. 6). It corresponds to an amount of $Pr^{4+}$ per f.u. — noted $[Pr^{4+}]$— given by $0.06 \times 0.7 \times (1-0.175) = 0.035$, and thus an amount of $Co^{4+}$ per f.u. equal to $(0.3-0.035) = 0.265$. In Fig. 9, one can see that for such a doping level (keeping in mind that $x$ corresponds to the ratio $Co^{4+}/Co$), the FM regime is clearly dominant, with $T_C > T_{SST}$ (if any). In Fig. 8, the high-$y$ side of the jump in $Pr^{4+}$ ($y$) corresponds to $y = 0.20$ (Pr valence 3.15), for which the main transition has now turned into a VSST (see Fig. 6). This $y$ value corresponds to $[Pr^{4+}] = 0.084$ and thus $[Co^{4+}] = 0.216$. It turns out that this latter value lies in a range of doping where one can speculate that the hierarchy between FM and VSST has been reversed, i.e. $T_{SST} > T_C$, [Fig 9(c)]. In the end, it thus appears that the jump in $Pr^{4+}$ ($y$) is remarkably consistent with the phase diagram of $(Pr_{1-y}Sm_y)_{0.7}Ca_3CoO_3$ when taking into account the influence of the doping level ($Co^{4+}/Co$) on the hierarchy between SST and FM ordering.

### 2. $T_C$ versus $y$
First of all, one must address the nature of the ferromagnetism in the low y range. This issue is still intensively debated in the prototypical case of y = 0. In 2004, it was claimed that Pr<sub>0.7</sub>Ca<sub>0.3</sub>CoO<sub>3</sub> is not a genuine ferromagnet [42] and that its magnetism is inhomogeneous [43]. The possibilities of a phase separated state [42] or of a spin glass [44] were proposed, but the question has remained unsolved. More recently, new experimental data reactivated the controversy, in particular spectra of small angle neutron scattering [36] and the analysis of Schottky terms in heat capacity measurements [28]. The former were found to support a model of phase separation (PS), whereas the latter led to claim an homogeneous magnetism. Overall, our data rather lends support to a PS picture, one of the most significant arguments being the absence of a clear peak in C(T), while there is a sharp rise in $\chi(T)$ upon cooling. We consider this is not compatible with a bulk ferromagnetism involving 100% of the volume. It remains that there is a very clear FM-like response, and that the domains in which it develops can be quite large [30].

About the dependence $T_C(y)$, it is known that a decrease in $\langle r_A \rangle$ reduces the Co-O-Co angle, which in turn opposes the setting of a FM state (via double-exchange) [28,45,46]. This effect is present when increasing the content of Sm<sup>3+</sup> that has a smaller ionic radius than Pr<sup>3+</sup>. As y is increased, it is thus expected to observe a decrease in the temperature of FM ordering, both for the $T_C$ and $T_{SRO}$ lines (which actually exhibits the same slope versus y in Fig. 6). To be more quantitative, let us consider the literature on cobaltates. Considering RE<sub>0.7</sub>AE<sub>0.3</sub>CoO<sub>3</sub>, we collected data of $T_C$ versus $\langle r_A \rangle$ for various rare-earths and alkaline-earths [28,47]. This data is found to obey a linear law within the relevant range of cationic radius : $dT_C/d\langle r_A \rangle = 2734$ K/Å (see [23]). In the (Pr<sub>1-y</sub>Sm<sub>y</sub>)<sub>0.7</sub>Ca<sub>3</sub>CoO<sub>3</sub> series, the dependence of $\langle r_A \rangle$ versus y is linear too : $d\langle r_A \rangle / d y = 0.7[r_A(\text{Sm}^{3+}) - r_A(\text{Pr}^{3+})] = -0.0329$ Å. Therefore, we anticipate a slope $dT_C / dy = (dT_C / d\langle r_A \rangle)(d\langle r_A \rangle / dy) = -90$ K, that is plotted on Fig. 6. It turns out that the experimental $dT_C / dy$ is in good agreement with this value. This supports the idea that the FM signatures in this system (including SRO) are related to the double-exchange mechanism.

### 3. $T^*$ versus y

In the VSST regime above $y_{crit}$, one observes that $T^*$ increases as a function of y. One expects the position of $T^*$ to be linked to the gap of the SST (Co<sup>3+</sup> LS towards Co<sup>3+</sup> HS) which depends not only on the crystalline electric field (CEF), but also on the cobalt bandwidth (W), as evidenced by isotopic effect (<sup>16</sup>O / <sup>18</sup>O) in y = 0.3 [37]. Actually, it was suggested that one should consider as the SST gap, the quantity $\Delta_{SST} = (\Delta_{CEF} - \Delta_{Hund}) - (W/2)$, where $\Delta_{Hund}$ is the Hund coupling energy, while W is proportional to the Co-Co transfer energy which itself varies as the angle Co-O-Co [48].

Increasing y in (Pr<sub>1-y</sub>Sm<sub>y</sub>)<sub>0.7</sub>Ca<sub>3</sub>CoO<sub>3</sub> induces a decrease in $\langle r_A \rangle$, which in turn decreases the distance Co-O and the angle Co-O-Co. As a consequence, $\Delta_{SST}$ is expected to increase owing to both a larger $\Delta_{CEF}$ (via decreasing Co-O) and a smaller W (via decreasing Co-O-Co). This dual effect can explain the increase of $T^*$ as y is increased. Quantitatively, it must be emphasized that the angle effect strongly dominates over the distance one [7-8]. One can also note that the impact of an increase in Co-O-Co on $T_{SST}$ is not linear [49], which is in good accordance with the observed rounded shape of $T^*(y)$ in Fig. 6.

### 4. Curie-Weiss regime at high temperature

Another aspect of the evolution of magnetism along the (Pr<sub>1-y</sub>Sm<sub>y</sub>)<sub>0.7</sub>Ca<sub>3</sub>CoO<sub>3</sub> series is the decrease of susceptibility at high temperature as y increases (see inset of Fig. 2). To isolate the Co response, one must first remove the contributions from Pr and Sm. For the former, we used the susceptibility measured on Pr<sub>0.7</sub>Ca<sub>0.3</sub>Ga<sub>0.7</sub>Ti<sub>0.3</sub>O<sub>3</sub> [representative of $\chi(\text{Pr}^{3+})$ in
conditions very close to ours), and for the latter the expression derived from SmCoO₃ by Ivanova et al. [χ(Sm³⁺) = (1.4 10⁻³ + 0.0276/T) emu/mol] [50]. Then, one needs to consider the diamagnetic component χdia = -0.63 10⁻⁴ emu/mol, as well as a temperature-independent term, referred to as χ₀. This χ₀ incorporates several contributions among which the most important are Pauli and van Vleck terms [51]. To complement the magnetic data, XAS experiments were carried out to investigate the Co³⁺ spin state at room temperature (see [23]). It was found that the nature of the HS/LS mixture is only slightly affected by the y value in this T range. The fitting of the XAS spectra yields a percentage Co³⁺HS/Co at room temperature of approximately 42%, 37% and 34% for y = 0, 0.3 and 0.36, respectively. To get μeff consistent with these XAS results, we were needed to set χ₀ = 5 10⁻⁴ emu/mol, which lies within the range of expected values (see [23]). In the end, our estimate of the cobalt susceptibility χCo at high temperature is obtained by calculating:

$$ \chi^{Co}(y, T) = \chi(y, T) - 0.7(1-y)\chi(\text{Pr}^{3+}, T) - 0.7y\chi(\text{Sm}^{3+}, T) - \chi_{dia} - \chi_{0}. \quad (1) $$

The reciprocal susceptibility curves [Fig. 10(a)] show the persistence of an upward shift as y is increased, demonstrating that this feature is intrinsic to the Co response and does not only comes from the difference in magnetism between Pr³⁺ and Sm³⁺. On closer inspection, one also observes that the 1/χCo(T) curves tend to exhibit a concave upward shape for the highest y values. However, these curves correspond to the lowest χ values, so they are expected to be the most affected by the experimental uncertainties; since the XAS experiments at room temperature have shown that the ratio Co³⁺HS/Co is weakly affected by y, we made a CW analysis of the curves in Fig. 10(a) by assuming the same slope for all of them (so just reducing the fitting range for highest y values). Figure 10(b) displays the θCW derived in such a way, from the linear intercepts to the temperature axis. As y is increased, one observes a continuous decrease in θCW with a striking change in sign from positive to negative.
<figure><img src="image_12.png" /><figcaption>FIG. 10. Reciprocal Co susceptibility at high temperatures, for all the y values. The dashed lines have the slope derived from the curve of y = 0. (b) Curie-Weiss (CW) temperatures as a function of y, when using the $χ^{Co}$ susceptibility of (a) and assuming a Co$^{3+}$ spin state independent of the Sm content at room temperature.</figcaption></figure>

Within the (Pr$_{1-y}$Sm$_y$)$_{0.7}$Ca$_3$CoO$_3$ system, the magnetic interactions bring into play a competition between a double-exchange (DE) mechanism involving Co$^{4+}$ LS-Co$^{3+}$ HS, and super-exchange (SE) couplings dominated by the one associated to Co$^{3+}$ HS-Co$^{3+}$ HS. For a matter of Co-O-Co angle, the ferromagnetic DE mechanism is progressively weakened as y is increased, which thus enhances the signature of the SE interaction Co$^{3+}$ HS-Co$^{3+}$ HS, which is antiferromagnetic. This phenomenon can explain the observed crossover between positive and negative θ$_{CW}$ values as a function of y. We note that a similar behavior was previously reported in La$_{1-x}$Ca$_x$CoO$_3$ [52]. Let us also add that the θ$_{CW}$ for the largest y = 0.5 (-175 K) becomes close to that of LaCoO$_3$, whose estimates span a range from -160 K to -250 K [51-55]. This can be ascribed to the fact that DE is virtually quenched for such a large y = 0.5, while the SE Co$^{3+}$ HS-Co$^{3+}$ HS in our compounds corresponds to a ratio Co$^{3+}$ HS/Co close to 40%, which is very similar to the situation in LaCoO$_3$.

5. Nature of the SRO features
In the present study, short-range ordering (SRO) features have been identified both in the FM and VSST regimes. Note that we prefer to keep the denomination SRO even though it was reported that some of the clusters can spread over rather large length scales, reaching several tens of Å [36]. The basic question to be addressed is the nature of these clusters and of the associated ferromagnetism.

To do so, let us consider the case of $y = 0$ (Pr$_{0.7}$Ca$_{0.3}$CoO$_{3}$). From XMCD of Co at 5 K (see [23]), we isolated the magnetic response of Co which yields a $\mu^{Co}(B)$ very well consistent with that derived when subtracting the Pr signal from a $M(B)$ curve [27]. The shape at low-$B$ is the one displayed in Fig. 5(a); increasing the field above 2 T confirms the absence of saturation up to 9 T (XMCD) and even up 14 T (magnetization). While the remanent magnetization of $0.3\mu_{B}$ per Co could well correspond to the response of Co$^{4+}$ LS ($S = 1/2$) [27,28], the larger values of magnetization observed in high field are problematic. Basically, this is incompatible with a scheme where all the Co$^{3+}$ are LS, so one has to consider that a fraction of them is in a higher spin state. About the alternative between intermediate or high spin states for Co$^{3+}$, our previous studies lead us to favor the second possibility, with a mixture LS/HS [15,18]. Following similar reasoning, Knížek et al. suggested the existence of a small fraction of Co$^{3+}$ HS related to oxygen defects [27]. Considering that Pr$_{0.7}$Ca$_{0.3}$CoO$_{3}$ is on the borderline of a SST (LS/HS), such a small fraction of Co$^{3+}$ HS at $T \ll T_{SST}$ could also simply be regarded as a mark of the low-$T$ tail of the transition. The clusters would correspond to the zones around these Co$^{3+}$ HS, into which the coexistence with Co$^{4+}$ LS neighbors can trigger FM interaction via DE. Accordingly, the SRO would mark the ferromagnetic ordering of these clusters, leading to a phase separated state since these clusters are embedded into a non-FM matrix where the Co$^{3+}$ are LS.

In Pr$_{0.7}$Ca$_{0.3}$CoO$_{3}$, the increase in susceptibility as $T$ is decreased is very broad, indicating an inhomogeneous magnetic ordering of the clusters. The most likely reason is the statistical variety of local configurations involving (Co$^{4+}$ LS / Co$^{3+}$ HS / Co$^{3+}$ LS) which can induce a broad distribution of SRO temperatures. In such a vision, the temperature we referred to as the “$T_{C}$” should be regarded as the value of Curie temperature associated with the most probable local configuration of cobalt cations.

Turning back to the $\mu^{Co}(B)$ curve at low-$T$, we claim it can be described by the combination of two mechanisms: alignment of FM domains and polarization of the background. The former is associated to the clusters involving the couple (Co$^{3+}$HS / Co$^{4+}$LS) and it is responsible for the “hard” FM features, i.e. remanence and coercivity; the latter is associated with the surrounding matrix involving (Co$^{3+}$LS / Co$^{4+}$LS), and it is responsible for the “smooth” increase of magnetization as the field is increased. Using rough spin-only estimates of the magnetic moments for Co$^{3+}$ HS (4 $\mu_{B}$) and Co$^{4+}$ LS (1 $\mu_{B}$), the assumption of a fraction Co$^{3+}$ HS/Co$^{3+}$ equal to about 10% would lead to a saturation magnetization of (0.7×0.1×4) + (0.3×1) = 0.58 $\mu_{B}$, compatible with XMCD and magnetization data.

The above description of FM clusters is also relevant to the VSST side of the phase diagram, both for the $T_{SRO}$ and the $T_{C}$-like lines. For each of them, one observes that their portions on the two sides of $y_{crit}$ are located in the continuation of one another, but there is a downward shift when entering the VSST regime. This originates from the fact that the VSST induces a decrease in the doping level (Co$^{4+}$/Co), which yields in turn a decrease in the temperature of FM ordering [see Fig. 9(c)].

The magnetoresistance can be useful to shed light on the nature of SRO [30]. Let us focus here on the ground state that was investigated by MR measurements at 5 K. On the VSST side (large $y$ values), the large negative MR is consistent with what is expected in phase-separated systems involving metallic-like FM clusters. Quantitatively, one can even note that -15% in 9 T for $y = 0.43$ is close to what is observed in (Pr$_{0.9}$Y$_{0.1}$)$_{0.7}$Ca$_{0.3}$CoO$_{3}$ for
similar values of *T*\* [30]. Supporting the similarity with Ref. [30], we also observed an hysteresis in the *MR*(*B*) curves (~ ± 0.2 *T* around zero-field) which is consistent with a vision of intercluster negative *MR*. In contrast, the *MR* in the FM regime (being both lower in absolute value and positive) is much more puzzling.

Actually, positive *MR* is quite rare in transition metal oxides. In a study on La₁xCαₓCoO₃ for *x* ~ 0.25, similar results were reported, but no clear conclusion could be reached about the origin of this positive *MR* [56]. Various possible origins for such positive *MR* at low-*T* in oxides are reviewed in [56], but none of them can be unambiguously applied to our data. Moreover, in the present case of (Pr₁₋ᵧSmᵧ)₀.₇Ca₃CoO₃ compounds, Fig. 5(b) shows a change in curvature of *MR*(*B*) as the field is increased, pointing to a competition between (at least) two mechanisms of opposite signs [57]. One can be reasonably confident about the nature of only one of them, i.e. the negative *MR* present in the VSST samples (large *y* values) which can likely be ascribed to a mechanism of tunneling between FM clusters within a non-FM matrix. As for the positive *MR*, we suggest it might result from the very peculiar type of phase separation in low *y* compositions, where the density (and maybe also the size) of FM clusters is much higher than for high *y*.

## B. Structural origin of the Pr mixed valence

A central issue for the understanding of the VSST is the origin of the stabilization of a Pr⁴⁺ fraction at low *T*. First, it can be recalled that Pr is prone to exhibit mixed valence (3+/4+) including in oxides, e.g. in Pr₆O₁₁. If focusing attention to the case of perovskite, the best known example is that of BaPrO₃, where Pr sits on the B sites. Mixed valence was also found with Pr on the A sites, for instance in PrSc₁₋ₓMgₓO₃ [59] or even in PrAlO₃, depending on the annealing conditions [60]. What is striking in the (Pr₁₋ᵧSmᵧ)₀.₇Ca₃CoO₃ series is that the mixed valence only takes place below a certain transition temperature. To the best of our knowledge, there is only one previous case of that type, occurring in the double perovskite Ba₂PrRu₁₋ₓIrₓO₆ (for 0.1 ≤ *x* ≤ 0.4), where it is related to the interplay between Ru⁵⁺ and Ir⁴⁺ [61,62].

In (Pr₁₋ᵧREᵧ)₁₋ₓCaₓCoO₃, Naito *et al*. carried out a comprehensive study over broad ranges of *x*, *y* and various RE, to identify the structural parameters allowing to observe VSST [9]. It was concluded that it requires small enough *r*<sub>A</sub> and some minimum degree of disorder in size, quantified by the atomic randomness σ² = Σᵢzᵢrᵢ² - ⟨r<sub>A</sub>⟩², where zᵢ and rᵢ are the concentration and ionic radius of each element in the A site, respectively [9]. Since VSST is intimately connected to the mixed valence of Pr, these criteria might be regarded as those necessary to induce a fraction of Pr⁴⁺ at low *T*. Note, however, that this approach could not account for the VSST in the archetypical compound Pr₀.₅Ca₀.₅CoO₃ for which σ² is very small.

Actually, the latest studies on cobaltates have suggested that the underlying parameter controlling the appearance of Pr⁴⁺ is rather the bond angle Co-O-Co. The apparent link between the VSST and the couple (*r*<sub>A</sub>, σ²) can be ascribed to the fact that Pr/RE substitution is in practice the easiest way to reduce this angle. It was also shown that the distortion of the CoO₆ octahedra plays also a role in itself, in such a way that an average value of Co-O-Co is only relevant in first approximation [63]. Comparing the structural parameters of Pr₀.₅Ca₀.₅CoO₃ (VSST), Pr₀.₅₅Ca₀.₄₅CoO₃ (no VSST), and Pr₀.₅₀Y₀.₅₀Ca₀.₄₅CoO₃ (VSST), García-Muñoz *et al*. claimed a leading role of the apical tilting of the CoO₆ octahedra [3], suggesting that the corresponding θᵢ angle should be below ~158° to allow the stabilization of a Pr⁴⁺ fraction at low *T*. Later, it was confirmed that such a critical angle can be consistent with the appearance of VSST for *x* > 0.45 within the fully oxygenated Pr₁₋ₓCaₓCoO₃ series [45]. In the present study on (Pr₁₋ᵧSmᵧ)₀.₇Ca₀.₃CoO₃, however, Fig. 1(b) shows that the θᵢ
corresponding to $y_{crit} \sim 0.18$ is noticeably lower, being close to 157.2°. At this stage, it is difficult to know whether this discrepancy is just a matter of experimental uncertainties, or if it rather indicates that the complexity of the charge transfer in these cobaltates cannot be reduced to a single angle, independently of other important parameters such as the doping level.

### C. Chemical composition and VSST

Experimentally, the VSST has been observed only in perovskites of formula $ACoO_3$, with Pr and Ca on the A sites. We have seen that the basic ingredients to get a VSST are the existence —at low $T$— of a RE in a mixed valence and of $Co^{3+}$ in the LS state. Strikingly, it turns out that this RE can only be Pr in practice [13,64]; none of the other RE susceptible to exhibit a mixed valence (e.g. Tb) can in itself trigger the VSST [12]; it is probably a matter of hybridization with the O $2p$ orbitals and respective positioning of the RE and Co bands [13]. On the basis of electronic-structure calculations, Knižek et al. evidenced the existence of a broad Pr $4f^2$ band located just below the Fermi level of $Pr_{0.5}Ca_{0.5}CoO_3$; replacing Pr by its closest neighbor Nd makes this feature disappear [13].

Therefore, the set of conditions to get VSST can be rewritten as: (i) presence of Pr at the A sites, (ii) mixed valence $Co^{3+}/Co^{4+}$ to accommodate the change in Pr valence, and (iii) average A site radius below a limit value, in order to get Co-O-Co small enough to stabilize at low $T$ the $Co^{3+}$ in LS state and a fraction of $Pr^{4+}$. In practice (ii) requires the incorporation of a divalent alkaline earth, and (iii) requires that it is $Ca^{2+}$, since obeying this “size condition” is impossible with other usual divalent cations, like $Sr^{2+}$ or $Ba^{2+}$. Finally, the combination of these various requirements to get VSST shows it is natural that this peculiar transition was observed only in (Pr,Ca)CoO$_3$ perovskites.

## V. CONCLUSION

Investigation of several physical properties led us to build a phase diagram of the system ($Pr_{1-y}Sm_y)_{0.7}Ca_{0.3}CoO_3$ ($0 < y < 0.5$), tracking the variations of the VSST temperature $T^*$, the Curie temperature $T_C$, and the ferromagnetic short-range ordering ($T_{SRO}$). This diagram exhibits a competition between a FM regime (low $y$) and a VSST regime (high $y$), with a crossover between them taking place around $y_{crit} \sim 0.18$.

The first basic question is the origin of $y_{crit}$, an issue for which x-ray absorption spectroscopy quantifying the variation of $Pr^{4+}$ versus $y$ was decisive. The ratio $Pr^{4+}/Pr$ is shown to increase from 0 ($y = 0$) till ~ 0.3 ($y = 0.5$), with an acceleration around $y_{crit}$. It is along this jump that the $Pr^{4+}/Pr^{3+}$ ratio reaches a value large enough to make the $Co^{4+}/Co^{3+}$ being shifted below the threshold for which $T_C < T^*$.

The second basic question is the underlying cause of such a stabilization of $Pr^{4+}$. We found that this phenomenon in ($Pr_{1-y}Sm_y)_{0.7}Ca_{0.3}CoO_3$ corresponds to an apical Co-O-Co being lower than ~157.2°, i.e. a value significantly smaller than the one reported in compounds closer to half-doping [3]. Despite this discrepancy that remains to be investigated, there is no doubt that the angles Co-O-Co play a very central role in the VSST systems since they also control the variations of $T_C(y)$ and $T^*(y)$.

In addition to the competition between FM and VSST transitions, we observed ferromagnetic short-range ordering over the whole $y$ range, indicating the presence of diluted FM clusters. Their amount remains small, even in the FM-like regime, and it becomes very tiny above $y_{crit}$. Both the $T_C(y)$ and $T_{SRO}(y)$ lines were found to be consistent with a standard double-exchange mechanism. Our analysis led us to suggest that these FM signatures are
associated with clusters involving Co⁴⁺ LS/Co³⁺ HS embedded in a background involving Co⁴⁺ LS/Co³⁺ LS.

Finally, it must be stressed that several features of the VSST remain puzzling. For instance, our data confirmed previous studies on the point that there is a y value for which the first-order character of the VSST seems to be enhanced [65]. The cause of such an optimum [y ~ 0.3 for (Pr₁-ySm_y)₀.₇Ca₀.₃CoO₃] is not obvious. Is the Pr⁴⁺ fraction too small for smaller y ? Is the cooperativity between the Pr and Co sublattices decreased for too large y ? These questions illustrate the fact that there is still much work to do before fully understanding the Valence and Spin State Transition in cobaltates.

## ACKNOWLEDGMENTS

The authors acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities. We also thank the UK Science and Technology Facilities Council (STFC) for provision of ISIS Xpress Access neutron beamtime.

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