Effects of Temperature and Pressure on the Magnetic Properties of La1–xPrxCoO3

For La1–xPrxCoO3 cobaltites (x = 0, 0.1, 0.2, and 0.3), the dependence of magnetic susceptibility χ(T) is studied in the temperature range 5–400 K. Also, the crystal structure of these cobaltites is investigated, and the effect of pressure up to 2 kbar on their susceptibility is measured at T=78 , 150, and 300 K. The specific dependencies χ(T) and the large negative pressure effect are assumed to arise from Co3+ ions contribution to the total susceptibility evaluated using La1−xPrxAlO3 as a reference system. The obtained experimental data on temperature and pressure effects in magnetism are analyzed within a two‐level model with energy gap Δ between the ground state of the system with zero spin of Co3+ ions and the excited higher‐spin state. In this model, magnetism of Co3+ ions is determined by the temperature‐induced population of the excited state, and magnitude of the pressure effect is governed by the volume dependence of Δ. The results of the analysis, supplemented by the theoretical calculations of the electronic structures of LaCoO3 and PrCoO3, indicate significant increase in Δ with decrease in the unit cell volume both under hydrostatic pressure and by substituting La with Pr having a smaller ionic radius.

DOI: 10.1002/pssb.202000085 For La 1-x Pr x CoO 3 cobaltites (x ¼ 0, 0.1, 0.2, and 0.3), the dependence of magnetic susceptibility χðTÞ is studied in the temperature range 5-400 K. Also, the crystal structure of these cobaltites is investigated, and the effect of pressure up to 2 kbar on their susceptibility is measured at T ¼ 78, 150, and 300 K. The specific dependencies χðTÞ and the large negative pressure effect are assumed to arise from Co 3þ ions contribution to the total susceptibility evaluated using La 1Àx Pr x AlO 3 as a reference system. The obtained experimental data on temperature and pressure effects in magnetism are analyzed within a two-level model with energy gap Δ between the ground state of the system with zero spin of Co 3þ ions and the excited higher-spin state. In this model, magnetism of Co 3þ ions is determined by the temperature-induced population of the excited state, and magnitude of the pressure effect is governed by the volume dependence of Δ. The results of the analysis, supplemented by the theoretical calculations of the electronic structures of LaCoO 3 and PrCoO 3 , indicate significant increase in Δ with decrease in the unit cell volume both under hydrostatic pressure and by substituting La with Pr having a smaller ionic radius.
One of the efficient ways to further investigate the phenomenon of spin crossover is to study the effect of high pressure on the magnetic properties of cobaltites. Such investigations for LaCoO 3 [19][20][21][22] and for a number of RCoO 3 compounds (R ¼ Pr, Nd, Sm, and Eu) [21] have revealed a strong decrease under pressure of the Co ions' contribution to the total susceptibility and a shift of the characteristic maximum on χðTÞ dependence to higher temperatures.
A number of investigations were based on the studies of the Co 3þ spin state in La 1Àx R x CoO 3 compounds. In these compounds, the substitution of La with rare-earth elements has provided a decrease in the cell volume due to a decrease in the ionic radius along the R 3þ series. The corresponding effects of chemical pressure on magnetic susceptibility of La 1Àx Pr x CoO 3 , [23] La 1Àx Nd x CoO 3 , [24] La 1Àx Sm x CoO 3 , [25] and La 1Àx Eu x CoO 3 [14,26] revealed some similarity in the behavior of magnetism of Co 3þ ions in these compounds with the relevant effects of physical pressure in LaCoO 3 . However, it should be noted that a quantitative analysis of the spin state of Co 3þ ions in such systems, based on their magnetic properties, requires proper account of the rare-earth background magnetism.
In this article, we provide the results of extensive studies of structural and magnetic properties of La 1Àx Pr x CoO 3 compounds. The main goal of this work is to explore the dependence of the spin state of cobalt ions in these compounds on temperature, as well as on the lattice volume changes, both under hydrostatic pressure and by substituting La with Pr, which has a smaller ionic radius. For this purpose, we have investigated the magnetic susceptibility of the isostructural La 1Àx Pr x CoO 3 cobaltites (0 ≤ x ≤ 0.3) in the temperature range 5 À 400 K, and also under applied hydrostatic pressure up to 2 kbar at fixed temperatures T ¼ 78, 150, and 300 K. The experimental data on the excitation energies Δ and their pressure derivatives were analyzed using the corresponding theoretical estimates for LaCoO 3 and PrCoO 3 obtained by the ab initio calculations based on the fixed spin moment method. [ Phase and structural characterizations of the samples were carried out using Rigaku D/Max-B and modernized DRON-3M powder diffractometers (Cu Kα radiation, λ ¼ 1.54185 Å). Crystal structure parameters including unit cell dimensions, coordinate, and isotropic displacement parameters of atoms were derived from the diffraction data collected in 2Θ range of 20 -125 by full profile Rietveld refinement applying WinCSD program package. [28] Examination of XRD patterns of the La 1Àx Pr x CoO 3 materials had revealed pure rhombohedral perovskite structure for the samples with x ¼ 0.1 and 0.2 ( Figure 1). The main features of XRD pattern of La 0.7 Pr 0.3 CoO 3 material were similar to the aforementioned specimens. Nevertheless, the careful examination of the pattern allowed to detect extra features, which cannot be described in a single R3c structural model ( Figure 1). This observation pointed to the coexistence of rhombohedral and orthorhombic perovskites in the sample with nominal composition La 0.7 Pr 0.3 CoO 3 . This coexistence was in excellent agreement with the data of thorough X-ray synchrotron powder diffraction investigation of RCoO 3 -R 0 CoO 3 (R, R 0 ¼ La, Pr, Nd, Sm) systems, [29] according to which the phase-separation region occured in La 1Àx Pr x CoO 3 perovskite materials at 0.25 ≤ x ≤ 0.4.
Phase composition and crystal structure of the materials studied were fully confirmed by full-profile Rietveld refinement. For the La 1Àx Pr x CoO 3 samples with x ¼ 0.1 and 0.2, an excellent fit between calculated and experimental profiles was achieved in the space group R3c (Figure 2, top panel).
In contrast, only including the additional Pbnm phase into the full profile Rietveld refinement procedure well-described all the diffraction features of the La 0.7 Pr 0.3 CoO 3 material, which cannot be satisfactorily fitted in the single-phase perovskite model  Table 1. In the refinement procedure, the unit cell dimensions, atomic coordinates, and displacement parameters of atoms were refined together with profile parameters and corrections for the adsorption and instrumental sample shift. The obtained structural parameters of La 1Àx Pr x CoO 3 perovskite materials studied in this work agreed well with the structural data for the parent LaCoO 3 and PrCoO 3 compounds and the mixed lanthanum-praseodymium cobaltites, [29,30] proving the existence of two kinds of solid solutions in LaCoO 3 -PrCoO 3 pseudobinary system.

Magnetic Properties
For the synthesized samples of La 1Àx Pr x CoO 3 , the temperature dependence of their magnetic susceptibility was measured in the range from 5 to 400 K in a magnetic field of 1 T, using a Quantum Design SQUID magnetometer. Similar measurements were also carried out for La 1Àx Pr x AlO 3 compounds, which were prepared by a combination of solid-state synthesis at 1373 K following by arc-melting in Ar atmosphere. [31] Comparing data for both systems made it possible to derive properly the contribution of cobalt ions to magnetic susceptibility of La 1Àx Pr x CoO 3 .
The obtained experimental data for La 1Àx Pr x CoO 3 and La 1Àx Pr x AlO 3 are shown in Figure 3 and 4, respectively, and in general, are in agreement with the relevant data in the study by Kobayashi et al. [23] The appreciable Curie-like rise of the susceptibility of La 1Àx Pr x CoO 3 was observed at low temperatures which obeys a relation where C imp =T term is assumed to originate from a small amount of the paramagnetic impurities and χ 0 is the host susceptibility.
The corresponding values of parameters in Equation (1), estimated from χðTÞ versus 1=T dependence, are shown in Table 2. The estimates of Pr ions magnetism at T ! 0 K are also shown in Table 2. This magnetism of the Pr ions mainly contributes to χ 0 value of La 1Àx Pr x CoO 3 compounds with increasing Pr content. For LaCoO 3 , our value of χ 0 ≃ 1.0 Â 10 À3 emu mol À1 (hereinafter referred to as χ 0ðLaCoO 3 Þ ) coincides in order of magnitude with the corresponding literature data, e.g., 0.65, 13] 0.50, [32] and 0.16, [14] in units of 10 À3 emu mol À1 . We assume that noticeable difference in the reported values of χ 0 may be due to manifestation of a small and different amount of the magnetically ordered clusters, which were usually observed in the real crystals of LaCoO 3 . [33][34][35][36][37] For all our samples of La 1Àx Pr x CoO 3 , the

Atoms, Sites
Parameters, Residuals c, Å 13.0885(5) 13.0797(9) 13.069(1) 13.0504(9) 7.594 (1) La/Pr, (12) Co, presence of these foreign phases was apparently confirmed by a sharp divergence of the χðTÞ dependencies at T % 85 K measured in H ¼ 0.01 T with cooling in a field (FC) and with heating in a field after cooling in zero field (ZFC). This typical low field manifestation of the foreign magnetic phases in cobaltites [33][34][35][36][37] was not detected in our FC and ZFC data for H ¼ 1 T.
In comparison with La 1Àx Pr x CoO 3 , in La 1Àx Pr x AlO 3 compounds, the impurity Curie-like effect was noticeably smaller and it can be omitted in the subsequent discussion. In addition, as shown in Figure 4b, the values of χ per mole of Pr for La 1Àx Pr x AlO 3 , estimated from data for different concentrations of Pr, coincide well with each other, that indicates an approximate additivity of the Pr contribution in this system. This additivity also simplified the account of the Pr magnetism when extracting the temperature-induced spin contribution of the Co 3þ ions from the total susceptibility of La 1Àx Pr x CoO 3 .
The uniform pressure effect on the magnetic susceptibility of La 1Àx Pr x CoO 3 was studied under helium gas pressure P up to 2 kbar, using a pendulum-type magnetometer. [38] To eliminate the effect on susceptibility of the temperature changes when pressure was applied, the measurements were carried out at fixed temperatures 78, 150, and 300 K. The relative experimental errors did not exceed 0.1% for the used magnetic field H ¼ 1.7 T.
The experimental dependencies of χðPÞ for the studied La 1Àx Pr x CoO 3 compounds are shown in Figure 5, 6, and 7, being close to linear within the experimental errors and the used interval of pressures. As shown from Figure 5, a huge decrease in the susceptibility with increasing pressure was found at T ¼ 78 K, which amounts to about 10% per kbar for LaCoO 3 . With increasing temperature, the pressure effect value decreased markedly, and it was an order of magnitude smaller at room temperature. For different temperatures, the obtained pressure derivatives of magnetic susceptibility, d lnχ/dP ≡ ðΔχ=χÞ=ΔP at P ! 0, for the studied compounds are shown in Table 3 together with the values of χ at P ¼ 0.

Details and Results of Electronic Structure Calculations for PrCoO 3
To shed light on the magnetic properties of La 1Àx Pr x CoO 3 system, we have carried out the calculations of electronic structure for LaCoO 3 and PrCoO 3 compounds. The details of corresponding calculations for LaCoO 3 are given in the studies by Panfilov et al. [20,21] In contrast to rhombohedral LaCoO 3 , PrCoO 3 is orthorhombic. As was shown in the studies by Pandey et al. and Topsakal et al., [39,40] the local spin density approximation (LSDA) predicts an incorrect metallic ground state of PrCoO 3 . Actually, its ground state is a paramagnetic insulator with the low-spin state of Co 3þ ion. [41] There is the singlet ground state  Open circles: data for x¼1 from the study by Kobayashi et al. [23] (some deviation from the general regularity below 100 K is apparently due to manifestation of the structural phase transition in PrAlO 3 [31] ).  www.advancedsciencenews.com www.pss-b.com of Pr 3þ ions, and only Van Vleck-type magnetization remains at low temperatures. [41,42] To obtain the semiconducting ground state of PrCoO 3 , it is necessary to use the density functional theory with on-site Coulomb interaction (DFTþU ) formalism. [39,40] The present calculations of electronic structure for orthorhombic PrCoO 3 were carried out using a linearized augmented plane wave method with full potential (FP-LAPW, Elk implementation). [43] The results of the FP-LAPW method were compared with the corresponding calculations carried out using the Quantum-Espresso code. [44,45] We have used the projectoraugmented wave (PAW) potentials, [46,47] which are directly applicable for the Quantum Espresso code. The DFTþU approach was used within the generalized gradient approximation (GGA) for the exchange-correlation functional. [48] The on-site Coulomb interaction, U, and exchange interaction, J, parameters were adopted according to the study by Pandey et al. [39] (U ¼ 3.5 eV, J ¼ 1.0 eV, for Co 3d, and U ¼ 3.5 eV, J ¼ 0.7 eV, for Pr 4f electrons, respectively).
Our calculations have provided a dielectric ground state for the LS configuration of PrCoO 3 with the energy gap about 1 eV, which is close to the experimental value. [39,40] For this LS state of Co 3þ , the valence band is formed by t 2g states of cobalt and 2p oxygen orbital, whereas the conduction band is formed by e g states of cobalt. The calculated density of electronic states (DOS) for the ground state of PrCoO 3 is shown in Figure 8a. The main features of the calculated electronic structure for the LS state of PrCoO 3 appeared to be in agreement with the results of previous calculations. [39,40] We have also calculated the volume dependence of the total energy EðVÞ and obtained the value of equilibrium volume V th ≅ 53.9 Å 3 for the formula unit of orthorhombic PrCoO 3 . This    www.advancedsciencenews.com www.pss-b.com theoretical value of the volume is appeared to be close to the experimental value at T ¼ 12 K (53.99 Å 3 ). [49] To study the magnetic properties of PrCoO 3 we have used the fixed spin moment (FSM) method. [27,50] The results of FSM calculations for the total energy E of PrCoO 3 are shown in Figure 9 as a function of magnetic moment of Co 3þ ion. A pronounced minimum in the EðMÞ dependence was revealed at M ≃ 2μ B , indicating the presence of the intermediate spin state of Co 3þ ion in PrCoO 3 (S ¼ 1). Its energy is slightly higher (≃ 0.05 eV) than the energy of the ground LS state of Co 3þ ions (S ¼ 0), whereas the HS state (S ¼ 2), according to our calculations, has a much higher energy (% 0.6 eV).
We have also calculated the volume dependence of the total energy difference between the IS and LS states in PrCoO 3 , Δ ¼ E IS À E LS , for isotropic volume changes, which is shown in the inset in Figure 9 and described by the derivative dΔ/d lnV ≃ À2.5 eV. It corresponds to a significant increase in Δ under pressure. In contrast, when the lattice of PrCoO 3 is expanding, the IS state approaches LS. Basically, this indicates the possibility of the LS-IS spin states crossover when the volume increases due to thermal expansion. In this connection, it should be noted, that shown in Figure 9b spin-polarized DOS of IS state was calculated with the FSM method for T ¼ 0 K. The band structure calculation at high temperatures is extremely complicated problem, not solved satisfactory within the density functional theory. Therefore, one cannot extrapolate this "ferromagnetic" half-metal IS state to the region of high temperatures. Actually, the experimental data of Tachibana et al. [51] definitely indicate, that PrCoO 3 is nonmagnetic insulator up to temperatures of about 600 K.

Discussion
It is commonly assumed that the unusual temperature dependence of χðTÞ in LaCoO 3 is caused by the temperature-induced gradual transition of the Co 3þ ions from the nonmagnetic LS state (S ¼ 0) to a magnetic state with an IS (S ¼ 1) and/or to the high spin state HS (S ¼ 2).
For La 1Àx Pr x CoO 3 , the χðTÞ dependence, considering paramagnetic impurities, is given by Here χ Co ðTÞ is the temperature-induced contribution of the Co 3þ ions; χ 0ðLaCoO 3 Þ , the temperature-independent host susceptibility which is presumably determined by the dominant Van Vleck paramagnetism of the Co 3þ ions, [13,16] C imp the impurity Curie constant, χ Pr ðTÞ the contribution of the Pr ions. To study the evolution of the spin state of cobalt ions in La 1Àx Pr x CoO 3 , it is necessary to extract properly their contribution, χ Co , from the total magnetic susceptibility of the compounds. Some problems arise in this way already in the reference LaCoO 3 compound. According to the literature data, the real crystals of this material contain a certain number of magnetically ordered clusters formed by crystal defects, [33] nanostructures, [34,35] surface magnetism of the Co ions, [36] or by foreign Co 3 O 4 phase, [37] which substantially distort the temperature dependence of the intrinsic magnetic susceptibility in the temperature range below 85 K. This makes it difficult to quantify the low-temperature data and, in particular, probably explains the considerable scatter of literature data for LaCoO 3 on the magnitude of χ 0 . In view of the foregoing, further analysis of the experimental data was carried out for a temperature region above 85 K, where manifestation of the foreign magnetic phases is assumed to be substantially suppressed.  To extract the contribution of the Co 3þ ions, χ Co , from the total magnetic susceptibility of La 1Àx Pr x CoO 3 compounds with Pr content x, we used the expression It follows from Equation (2), assuming χ Pr ðTÞ ¼ x ⋅ χ PrAlO 3 ðTÞ. Here we have accepted that for all compounds the value χ 0ðLaCoO 3 Þ ≃ 0.2 Â 10 À3 emu mol À1 , which is equal to the theoretical estimate of the Van Vleck paramagnetism of the Co 3þ ions [52] and fairly close to the observed χ 0 value in the most perfect crystals of LaCoO 3 . [14,20] The individual values of the impurity Curie constant, C imp , were taken from Table 2. To estimate the contribution to χðTÞ of the Pr ions, x ⋅ χ PrAlO 3 ðTÞ, we have taken the temperature dependence of molar susceptibility of PrAlO 3 , χ PrAlO 3 ðTÞ, averaged over our data in Figure 4b. The latter is characterized by the value χ PrAlO 3 ð0Þ ≃ 10.6 Â 10 À3 emu mol À1 , which was used to estimate the values of low temperature contribution of the Pr ions, x ⋅ χ PrAlO 3 ð0Þ, shown in Table 2. For T ≥ 150 K, the χ PrAlO 3 ðTÞ dependence obeys the Curie-Weiss law with reasonable values of the Curie constant C ≃ 1.7 K emu mol À1 and the paramagnetic Curie temperature Θ ≃ À75 K.
The resulted dependencies of χ Co ðT, xÞ are shown in Figure 10. They demonstrate that with increasing Pr content, there is a noticeable shift of the χ Co ðTÞ maximum to higher temperatures with a simultaneous decrease in its height. This effect is very similar to the behavior of the χðTÞ isobars in LaCoO 3 with increasing pressure, [19] and it can be considered as manifestation of the chemical pressure effects in La 1Àx Pr x CoO 3 due to the lattice volume decrease with increase in the Pr content.
As was shown, for example, in the studies by Zobel et al. and Baier et al. [13,14] for LaCoO 3 , at low and moderate temperatures, the χ Co ðTÞ term in Equation (2) can be properly described with the LS!IS transition scenario by an expression for the two-level system [13][14][15] with the energy difference Δ for these levels Here, the factor C=T describes the Curie-type susceptibility of the excited state, N A is the Avogadro number, μ B the Bohr magneton, k B the Boltzmann constant, g the Lande factor, and S the spin number. The factor wðTÞ determines the population of the excited state with temperature where 2S þ 1 and ν are the spin and orbital degeneracies of excited state, Δ is the difference between the energies of excited and ground states, expressed in units of temperature T. In addition, in the framework of this approach, the parameter Δ also depends on temperature by the relation resulted from Equation (5) [16] ΔðTÞ ¼ T ln νð2S þ 1Þ 1 À wðTÞ wðTÞ (6) In the following examination of the experimental data within the aforementioned approach, we used the set of model parameters from the studies by Zobel et al., Baier et al., and Knížek et al.: [13,14,16] is assumed, that the orbital degeneracy of IS state is lifted due to local distortions of the crystal lattice).
Using the experimental dependence χ Co ðT, xÞ ( Figure 10) and Equation (4) and (6), we have estimated the temperature dependence of the excited-state energy, ΔðTÞ, in La 1Àx Pr x CoO 3 compounds for different Pr content x, which is shown in Figure 11. As shown, there is a noticeable decrease in ΔðTÞ with increasing temperature. In particular, for x ¼ 0, the value of Δ ≃ 155 K at T ≃ 80 K falls down to Δ ≃ 0 at T ≃ 250 K, being close in magnitude and temperature dependence to the available literature  www.advancedsciencenews.com www.pss-b.com data for LaCoO 3 . [16] Another feature of the ΔðT, xÞ behavior is the strong growth of Δ at fixed temperature with increasing x. According to Figure 11, the rate of Δ change with x is about ∂Δ= ∂x % 520, 650, and 770 K at T ≃ 150, 200, and 300 K, respectively, giving the averaged value ∂Δ= ∂x ¼ 650 AE 120 K. One can presume that this effect is due to a decrease in the cell volume with increasing Pr concentration x. Therefore, we have estimated the chemical pressure effect on Δ using our room temperature experimental data on the volume change with x, ∂ ln V= ∂x ≃ À0.03, and the bulk modulus value B ≃ 1.5 Mbar. [53] It should be noted that to specify properly the magnitude of the chemical pressure effect at different temperatures, it is necessary to consider the temperature dependencies of the bulk modulus BðTÞ and, especially, the ∂ ln VðTÞ= ∂x value, originated from difference in the thermal expansion of the compounds due to the peculiarities of manifestation of the spin crossover. [13,14,54,55] To analyze our experimental data on the hydrostatic pressure effect in magnetic susceptibility, we assumed that its magnitude is predominantly determined by the contribution of χ Co ðTÞ, i.e., dχðTÞ =d P ≃ dχ Co ðTÞ=dP. According to Equation (4) and (6), the derivative dχ Co ðTÞ=dP can be expressed as follows Here, the only fitting parameter is the derivative dΔ/dP, whose value is chosen according to the best agreement of the expression (8) with experiment.
The obtained for La 1Àx Pr x CoO 3 experimental values of dχ/dPð≡ χd ln χ=dP, see Table 3), are shown in Figure 12, as a function of Pr content at T ¼ 78, 150, and 300 K. Here, the solid lines correspond to the model description, according to Equation (8), using the values of χ Co in Figure 10, the Curie constant C ¼ 1 K emu mol À1 and the values of dΔ/dP ¼ 14, 13, and 16 K kbar À1 at T ¼ 78, 150, and 300 K, respectively. As shown, there is a reasonable agreement of the model (8) with the experimental data at T ¼ 150 and 300 K, whereas at T ¼ 78 K, the agreement is somewhat worse. We believe that this is due to using in Equation (8), the overestimated values of χ Co , arising from the manifestation of foreign impurity phases, which probably takes place at lower temperatures. In Figure 10, the proposed dependencies χ Co ðTÞ in La 1Àx Pr x CoO 3 are shown by dashed lines for different x in the range 78 À 150 K. This correction provides agreement between the model and the experimental data at T ¼ 78 K (dashed line in Figure 12), and, in turn, improves the shape of the ΔðTÞ dependence (dashed lines in Figure 11). It should be noted that the aforementioned improvements in the model description of the low temperature experimental data provide convincing evidence in favor of the proposed refinement of the χ Co ðTÞ dependencies in Figure 10.
Let us now discuss the hydrostatic pressure effect on the excited state energy Δ. As was estimated by fitting the model parameter dΔ/dP in Equation (8) to obtain the best agreement with experimental data, the value of dΔ/dP falls in the range of 13-16 K kbar À1 at different temperatures, being the lowest in magnitude at T ¼ 150 K. The non-monotonic temperature dependence of this parameter is presumably related to the fact, that the physical meaning value is the derivative of Δ with respect to volume, and not to pressure. Then assuming the parameter dΔ/d lnV to be a constant for the studied compounds and using the relation we expect that the dependence of dΔ/dP on temperature can arise from a temperature dependence of the bulk modulus, BðTÞ. In the absence of direct data on the BðTÞ behavior for La 1Àx Pr x CoO 3 compounds, it should be noted that essential temperature dependence of some elastic constants was observed in LaCoO 3 . [56,57] This dependence, along with the generally accepted tendency for B to decrease with increasing temperature, shows a maximum between 150 and 200 K. Such behavior should lead to a minimum of dΔ/dP value in this temperature range, which is in a qualitative agreement with our experimental data. Summing up the results of analysis of the pressure effects on magnetic susceptibility in La 1Àx Pr x CoO 3 compounds, we have obtained the temperature averaged value of the pressure derivative for energy of the excited state to be Substituting this value in Equation (9) and using the room temperature value B ≃ 1.5 Mbar, [53] we estimate the volume derivative of Δ equal to www.advancedsciencenews.com www.pss-b.com dΔ=dlnV ≃ À21.5 Â 10 3 K ≃ À1.9 eV (11) The large and negative volume effect on Δ is also supported by theoretical studies for LaCoO 3 and PrCoO 3 . The detailed calculations of the excited state energy Δ and its volume dependence for LaCoO 3 have given the values Δð0Þ ≃ 230 K and dΔ/d lnV ≃ 29 Â 10 3 K ≃ À2.5 eV. [20,21] For PrCoO 3 compound, the present DFTþU calculations have provided the corresponding values Δð0Þ ≃ 570 K and dΔ/d lnV ≃ 29 Â 10 3 K ≃ À2.5 eV. Therefore, for boundary compounds LaCoO 3 and PrCoO 3 , the theoretical Δ were found substantially different, and in a qualitative agreement with the behavior of Δ in La 1Àx Pr x CoO 3 compounds for increasing concentration of Pr ( Figure 11). In contrast, the volume derivative of Δ appeared to be almost the same in LaCoO 3 and PrCoO 3 , dΔ/d lnV ≃ À2.5 eV, in a reasonable agreement with the experimental estimations for La 1Àx Pr x CoO 3 compounds, based on the analysis of pressure effects in magnetic susceptibility (Equation (11)). It should be noted that some difference between the experimental and calculated values of dΔ/d lnV may be due to uncertainty in experimental bulk moduli, according to Equation (9).
We believe that the estimated strong volume dependence of the excited state energy Δ determines the main mechanism of its temperature dependence originated from the change in volume via thermal expansion. Namely, for LaCoO 3 , a volume growth of about 1.6% [54] under heating from 0 to 300 K should result in a decrease in Δ by about 330 K, which is reasonably consistent with the behavior of ΔðTÞ in Figure 11.
Note that, some refinement of the analysis results and improvements of the used model should consider few factors, which were not considered here. One of them is a possible manifestation in magnetism of the HS states at higher-temperature region. Further, magnetic interactions between the Co 3þ moments could play some role in the excited states. In addition, to convert experimentally measured pressure derivatives of susceptibility into volume derivatives, one need data on elastic properties of the systems under consideration and their temperature dependence, which are absent at the moment. Nevertheless, we expect that these possible improvements in the model analysis will not lead to noticeable refinements of the obtained parameters, which, in particular, for LaCoO 3 are Δ ≃ 155 K at T ¼ 78 K, dΔ=dP ≃ 14 K kbar À1 .
These estimates are closely consistent with analogous data obtained by Panfilov et al. [20] from the magnetovolume effect study in single-crystalline LaCoO 3 .

Conclusions
In summary, we have studied the effects of temperature and hydrostatic pressure on magnetic susceptibility of La 1Àx Pr x CoO 3 compounds (x ¼ 0, 0.1, 0.2, and 0.3), supplemented by the investigation of their crystal structure. The entire set of the obtained experimental data on temperature and pressure effects in the magnetism of this family of compounds has been consistently described within the LS-IS scenario in terms of changes in the population of the excited IS state of Co 3þ ions with variations in temperature and lattice volume under hydrostatic and chemical pressure.
One of the main results of this work is a quantitative estimation of the anomalously large volume dependence of the excited state energy Δ, which is presumably a primary source of the temperature dependence of this parameter due to the effect of thermal expansion. The revealed large and negative volume effect on Δ is consistent with the results of ab initio calculations for the boundary compounds, LaCoO 3 and PrCoO 3 , which also supports the LS-IS scenario.
In addition, as shown from Equation (7) and (10), the observed for La 1Àx Pr x CoO 3 similarity between effects of physical and chemical pressure indicates a strong correlation of the Co 3þ spin state with the lattice volume.