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The ground state properties of the mixed-valence cobaltites Nd$_{0.7}$Sr$_{0.3}$CoO$_3$, Nd$_{0.7}$Ca$_{0.3}$CoO$_3$ and Pr$_{0.7}$Ca$_{0.3}$CoO$_3$

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 and spontaneous moments of cobalt are gradually suppressed - $T_C=130$ K, 55 K and 25 K and $m = 0.68 μ_B$, 0.34 $μ_B$ and 0.23 $μ_B$ for Nd$_{0.7}$Sr$_{0.3}$CoO$_3$, Pr$_{0.7}$Ca$_{0.3}$CoO$_3$ and Nd$_{0.7}$Ca$_{0.3}$CoO$_3$, respectively. The moment reduction with respect to moment of the conventional ferromagnet La$_{0.7}$Sr$_{0.3}$CoO$_3$ ($T_C=230$ K, $m = 1.71 μ_B$) in so-called IS/LS state for Co$^{3+}$/Co$^{4+}$, was originally interpreted using phase-separation scenario. Based on the present results, mainly the analysis of Schottky peak originating in Zeeman splitting of the ground state Kramers doublet of Nd$^{3+}$, we find, however, that ferromagnetic phase in Nd$_{0.7}$Ca$_{0.3}$CoO$_3$ and likely also Pr$_{0.7}$Ca$_{0.3}$CoO$_3$ is uniformly distributed over all 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 \textit{et al.} [Phys. Rev. B \textbf{80}, 024423 (2009)]. The ground state of Nd$_{0.7}$Sr$_{0.3}$CoO$_3$ with an intermediate cobalt moment is inhomogeneous due to competing of LS/LS and IS/LS phases. In the theoretical part of the study, the crystal field split levels for $4f^3$ (Nd$^{3+}$), $4f^2$ (Pr$^{3+}$) and $4f^1$ (Ce$^{3+}$ or Pr$^{4+}$) are calculated and their magnetic characteristics are presented.