The orthoperovskites TbCoO$_3$ and DyCoO$_3$ with Co$^{3+}$ in a non-magnetic low-spin state have been investigated by neutron diffraction down to 0.25 K. Magnetic ordering is evidenced below $T_N=3.3$ K and 3.6 K, respectively, and the ordered arran
gements are of canted type, A$_x$G$_y$ for TbCoO$_3$ and G$_x$A$_y$ for DyCoO$_3$ in Bertauts notation. The experiments are confronted with the first-principle calculations of the crystal field and magnetism of Tb$^{3+}$ and Dy$^{3+}$ ions, located in the $Pbnm$ structure on sites of $C_s$ point symmetry. Both these ions exhibit an Ising behavior, which originates in the lowest energy levels, in particular in accidental doublet of non-Kramers Tb$^{3+}$ ($4f^8$ configuration) and in ground Kramers doublet of Dy$^{3+}$ ($4f^9$) and it is the actual reason for the non-collinear AFM structures. Very good agreement between the experiment and theory is found. For comparison, calculations of the crystal field and magnetism for other systems with Kramers ions, NdCoO$_3$ and SmCoO$_3$, are also included.
Crystal and magnetic structures of the $x=0.2$ member of La$_{rm 0.8-x}$Tb$_{rm x}$Ca$_{0.2}$CoO$_3$ perovskite series have been determined from the powder neutron diffraction. Enhancement of the diffraction peaks due to ferromagnetic or cluster glas
s ordering is observed below $T_C=55$ K. The moments evolve at first on Co sites, and ordering of Ising-type Tb$^{3+}$ moments is induced at lower temperatures by a molecular field due to Co ions. The final magnetic configuration is collinear F$_x$ for cobalt subsystem, while it is canted F$_x$C$_y$ for terbium ions. The rare-earth moments align along local Ising axes within textit{ab}-plane of the orthorhombic $Pbnm$ structure. The behavior in external fields up to $70-90$ kOe has been probed by the magnetization and heat capacity measurements. The dilute terbium ions contribute to significant coercivity and remanence that both steeply increase with decreasing temperature. A remarkable manifestation of the Tb$^{3+}$ Ising character is the observation of a low-temperature region of anomalously large linear term of heat capacity and its field dependence. Similar behaviours are detected also for other terbium dopings $x=0.1$ and 0.3.
The rhodium doping in the LaCo$_{1-x}$Rh$_{x}$O$_3$ perovskite series ($x=0.02-0.5$) has been studied by X-ray diffraction, electric transport and magnetization measurements, complemented by electronic structure GGA+U calculations in supercell for di
fferent concentration regimes. No charge transfer between Co$^{3+}$ and Rh$^{3+}$ is evidenced. The diamagnetic ground state of LaCoO$_3$, based on Co$^{3+}$ in low-spin (LS) state, is disturbed even by a small doping of Rh. The driving force is the elastic energy connected with incorporation of a large Rh$^{3+}$ cation into the matrix of small LS Co$^{3+}$ cations, which is relaxed by formation of large Co$^{3+}$ in high-spin (HS) state in the next-nearest sites to the inserted Rh atom. With increasing temperature, the population of Co$^{3+}$ in HS state increases through thermal excitation, and a saturated phase is obtained close to room temperature, consisting of a nearest-neighbor correlation of small (LS Co$^{3+}$) and large (HS Co$^{3+}$ and LS Rh$^{3+}$) cations in a kind of double perovskite structure. The stabilizing role of elastic and electronic energy contributions is demonstrated in supercell calculations for dilute Rh concentration compared to other dopants with various trivalent ionic radius.
The magnetic, electric and thermal properties of the ($Ln_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_3$ perovskites ($Ln$~=~Pr, Nd) were investigated down to very low temperatures. The main attention was given to a peculiar metal-insulator transition, whic
h is observed in the praseodymium based samples with $y=0.075$ and 0.15 at $T_{M-I}=64$ and 132~K, respectively. The study suggests that the transition, reported originally in Pr$_{0.5}$Ca$_{0.5}$CoO$_3$, is not due to a mere change of cobalt ions from the intermediate- to the low-spin states, but is associated also with a significant electron transfer between Pr$^{3+}$ and Co$^{3+}$/Co$^{4+}$ sites, so that the praseodymium ions occur below $T_{M-I}$ in a mixed Pr$^{3+}$/Pr$^{4+}$ valence. The presence of Pr$^{4+}$ ions in the insulating phase of the yttrium doped samples (Pr$_{1-y}$Y$_{y}$)$_{0.7}$Ca$_{0.3}$CoO$_3$ is evidenced by Schottky peak originating in Zeeman splitting of the ground state Kramers doublet. The peak is absent in pure Pr$_{0.7}$Ca$_{0.3}$CoO$_3$ in which metallic phase, based solely on non-Kramers Pr$^{3+}$ ions, is retained down to the lowest temperature.
