In this paper, we study the ceramics of cobaltite [Tb0.5Nd0.5CoO3]1−yCy with equiatomic contents of terbium and neodymium and with the addition of a carbon material flakes (СMF) with the content of carbon in the range of weight fraction 0 < y < 0.01. The ceramics were obtained by the method of solid-phase reactions according to the standard ceramic technology in air. Using X-ray diffraction and energy-dispersive analysis, it was established that the initial (undoped) solid solution is single-phase with perovskite structure. It was shown that Co3+ ions in undoped ceramics under study are in a non-magnetic low-spin state over the entire temperature range under consideration (2–320 K), and the entire contribution to the magnetization is due to Tb3+ and Nd3+ ions. An analysis of the temperature dependences of the electrical resistance R(T) shows that the initial solid solution behaves like a dielectric with a reduced activation energy of about 0.3–0.35 eV in the temperature range of 280–320 K, due to hopping conduction with a constant activation energy (constant range hopping) by defects in Tb0.5Nd0.5CoO3 matrix. At lower temperatures (200 – 275 K) in the initial (undoped) Tb0.5Nd0.5CoO3 samples, the Mott-type hopping conductivity mechanism with a variable range hopping and high values of the characteristic temperature To ∼ 109 K was observed. Simultaneously, at 300 K, we observed hopping conductivity on alternating current according to the law σ(ω) ∼ ω-α(ω), where the exponent α, which determines a hopping probability, depends on the frequency. In [Tb0.5Nd0.5CoO3]1−yCy samples, heavily doped with СMF with y = 0.01, carrier transport in the entire studied temperature range of 2–320 K mainly occurs along highly conductive carbon-based channels, formed inside of Tb0.5Nd0.5CoO3 matrix by СMF. At temperatures below 15–20 K, these samples show hopping behavior of R(T) with a variable range hopping over localized states, described by the Mott–Kirkpatrick law. In the temperature range 20–100 K electrical resistance versus temperature R(T) along carbon-based channels obey the law R(T) ∼ Ln T. In this case, the relative magnetoresistance MR(T, B) is characterized by a negative sign at temperatures below 10 K in magnetic fields less than 1 T. This behavior of the R(T, B) dependences were described on the basis of the theory of quantum corrections to the Drude conductivity for two-dimensional samples under conditions of weak localization, which is consistent with the behavior of layered carbon-based materials known from the literature. At T > 150 K curves R(B) follow to Lorentz-like positive magnetoresistive effect in Tb0.5Nd0.5CoO3 matrix in the whole magnetic field range.
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