Mechanisms of the magnetoresistance hysteresis in a granular HTS with the paramagnetic contribution by the example of HoBa$_{2}$Cu$_{3}$O$_{7-\delta}$

The hysteretic behavior of magnetoresistance $R(H)$ of the granular high-temperature superconductor (HTS) HoBa$_{2}$Cu$_{3}$O$_{7-\delta}$ has been investigated. The YBCO superconductors with a rare-earth element (Nd, Ho, Er, Sm, Yb, or Dy) with the magnetic moment in the yttrium site are characterized by a significant paramagnetic contribution to the total magnetization. The main goal of this study has been to establish the possible effect of this paramagnetic contribution on the magnetotransport properties, which are determined by tunneling of superconducting current carriers through the grain boundaries. An analysis of the results obtained basing on the concept of an effective field in the intergrain medium showed that the distribution of the magnetic induction lines from the paramagnetic moments is fundamentally different from that of the Meissner currents and Abrikosov vortices. The magnetic induction lines from the paramagnetic moments are not concentrated in the region of grain boundaries and therefore insignificantly affect the magnetotransport properties of a granular HTS. At the same time, the magnetic induction lines are strongly concentrated in the grain boundaries, which is caused by the Meissner currents and Abrikosov vortices, due to the features of their properties. Specifically, the magnetic flux compression determines the magnetotransport (in particular, the $R(H)$ hysteresis) properties of granular HTSs, including 1–2–3 ones, with a rare-earth ion with the magnetic moment.