Model of the behavior of a granular HTS in an external magnetic field: temperature evolution of the magnetoresistance hysteresis

A model for describing the magnetoresistance behavior in a granular high-temperature superconductor (HTS) that has been developed in the last decade explains a fairly extraordinary form of the hysteretic $R(H)$ dependences at $T=\operatorname{const}$ and their hysteretic features, including the local maximum, the negative magnetoresistance region, and the local minimum. In the framework of this model, the effective field $\mathbf{B}_{\operatorname{eff}}$ in the intergrain medium has been considered, which represents a superposition of the external field and the field induced by the magnetic moments of HTS grains. This field can be written in the form $\mathbf{B}_{\operatorname{eff}}(H)=\mathbf{H}+4\pi\alpha\mathbf{M}(H)$, where $\mathbf{M}(H)$ is the experimental field dependence of the magnetization and $\alpha$ is the parameter of crowding of the magnetic induction lines in the intergrain medium. Therefore, the magnetoresistance is a function of not simply an external field, but also the “internal” effective field $R(H)=f(\mathbf{B}_{\operatorname{eff}}(H))$. The magnetoresistance of the granular YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ HTS has been investigated in a wide temperature range. The experimental hysteretic $R(H)$ dependences obtained in the high-temperature range (77–90 K) are well explained using the developed model and the parameter $\alpha$ is 20–25. However, at a temperature of 4.2 K, no local extrema are observed, although the expression for $\mathbf{B}_{\operatorname{eff}}(H))$ predicts them and the parameter $\alpha$ somewhat increases ($\sim$ 30–35) at this temperature. An additional factor that must be taken into account in this model can be the redistribution of the microscopic current trajectories, which also affects the dissipation in the intergrain medium. At low temperatures under the strong magnetic flux compression ($\alpha\sim$ 30–35), the microscopic trajectories of the current $\mathbf{I}_m$ can change and tunneling through the neighboring grain is preferred, but the angle between $\mathbf{I}_m$ and $\mathbf{B}_{\operatorname{eff}}$ will be noticeably smaller than 90$^\circ$, although the external (and effective) field direction is perpendicular to the macroscopic current direction.