Enhancement of the intrinsic pinning by a magnetic field in a single crystal of high-temperature superconductor TmBa$_{2}$Cu$_{3}$O$_{y}$

This paper presents a comparative study of the complex permeability $\mu^*$ of single crystals of hightemperature superconductors $R$Ba$_{2}$Cu$_{3}$O$_{y}$ ($R$ = Y, Tm) as a function of the magnetic field applied along the crystallographic $ab$-plane. Contributions to $\mu^*$ from the oscillatory motion of vortices perpendicular to layers of the crystal lattice, $\mu_v$, and realization of the critical state along the layers are obtained. It is found that, as the temperature approaches $T_{c}$, the behavior of the field dependences of $\mu_v$ and the critical current is substantially different for the given samples. This effect is related to the manifestation of an additional unusual mechanism of intrinsic pinning, which arises when Y$^{3+}$ is replaced with the Tm$^{3+}$ magnetic ion. The revealed specificities of the interaction of vortices with the magnetic ion layer suggest that, most probably, they have a magnetic nature and are not related to the variation in the condensation energy in the core of the vortex.