Magnetic-field, temperature, geometry, and angle-dependent studies of vortex pinning in vibrating high-Tcsuperconductor crystals

From the measurement of the resonance frequency and energy dissipation, we have studied the vortex pinning properties of several vibrating high-${\mathit{T}}_{\mathit{c}}$ superconductor crystals ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{s}+\mathit{x}}$, and oxygen-reduced Y(6% Gd)${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.83}$. We have studied the response of the crystals under magnetic field (0 T≤B≤8 T), temperature (10 K≤T≤120 K), angle between field and ${\mathrm{CuO}}_2$ planes ($0^{\mathrm{°}}$≤θ≤90°), and for different geometrical arrangements and driving forces. We can understand the enhancement of the resonance frequency with field taking into account the geometry of the crystals and their orientations. In a certain temperature and field range our results indicate that ‘‘Josephson vortices’’ in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{x}}$ remain pinned. At angles 0°