Lock-in oscillations in magnetic hysteresis curves of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ single crystals

We report the first direct experimental evidence of intrinsic pinning in hysteresis loops of untwinned ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ single crystals, for magnetic fields perpendicular to the c axis. We have observed oscillations in the M-H loops that are well explained when one considers the layered structure of this compound. The oscillations are found to be periodic in ${\mathit{H}}_{\mathit{a}}^{\mathrm{-}1/2}$ and are induced by a succession of transitions between states for which the vortex lattice is commensurate with the crystal lattice periodicity in the direction perpendicular to the ${\mathrm{CuO}}_2$ planes. The following anisotropy parameters were extracted from the experimental results: ${\mathrm{\Gamma }}_{\mathit{c}\mathit{b}}$=(${\mathit{m}}_{\mathit{c}}$/${\mathit{m}}_{\mathit{b}}$ ${)}^{1/2}$=6.3, ${\mathrm{\Gamma }}_{\mathit{c}\mathit{a}}$=(${\mathit{m}}_{\mathit{c}}$/${\mathit{m}}_{\mathit{a}}$ ${)}^{1/2}$=5.6, and ${\mathrm{\Gamma }}_{\mathit{a}\mathit{b}}$=(${\mathit{m}}_{\mathit{a}}$/${\mathit{m}}_{\mathit{b}}$ ${)}^{1/2}$=1.13.