Anisotropic fluctuation magnetoconductivity in a ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystal above ${\mathit{T}}_{\mathit{c}}$

The in- and out-of-plane magnetoresistance of a single crystal of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ has been measured at temperatures above ${\mathit{T}}_{\mathit{c}}$ in magnetic fields up to 12 T. A Montgomery-type contact configuration was used with corrections for the finite size of the contacts taken into account. For temperatures up to 2.5 K above ${\mathit{T}}_{\mathit{c}}$ the data are well described by both the Aronov-Hikami-Larkin theory for a layered superconductor (applicable only for the in-plane magnetoconductivity) and the Ginzburg-Landau theory for a three-dimensional anisotropic superconductor (applicable for both the in-plane and the out-of-plane magnetoconductivity). All three analyses give consistent results for the coherence lengths.