Magnetoresistance and thermodynamic fluctuations in single-crystal ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathrm{y}}$

Magnetoresistance in the a-b plane of a single crystal of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathrm{y}}$ has been measured. The field dependence of fluctuation conductivity is evaluated from the magnetoresistance slightly above $T_c$ by considering the Aslamazov-Larkin contribution. The coherence lengths ${\xi }_{\mathrm{ab}}$(0) and ${\xi }_c$(0) are estimated as 13 and 2 Å, respectively. These values are half those obtained from ${\mathrm{dH}}_{c2}$/dT below $T_c$. Differences in ξ(0) estimated by different methods are discussed.