Effects of finite size on critical phenomena: The resistivity anomaly in Ni films

Abstract

The electrical resistivity of Ni films ranging in thickness from 250 to 24000 \AA{} has been measured precisely near the Curie point. A shift in the temperature of the point where $\frac{d\ensuremath{\rho}}{\mathrm{dT}}$ is maximum is observed which goes as ${n}^{\ensuremath{-}\ensuremath{\lambda}}$, where $n$ is the number of atomic layers and the shift exponent $\ensuremath{\lambda}$ is found to be 1.01\ifmmode\pm\else\textpm\fi{}0.10. The amplitude of the $\frac{d\ensuremath{\rho}}{\mathrm{dT}}$ anomaly is observed to go as $\mathrm{ln}(n)$. Moreover, the shape of the anomaly is observed to broaden as one decreases $n$. Attempts to scale the data for all films along the lines suggested by Fisher and Barber are only partially successful and gave a rounding exponent $\ensuremath{\theta}$ of about 0.6. This value of $\ensuremath{\theta}$ is not considered to be reliable.