Critical Phenomena in the Double-Exchange Ferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>La</mml:mi></mml:mrow><mml:mrow><mml:mn>0.7</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>Sr</mml:mi></mml:mrow><mml:mrow><mml:mn>0.3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>MnO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We report a dc magnetization study of the critical phenomena in a high-quality single crystal of the double-exchange ferromagnet ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_{3}$. We have determined the critical temperature $({T}_{C}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}354.0\ifmmode\pm\else\textpm\fi{}0.2\mathrm{K})$ and the critical exponents, $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.37\ifmmode\pm\else\textpm\fi{}0.04$ and $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.22\ifmmode\pm\else\textpm\fi{}0.03$. Here $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ are the critical exponents for the temperature dependence of the spontaneous magnetization just below ${T}_{C}$ and initial susceptibility just above ${T}_{C}$. Using these values of $\ensuremath{\beta}$, $\ensuremath{\gamma}$, and ${T}_{C}$, we find that the magnetization-field-temperature $(M\ensuremath{-}H\ensuremath{-}T)$ behavior below and above ${T}_{C}$ obeys scaling, following a single equation of state in which $M/({1\ensuremath{-}T/T}_{C}{)}^{\ensuremath{\beta}}$ is uniquely related to $H/({1\ensuremath{-}T/T}_{C}{)}^{\ensuremath{\beta}+\ensuremath{\gamma}}$.