Determination of the magnetization scaling exponent for single crystal La${}_{0.8}$Sr${}_{0.2}$MnO${}_3$ by broadband microwave surface impedance measurements

Employing a broadband microwave reflection configuration, we have measured the complex surface impedance, $Z_S(\omega ,T)$, of single crystal La${}_{0.8}$Sr${}_{0.2}$MnO${}_3$, as a function of frequency (0.045-45 GHz) and temperature (250-325 K). Through the dependence of the microwave surface impedance on the magnetic permeability, $\widehat{\mu }(\omega ,T)$, we have studied the local magnetic behavior of this material, and have extracted the spontaneous magnetization, $M_0(T)$, in {\em zero applied field}. The broadband nature of these measurements and the fact that no external field is applied to the material provide a unique opportunity to analyze the critical behavior of the spontaneous magnetization at temperatures very close to the ferromagnetic phase transition. We find a Curie temperature $T_C=305.5\pm 0.5$ K and scaling exponent $\beta =0.45\pm 0.05$, in agreement with the prediction of mean-field theory. We also discuss other recent determinations of the magnetization critical exponent in this and similar materials and show why our results are more definitive.