Critical behavior of the optical absorption edge in CdCr2Se4

The first measurements of the temperature dependence of a semiconductor's optical gap $E_g\mathrm{}\left(T\right)\mathrm{}$ in the close vicinity of a critical point $T_c$ are reported herein. The measurements were carried out on the ferromagnetic semiconductor Cd${\mathrm{Cr}}_2$ ${\mathrm{Se}}_4$ ($T_c$ = 130.6°K) for which a well-known red shift of $E_g\mathrm{}\left(T\right)\mathrm{}$ with decreasing temperature occurs. The results in the temperature range ${10}^{-1\mathrm{}}\ge \mathrm{}\left|t\right|\mathrm{}\equiv \left|\frac{T}{T_c-1\mathrm{}}\right|\gtrsim 5\times {10}^{-4\mathrm{}}$ are analyzed in terms of the specific-heat universal constants: the exponents ${\alpha }^{\pm }$ and the ratio $\frac{A^{+}}{A^{-}}$. It is found that with the constraint $T_c^{+}=T_c^{-}$ the values ${\alpha }^{+}=-0.020\mathrm{}\pm 0.004$, ${\alpha }^{-}=-0.038\mathrm{}\pm 0.003$, and $\frac{A^{+}}{A^{-}}=0.60\mathrm{}\pm 0.05$ are obtained. If the constraints ${\alpha }^{+}={\alpha }^{-}=-0.020\mathrm{} or {\alpha }^{+}={\alpha }^{-}=-0.038\mathrm{}$ are applied the ratio $\frac{A^{+}}{A^{-}}=0.64\mathrm{}\pm 0.05$ is found. The present results, in accord with previous results of magnetization measurements, indicate clearly that the above $\mathrm{}\left|t\right|\mathrm{}$ range is a transition region between mean-field and asymptotic critical behavior. This is understood to be due to the relatively long-range magnetic interactions in the present material.