Study of magnetic and hyperfine interactions in the quaternary amorphous alloy ${\mathrm{Fe}}_{81}$${\mathrm{B}}_{13.5}$${\mathrm{Si}}_{3.5}$${\mathrm{C}}_2$

Transmission ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer spectroscopy has been used to investigate magnetic and hyperfine interactions in the quaternary metallic glass ${\mathrm{Fe}}_{81}$ ${\mathrm{B}}_{13.5}$ ${\mathrm{Si}}_{3.5}$ ${\mathrm{C}}_2$ (Metglas® 2605SC) over a temperature interval 77-900 K. The Curie temperature $T_C$ and the complete crystallization temperature are found to be 698±2 K and 835±2 K, respectively. The reduced average hyperfine magnetic field $\frac{H_{\mathrm{eff}}\mathrm{}\left(T\right)\mathrm{}}{H_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}}$ vs $\frac{T}{T_C}$ shows a flatter curve in comparison with the Brillouin curve for $S=1\mathrm{}$. This behavior is explained on the basis of Handrich's model of amorphous ferromagnetism in which the parameter $\delta$, which is a measure of fluctuations in the exchange interactions, is assumed to have a temperature dependence $\delta ={\delta }_0\left(\frac{1-T^2}{T_C^2}\right)$, as proposed earlier by us, with ${\delta }_0=0.60\mathrm{}$. The average hyperfine field $H_{\mathrm{eff}}\mathrm{}\left(T\right)\mathrm{}$ could also be fitted to the expression $H_{\mathrm{eff}}\mathrm{}\left(T\right)=H_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}$ [$1-B_{\frac{3}{2}}{\left(\frac{T}{T_C}\right)}^{\frac{3}{2}}-C_{\frac{5}{2}}{\left(\frac{T}{T_C}\right)}^{\frac{5}{2}}-\cdots$], with $H_{\mathrm{eff}}\mathrm{}\left(0\right)=290\mathrm{}\pm 5$ kOe, $B_{\frac{3}{2}}=0.29\mathrm{}\pm 0.02$ and $C_{\frac{5}{2}}=0.29\mathrm{}\pm 0.02$ in the range $0.11<\mathrm{}\frac{T}{T_C}<0.92\mathrm{}$, which indicates the presence of spin-wave excitations over rather large temperature interval. The distribution of a hyperfine-magnetic-field $P\left(H\right)\mathrm{}$ curve at each temperature has a prominent and almost symmetrical peak. The full width at half maximum of the peak decreases monotonically with increase in temperature. Temperature dependence of $H_{\mathrm{eff}}\mathrm{}\left(T\right)\mathrm{}$ has been further analyzed to obtain the critical exponent $\beta$, and is found to be 0.31±0.02 in the temperature range $0.11\le \frac{T}{T_C}\le 0.9$.