Specific heat of a dilute magnetic alloy with magnetic interactions: ZnMn

Abstract

We have measured the specific heat of pure Zn and of a series of five ZnMn alloys (60, 112, 213, 530, and 1200 ppm Mn) as a function of temperature $T$ from 0.7 to 4 K in zero external magnetic field. The excess specific heat, $\Delta C=C\left(\mathrm{alloy}\right)-C\left(\mathrm{pure}\mathrm{Zn}\right)$, is proportional to the square of the Mn concentration $n$ for $\frac{T}{n}>6\mathrm{}\times {10}^{-3\mathrm{}}$ K/ppm and $n>\mathrm{}200\mathrm{}$ ppm Mn, indicating the presence of magnetic interactions between the Mn impurities in the three most concentrated alloys. We find that $\Delta C$ as measured for the 213, 530, and 1200 ppm alloys also obeys the scaling law of Blandin and Souletie for impurities interacting via a $\frac{1}{r^3}$ Ruderman-Kittel-Kasuya-Yosida (RKKY) potential, $\frac{\Delta C}{n}=f\left(\frac{T}{n}\right)$. $\Delta C$ for the 60- and 112-ppm-Mn alloys contains an additional contribution above that due to interactions, presumably the result of single-impurity effects. We propose a simple analytic expression for the excess specific heat due to interacting Mn impurities in Zn, viz., $\Delta C=\frac{\mathrm{AT}}{(1+\frac{B{T}^2}{n^2})}$. From $\Delta C$ we have derived expressions for the free energy, internal energy, and entropy. In addition to being in good agreement with our experiment results and obeying the scaling laws of Blandin and Souletie, these thermodynamic functions coincide in the high-temperature limit with the predictions of Larkin and Khmel'nitskii for the thermodynamic functions of an alloy with magnetic impurities interacting via RKKY. Comparing theory and experiment for $\Delta C$, we find $S=\frac{3}{2}$ for the spin of the Mn impurity and $V_0=(0.91\mathrm{}\pm 0.01)\times {10}^{-36\mathrm{}}$ erg ${\mathrm{cm}}^3$ for the strength of the RKKY interaction between two Mn impurities.