Magnetization of a dilute magnetic alloy with magnetic interactions: ZnMn

We have measured the magnetization $M$ up to 50 kG at low temperatures (1.2-4.2 K) of a series of ZnMn alloys ($n=60\mathrm{}-2500$ ppm Mn). For the alloys studied, the measured magnetization is dominated by impurity-impurity interactions via the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) potential $V\left(r\right)=\frac{\left(V_{0}cos2k_{F}r\right)}{r^3}$. These interactions reduce $M$ below the Brillouin function $B_S\left(\frac{H}{T}\right)$ appropriate for free spins, and also inhibit the approach to saturation of $M$. In the limit $n\to 0$, the measured $M$ remains below the free-spin Brillouin function. For the $n=60, 112, \mathrm{and} 213$ ppm Mn alloys and for $g{\mu }_{B}H\gg k_{B}T$, we find $M=g{\mu }_{B}Sn[1-\frac{H_0\mathrm{}(n,T)\mathrm{}}{H}]$, where $S$ is the spin of the Mn impurity and $H_0\mathrm{}(n,T)=A{k}_{B}T+Bn{V}_0$. For these alloys we find $\frac{A}{B}=0.16\mathrm{}\pm 0.03$ and $V_0=(1.7\mathrm{}\pm 0.4)\times {10}^{-36\mathrm{}}$ erg ${\mathrm{cm}}^3$. The term $A{k}_{B}T$ in $H_0\mathrm{}(n,T)\mathrm{}$ may represent a single-impurity (Kondo) effect, while the term $\mathrm{Bn}{V}_0$ clearly represents the effects of the RKKY potential. Scaling behavior is observed for the magnetization once the concentration dependence of the impurity spin $S$ is accounted for the in the following way: $\frac{M}{\mathrm{nS}\left(n\right)\mathrm{}}=F_1(\frac{T}{n},\frac{H}{n})$. However, deviations from scaling of $M$ are observed for the 2500-ppm Mn alloy where evidence has been found for additional interactions not of the RKKY type. The scaling behavior of the zero-field magnetic susceptibility is also presented.