Magnetic interactions in spin-glasslike ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ dilute magnetic semiconductors

We investigated the nature of the magnetic phase transition in ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ mixed crystals with chemical composition changing in the range of $0.083\le x\le 0.142$ and $0.012\le y\le 0.119$. The dc magnetization measurements performed in magnetic fields up to 90 kOe and temperature range 2–200 K showed that the magnetic ordering at temperatures below $T=50\text{K}$ exhibits features characteristic for both spin-glass and ferromagnetic phases. The modified Sherrington-Southern model was applied to explain the observed transition temperatures. The calculations showed that the spin-glass state is preferred in the range of the experimental carrier concentrations and Mn contents. The value of the Mn hole exchange integral was estimated to be $J_{pd}=0.45\pm 0.05\text{eV}$. The experimental magnetization vs temperature curves were reproduced satisfactorily using the noninteracting spin-wave theory with the exchange constant $J_{pd}$ values consistent with those calculated using modified Sherrington-Southern model. The magnetization vs magnetic field curves showed nonsaturating behavior at magnetic fields $B<90\text{kOe}$ indicating the presence of strong magnetic frustration in the system. The experimental results were reproduced theoretically with good accuracy using the molecular-field-approximation-based model of a disordered ferromagnet with long-range Ruderman-Kittel-Kasuya-Yosida interaction.

Figure 1

Experimental (points) and theoretical (lines) magnetization as a function of temperature for samples cooled in the absence (closed symbols) and the presence (open symbols) of external magnetic field $B=50\text{Oe}$ for two selected ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ samples with different chemical composition (labels).

Figure 2

The Curie-Weiss temperature normalized to the Mn molar fraction $y$ as a function of the carrier concentration $n$ calculated theoretically (lines) using values of the exchange integral $J_{pd}$ varying between 0.4 and 0.8 eV with step 0.05 eV, and the experimental values (points) obtained for the studied ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ crystals grouped with respect to the amount of Mn ions in the alloy $y$ (see legend).

Figure 3

The spin-glass transition temperatures $T_{SG}$ as a function of the Mn molar fraction $y$ calculated (lines) for two different values of the exchange integral $J_{pd}$ and different values of carrier concentration $n$ (see legend), and the experimentally determined values of $T_{SG}$ for ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ crystals with different chemical content $y$. The points were grouped with respect to the different carrier concentrations (see legend).

Figure 4

(a) Hysteresis loops measured at selected constant temperatures (see legend) for selected ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ sample (chemical composition shown in legend) and (b) spontaneous magnetization $M_R$ and coercive field $H_C$ as a function of temperature for a few selected ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ samples with different chemical composition (see legend).

Figure 5

Isothermal magnetization curves $M\left(B\right)$ measured (points) and reproduced using the mean-field model described in the Appendix (lines) for the parameters $J_{pd}=0.75\text{eV}$, $y=0.034$, $p=0.71$, $\lambda =15\text{Å}$, and $J_{AF}/k_{\text{B}}=-20\text{K}$ at different temperatures (see legend) for selected ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ sample with $x=0.142\pm 0.014$ and $y=0.034\pm 0.003$.

Figure 6

The Arrot plot for two selected ${\text{Ge}}_{1-x-y}{\text{Sn}}_x{\text{Mn}}_y\text{Te}$ crystals with different chemical composition (see legend).