Enhanced ferromagnetic transition temperature induced by a microscopic structural rearrangement in the diluted magnetic semiconductor ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\text{Te}$

The correlation between magnetic properties and microscopic structural aspects in the diluted magnetic semiconductor ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ is investigated by x-ray diffraction and magnetization as a function of the Mn concentration $x$. The occurrence of high ferromagnetic-transition temperatures in the rhombohedrally distorted phase of slowly cooled ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ is shown to be directly correlated with the formation and coexistence of strongly distorted Mn-poor and weakly distorted Mn-rich regions. It is demonstrated that the weakly distorted phase fraction is responsible for the occurrence of high-transition temperatures in ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$. When the Mn concentration becomes larger, the Mn-rich regions start to switch into the undistorted cubic structure, and the transition temperature is suppressed concurrently. By identifying suitable annealing conditions, we successfully increased the transition temperature to above 200 K for Mn concentrations close to the cubic phase. Structural data indicate that the weakly distorted phase fraction can be restored at the expense of the cubic regions upon the enhancement of the transition temperature, clearly establishing the direct link between high-transition temperatures and the weakly distorted Mn-rich phase fraction.

Figure 1

Extended phase diagram of ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ including data of annealed samples which exhibit higher $T^{*}$ values than observed before. Filled symbols refer to the $T^{*}$ of controlled-cooled (filled circles) or annealed (filled triangles), open symbols to quenched samples, respectively. Colored symbols of various shapes identify samples for which different heat treatments were applied, see text. Pairs of quenched and controlled-cooled samples with similar Mn concentrations for which high-resolution SXRD measurements were carried out are indicated with black open or filled circle symbols, respectively. The labels (c) to (g) refer to panels in Fig. 4 where the respective data are shown. In addition, SXRD data on the maximum-$T^{*}$ sample, labeled (h) and indicated by a filled green diamond, are also shown in Fig. 4. Some of the data points were reproduced from Ref. [49]. The dotted lines are guides to the eyes and the gray-shaded area indicates the structural-transition range. The latter is only an approximation and does not indicate exact phase boundaries (see text and Sec. S9 in the Supplemental Material [52] for details).

Figure 2

Temperature-dependent XRD patterns around the ${104}_{\mathrm{h}}$ and ${110}_{\mathrm{h}}$ reflections (in hexagonal setting) of an initially quenched sample with $x_{\mathrm{a}}=0.069$. First, the powder sample was heated up to about 900 K into its high-temperature cubic phase. Then the temperature was slowly lowered. (a) XRD patterns taken at $T=539$ K as a function of elapsed time after the temperature had settled. (b) XRD patterns taken as a function of elapsed time, after lowering the temperature to $T=499$ K. (c) Comparison of XRD data taken at room temperature before and after the high-temperature experience. The dashed lines indicate the position of both reflections for pristine GeTe. The different positions $2\theta$ of the XRD peaks in the three panels are due to the temperature-induced change of the lattice constants (see text for details).

Figure 3

(a)–(c) Magnetization in $B=0.1$ T measured after annealing experiments on three different samples with (a) $x_{\mathrm{a}}=0.060$, (b) $x_{\mathrm{a}}=0.139$, and (c) $x_{\mathrm{a}}=0.206$. Temperature-dependent data (field cooled FC) is shown for the as-grown controlled-cooled samples (blue data points) and after annealing for one day (red), one week (green), and three weeks (black dotted lines) at the optimal spinodal decomposition temperature of 500 K. (d)–(f) Summarize the field dependencies of the magnetization at $T=2$ K after each annealing step of the samples shown in (a)–(c) (zero-field cooled ZFC), see text. The red-dotted line in (a) indicates exemplarily the definition of $T^{*}$.

Figure 4

High-resolution SXRD patterns at room temperature. (a) Typical peak profile for pristine rhombohedral GeTe (space group $R3m)$. (b) Corresponding data for a cubic ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ sample with $x_{\mathrm{a}}=0.231$ (space group $Fm\overline{3}m)$. In the cubic phase all peaks shown in the panel are single peaks. (c)–(h) SXRD data around the rhombohedral ${104}_{\mathrm{h}}$ and ${110}_{\mathrm{h}}$ reflections for selected samples. The corresponding data points in the phase diagram in Fig. 1 are indicated by the same labels (c)–(h). Each panel (c)–(g) contains data for a controlled-cooled (labeled “cc”, blue) and a quenched (“q”, red) sample with similar Mn concentrations for comparison. (h) The corresponding data for the annealed (“an”, green) sample with the highest $T^{*}$, see text for details. The vertical dotted lines in the panels indicate the positions of the ${104}_{\mathrm{h}}$ and ${110}_{\mathrm{h}}$ reflections in pristine GeTe.

Figure 5

(a) Lattice parameters of ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$: The lattice parameters in the rhombohedral phase are given in their pseudocubic setting $\tilde{a}=\sqrt{2}{a}_{\mathrm{h}},\tilde{c}=c_{\mathrm{h}}/\sqrt{3}$ for a better comparison. Circle symbols refer to $a_{\mathrm{h}}$, squares to $c_{\mathrm{h}}$, and triangles to the lattice parameter $a_{\mathrm{c}}$ in the cubic phase. Open symbols are used for quenched, filled symbols for controlled-cooled and annealed samples. In the high-$T^{*}$ phase of controlled-cooled samples, a multiphase scenario of two rhombohedral phase fractions is assumed (R1 and R2; blue and red). Upon increasing $x_{\mathrm{a}}\gtrsim 0.080$, a cubic phase fraction starts to grow in addition; see text for details. The labels (C + R; cyan) and (R + C; orange) indicate two samples which could be refined best when assuming a cubic main phase plus a single rhombohedral phase fraction or a single rhombohedral main phase plus a cubic phase fraction, respectively. As in Fig. 1, the gray-shaded area indicates the structural-transition range. Dotted lines are guides to the eyes. (b) Volume fraction of the different structural phases for selected quenched (“q”), controlled-cooled (“cc”), and annealed samples (“an”). The dotted arrows indicate their position, i.e., Mn concentrations $x_{\mathrm{a}}$ in (a). The black circle symbols are the respective ferromagnetic $T^{*}$ values (right axis), see text.