Exchange interaction and its tuning in magnetic binary chalcogenides

Using a first-principles Green's function approach we study magnetic properties of the magnetic binary tetradymite chalcogenides ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and ${\mathrm{Sb}}_2{\mathrm{Te}}_3$. The magnetic coupling between transition-metal impurities is long range, extends beyond a quintuple layer, and decreases with increasing number of $d$ electrons per $3d$ atom. We find two main mechanisms for the magnetic interaction in these materials: the indirect exchange interaction mediated by free carriers and the indirect interaction between magnetic moments via chalcogen atoms. The calculated Curie temperatures of these systems are in good agreement with available experimental data. Our results provide deep insight into exchange interactions in magnetic binary tetradymite chalcogenides and open a way to design new materials for promising applications.

Figure 1

Schematic view of magnetic interactions in Sb${}_{2-x}$TM${}_x$Te${}_3$: exchange interactions between (a) different layers and (b) within a single layer. The corresponding exchange constants for Ti, V, Cr, Mn, Fe, and Co are shown in Fig. 2. The same plot applies to Bi${}_{2-x}$TM${}_x$Se${}_3$ and Bi${}_{2-x}$TM${}_x$Te${}_3$.

Figure 2

Exchange constants (in meV) in magnetic Bi${}_{1.80}$TM${}_{0.20}$Se${}_3$, Bi${}_{1.80}$TM${}_{0.20}$Te${}_3$, and Sb${}_{1.80}$TM${}_{0.20}$Te${}_3$ (TM = Ti, V, Cr, Mn, Fe, Co). See the schematic view of magnetic interactions in Fig. 1.

Figure 3

Spin resolved DOS of the TM atoms in Sb${}_{1.8}$TM${}_{0.2}$Te${}_3$ [(a) $\text{TM}=\text{Ti}$, (b) V, (c) Cr, (d) Mn, (e) Fe, (f) Co, and (g) Ni]. Panel (h) shows the spin-resolved DOS of Cr in Ag${}_{0.25}$Sb${}_{1.8}$Cr${}_{0.2}$Te${}_3$. Red (blue) line stands for the majority (minority) spin channel. The vertical dashed lines indicate the Fermi energy.

Figure 4

Spin density $m\left(z\right)$ (see text) of Sb${}_{2-x}$Cr${}_x$Te${}_3$ for $x=0.1$ and $x=0.2$ in the [0001] direction integrated over all in-plane coordinates $x$ and $y$. The $z$ range covers two QLs.

Figure 5

Calculated critical temperature $T_{\mathrm{C}}$ versus concentration $x$ of Ti, V, Cr, and Mn in Sb${}_{2-x}$TM${}_x$Te${}_3$. The critical temperature $T_{\mathrm{C}}$ is determined from Monte Carlo simulations with randomly distributed impurities (black-filled triangles) and with cluster percolation (red-filled circles). $T_{\mathrm{C}}$ is compared to experimental data (green and blue markers) [19, 20]. In the case of Cr, there is a transition from a ferromagnetic state for $x<0.8$ (light-blue background) to an antiferromagnetic state at higher concentrations (light-red background).