First-principles study of magnetic interactions in $3d$ transition metal-doped phase-change materials

Recently, magnetic phase-change materials have been synthesized experimentally by doping with $3d$ transition metal impurities. Here, we investigate the electronic structure and the magnetic properties of the prototypical phase-change material ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ (GST) doped with V, Cr, Mn, and Fe by density functional calculations. Both the supercell method and the coherent potential approximation (CPA) are employed to describe this complex substitutionally disordered system. As regards the first approach, we consider a large unit cell containing 1000 sites to model the random distribution of the cations and of the impurities in doped cubic GST. Such a large-scale electronic structure calculation is performed using the program kkrnano, where the full potential screened Korringa-Kohn-Rostoker Green's function method is optimized by a massively parallel linear scaling (order-$N$) all-electron algorithm. Overall, the electronic structures and magnetic exchange coupling constants calculated by kkrnano agree quite well with the CPA results. We find that ferromagnetic states are favorable in the cases of V and Cr doping, due to the double exchange mechanism, whereas antiferromagnetic superexchange interactions appear to be dominant for Fe- and Mn-doped GST. The ferromagnetic interaction is particularly strong in the case of Cr. As a result, high Curie temperatures close to room temperatures are obtained for large Cr concentrations of 15%.

Figure 1

Structural model for the NaCl-type phase of ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ doped with TM impurities. Orange, green, magenta, and blue spheres indicate Ge, Sb, TM, and Te atoms, respectively.

Figure 2

Local density of states (LDOSs) of (a) Ge, (b) $V^c$, (c) Sb and (d) Te in Cr-doped cubic GST calculated by kkrnano. The LDOSs for majority and minority spin states on all the individual sites are shown. The averaged LDOSs over the individual sites are indicated by the thick lines in the corresponding colors.

Figure 3

$3d$ local density of states (LDOSs) of (a) V-, (b) Cr-, (c) Mn-, and (d) Fe-doped cubic GST calculated by kkrnano. The LDOSs for majority and minority spin states on all the individual TM sites are shown. The concentration of the TM impurities is 3.1%.

Figure 4

$3d$ LDOSs of (a) V-, (b) Cr-, (c) Mn-, and (d) Fe-doped cubic GST calculated by CPA. The TM impurity concentration is 3.1% for all the models. The solid and dashed lines indicate the $t_{2g}$ and $e_g$ components, respectively. The bonding ($e_g^b$) and antibonding ($e_g^a$) states are indicated by black arrows. The total density of states are also shown by the black lines.

Figure 5

Local magnetic moments of the 28 individual TM impurities within the Wigner-Seitz spheres in V-, Cr-, Mn-, and Fe-doped cubic GST. The local moments are obtained from the kkrnano simulations by integrating within the Wigner-Seitz spheres. The magnetic moments averaged over the individual sites are indicated by the dashed lines.

Figure 6

Exchange coupling constants ($J_{ij}\mathrm{s}$) as a function of the distance between two TM impurities in (a) V, (b) Cr, (c) Mn, and (d) Fe 3.1% doped cubic GST, calculated by kkrnano (red squares) and CPA (blue lines). The kkrnano values of $J_{ij}$ calculated by averaging over all the pairs at a given distance are also shown by the red lines. A positive (negative) value means ferromagnetic (antiferromagnetic) interaction.

Figure 7

Configuration averaged exchange coupling constant $J_{ij}\left(E\right)$ between second nearest-neighbor TM impurities (blue line, right scale) and $3d$ LDOSs (red line, left scale) as a function of energy for (a) V-, (b) Cr-, and (c) Fe-doped GST calculated by kkrnano.

Figure 8

Configuration averaged exchange coupling constant $J_{ij}\left(E\right)$ between second nearest-neighbor Mn impurities (blue line, right scale) and $3d$ LDOSs (red line, left scale) as a function of energy for Mn-doped GST calculated by (a) kkrnano and (b) CPA.