Electronic structure and magnetic exchange coupling in ferromagnetic full Heusler alloys

Density-functional studies of the electronic structures and exchange interaction parameters have been performed for a series of ferromagnetic full Heusler alloys of general formula ${\mathrm{Co}}_2\mathrm{Mn}Z$ $(Z=\mathrm{Ga},\mathrm{Si},\mathrm{Ge},\mathrm{Sn})$, ${\mathrm{Rh}}_2\mathrm{Mn}Z$ $(Z=\mathrm{Ge},\mathrm{Sn},\mathrm{Pb})$, ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}$, ${\mathrm{Cu}}_2\mathrm{Mn}\mathrm{Sn}$, and ${\mathrm{Pd}}_2\mathrm{Mn}\mathrm{Sn}$, and the connection between the electronic spectra and the magnetic interactions have been studied. Different mechanisms contributing to the exchange coupling are revealed. The band dependence of the exchange parameters, their dependence on volume and valence electron concentration have been thoroughly analyzed within the Green function technique. The difference between the exact adiabatic approach and the long-wavelength approximation is discussed.

Figure 1

The $\mathrm{L}{2}_1$ structure type composed of four interpenetrating fcc lattices.

Figure 2

Schematic hybridization between the minority spin orbitals of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$, first between two Co atoms (top), then between two Co atoms and a neighboring Mn atom (bottom). The coefficients label the degeneracies of the orbital sets (see notations in Ref. 10).

Figure 3

Total and partial DOS for the compound ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$. The character of each peak belonging to the minority spin states has been indicated, and the Fermi level is set to the energy zero.

Figure 4

Density of states and $J^0\left(E\right)$ for the Mn (solid line) and Co (dashed line) atoms of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$ (top) and ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ (bottom). The Fermi level is at zero energy for ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ (29 valence electrons) and shifted to the left for ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$ (28 valence electrons) by the rigid-band shift $\mathrm{\Delta }{E}_F$.

Figure 5

Density of states of the compounds ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Si}$ (solid line), ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ (dashed line), and ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Sn}$ (dotted line). The Fermi level is at the energy zero.

Figure 6

Course of $J_{\mathrm{Mn}}^0$ (solid line) and $J_{\mathrm{Co}}^0$ (dashed line) as a function of the lattice parameter in ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Si}$. Filled circles correspond to $J_{\mathrm{Mn}}^0$ and empty ones to $J_{\mathrm{Co}}^0$ for the real ${\mathrm{Co}}_2\mathrm{Mn}Z$ systems ($Z=\mathrm{Si}$, Ge and Sn) calculated at their experimental lattice parameters.

Figure 7

Total (solid line) and partial densities of states (dashed line) of Rh and Co in ${\mathrm{Rh}}_2\mathrm{Mn}\mathrm{Sn}$ and ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Sn}$. The Fermi level is at the energy zero.

Figure 8

The calculated effective exchange parameters $J_{\mathrm{Mn}}^0$ (solid) and $J_{\mathrm{Rh}}^0$ (dashed line) as a function of band filling for ${\mathrm{Rh}}_2\mathrm{Mn}\mathrm{Ge}$. Vertical lines corresponds to 28 $\left({\mathrm{Rh}}_2\mathrm{Mn}\mathrm{Al}\right)$ and 29 $\left({\mathrm{Rh}}_2\mathrm{Mn}\mathrm{Ge}\right)$ electrons per unit cell. The energy zero corresponds to the Fermi level of ${\mathrm{Rh}}_2\mathrm{Mn}\mathrm{Ge}$.

Figure 9

The calculated effective parameters $J_{\mathrm{Mn}}^0$ (solid line) and $J_{\mathrm{Co}}^0$ (dashed line) as a function of band filling in ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Sn}$. Vertical lines correspond to 27 $\left({\mathrm{Fe}}_2\mathrm{Mn}\mathrm{Sn}\right)$, 29 $\left({\mathrm{Co}}_2\mathrm{Mn}\mathrm{Sn}\right)$, 31 $\left({\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Sn}\right)$, and 33 $\left({\mathrm{Cu}}_2\mathrm{Mn}\mathrm{Sn}\right)$ electrons per unit cell.