Evidence of kinetic-energy-driven antiferromagnetism in double perovskites: A first-principles study of La-doped ${\text{Sr}}_2{\text{FeMoO}}_6$

Using first-principles density-functional calculations, together with exact diagonalization of Fe-Mo Hamiltonian constructed in a first-principles Wannier-function basis, we studied the electronic structure of La-doped double-perovskite compound ${\text{Sr}}_2{\text{FeMoO}}_6$. Our calculation shows stabilization of kinetic-energy-driven antiferromagnetic phase for La-rich compounds, in agreement with the results obtained on the basis of previous model calculations.

Figure 1

(Color online) The Fe sublattice ordering of ${\text{Sr}}_{2-x}{\text{La}}_x{\text{FeMoO}}_6$. Shown are the $A$-type(left panel) and $G$-type (right panel) antiferromagnetic arrangement of Fe spins. In case of $A$-type antiferromagnetism the Fe spins in-plane are ferromagnetically coupled while Fe spins between two adjacent plans are antiferromagnetically coupled. For $G$-type antiferromagnetism, the Fe spins are antiferromagnetically coupled both out-of-plane and in-plane. The shaded box indicate the unit cell of two formula unit supercell.

Figure 2

(Color online) The energy difference between FM and $\text{AFM-}A$ phase plotted as a function of La concentration. The FM phase becomes unstable beyond a critical concentration of La both within GGA and $\text{GGA}+U$.

Figure 3

(Color online) The GGA density of states corresponding to SFMO, SLFMO, ${\text{Sr}}_{0.5}{\text{La}}_{1.5}{\text{FeMoO}}_6$ (L3SFMO), and LFMO in ferromagnetic configuration. The density of states projected onto Fe, Mo, and O are represented by solid black, green (gray), and shaded gray area. The upper and lower panels correspond to majority- and minority-spin channels. Zero of the energy is set at the GGA Fermi energy.

Figure 4

(Color online) The density of states corresponding to SFMO, SLFMO, L3SFMO, and LFMO in the $A$-type antiferromagnetic configuration. The density of states projected onto Fe, Mo, and O are represented by solid black, green (gray), and shaded gray area. Zero of the energy is set at the GGA Fermi energy.

Figure 5

(Color online) Schematic showing the mechanism stabilizing the AFM phase over FM phase. As the La doping is increased, the Fermi level $\left(E_f\right)$ shifts toward right.

Figure 6

(Color online) DOS for LFMO in FM and $\text{AFM-}A$ phase, using $\text{GGA}+U$.

Figure 7

(Color online) Top panels: Positioning of various energy levels as obtained by NMTO-downfolding calculation before and after switching on the hybridization between the magnetic and nonmagnetic ions. Bottom panels: Effective $\text{Mo}{t}_{2g}$ Wannier orbitals corresponding to massively downfolded NMTO Hamiltonian in the down-spin channel. Shown are the orbital shapes (constant-amplitude surfaces) with lobes of opposite signs colored as blue (dark gray) and cyan (light gray). The central part of the Wannier orbitals are shaped according to $\text{Mo}{t}_{2g}$ symmetry while the tails are shaped according to $\text{Fe}{t}_{2g}$ and $\text{O-}p$ symmetries. Significant amount of weights are seen in O and Fe site which reflects the strong hybridization between Fe, Mn, and O. For LFMO, finite weights are seen also at La sites, occupying the hollows formed between Mo-O and Fe-O bonds, which is of $\text{La}3z^2$ character.

Figure 8

The energy differences between the FM and $G$-type AFM phase (solid line) and the FM and $A$-type AFM phase (dashed line) plotted as a function of the number of conduction electrons, as obtained by exact diagonalization of the low-energy Hamiltonian for a $8\times 8\times 8$ lattice. Only the region outside the hashed regions, from carrier concentration 1 to 3 is of relevance for ${\text{Sr}}_{2-x}{\text{La}}_x{\text{FeMoO}}_6$.

Figure 9

The ferromagnetic $T_c$ (solid line) and the antiferromagnetic transition temperature $T_N$ (dashed line) plotted as a function of the number of conduction electrons, as obtained by exact diagonalization of the low-energy Hamiltonian for a $8\times 8\times 8$ lattice. As in Fig. 8, the region outside the hashed regions, from carrier concentration 1 to 3 is of relevance for ${\text{Sr}}_{2-x}{\text{La}}_x{\text{FeMoO}}_6$.