Origin of magnetism and trend in $T_c$ in Cr-based double perovskites: Interplay of two driving mechanisms

Employing first principles density functional calculations, together with solution of the low-energy, model Hamiltonian constructed in a first principles manner, we explored the origin of magnetism and the $T_c$ trend in Cr-based double perovskite series, Sr${}_2$Cr$B^{\prime }$O${}_6$ ($B^{\prime }=$ W/Re/Os). Our study shows that the apparently puzzling $T_c$ trend in Sr${}_2$Cr$B^{\prime }$O${}_6$ ($B^{\prime }=$ W/Re/Os) series can be understood in terms of the interplay of the hybridization driven mechanism and the superexchange mechanism.

Figure 1

Left panels: GGA DOS projected onto Cr $d$ (black solid lines), $B^{\prime }$ $d$ (red/gray solid lines), and O $p$ (shaded area). Zero of the energy is set at $E_F$. The numbers within the boxes indicate the Cr $t_{2g}$ contribution in the bands crossing $E_F$, with respect to that of $B^{\prime }$. Right panel: Calculated net magnetic moment and magnetic moments at Cr, $B^{\prime }$, and O sites. The numbers within the brackets denote the results of GGA$+$SO calculations, the first entry being the spin moment and the second entry being the orbital moment. From top to bottom, the plots correspond to SCWO, SCRO, and SCOO, respectively.

Figure 2

The energy level diagram (upper panel) and massively downfolded Wannier functions (lower panels) for Sr${}_2$Cr$B^{\prime }$O${}_6$ series. For Wannier function plots, constant value surfaces have been plotted with two oppositely signed lobes colored differently. From left to right in lower panel, the plots correspond to SCWO, SCRO, and SCOO, respectively. The numbers in the energy level diagram are in units of eV.

Figure 3

PM-FM energy differences plotted as a function of valence electron count, as obtained in exact diagonalization calculation. The diamond (square) symbols connected by dashed (solid) lines correspond to calculations corresponding to the Hamiltonian without (with) the $J_2$ term.