Active role of nonmagnetic cations in magnetic interactions for double-perovskite $\mathrm{S}{\mathrm{r}}_{2}B\mathrm{Os}{\mathrm{O}}_6(B=\mathrm{Y},\mathrm{In},\mathrm{Sc})$

Using first-principles density-functional theory, we have investigated the electronic and magnetic properties of recently synthesized and characterized $5d$ double-perovskites $\mathrm{S}{\mathrm{r}}_{2}B\mathrm{Os}{\mathrm{O}}_6(B=\mathrm{Y},\mathrm{In},\mathrm{Sc})$. The electronic structure calculations show that in all compounds the $\mathrm{O}{\mathrm{s}}^{5+}$ ($5d^3$) site is the only magnetically active one, whereas ${\mathrm{Y}}^{3+}, \mathrm{I}{\mathrm{n}}^{3+}$, and $\mathrm{S}{\mathrm{c}}^{3+}$ remain in nonmagnetic states with Sc/Y and In featuring $d^0$ and $d^{10}$ electronic configurations, respectively. Our studies reveal the important role of closed-shell ($d^{10}$) versus open-shell ($d^0$) electronic configurations of the nonmagnetic sites in determining the overall magnetic exchange interactions. Although the magnetic $\mathrm{O}{\mathrm{s}}^{5+}$ ($5d^3$) site is the same in all compounds, the magnetic superexchange interactions mediated by nonmagnetic Y/In/Sc species are strongest for $\mathrm{S}{\mathrm{r}}_2\mathrm{ScOs}{\mathrm{O}}_6$, weakest for $\mathrm{S}{\mathrm{r}}_2\mathrm{InOs}{\mathrm{O}}_6$, and intermediate in the case of the Y ($d^0$) due to different energy overlaps between Os-$5d$ and Y/In/Sc-$d$ states. This explains the experimentally observed substantial differences in the magnetic transition temperatures of these materials, despite an identical magnetic site and underlying magnetic ground state. Furthermore, short-range Os-Os exchange interactions are more prominent than long-range Os-Os interactions in these compounds, which contrasts with the behavior of other $3d-5d$ double perovskites.

Figure 1

GGA FM density of states. The top to bottom panels show the DOS for SYOO, SIOO, and SSOO, projected onto the Y-$4d$-Os-$5d$, the In-$4d$-Os-$5d$ and Sc-$3d$-Os-$5d$ states, respectively, along with the O-$2p$ states. The two channels for each panel represent majority and minority spin channels. The $E_{\mathrm{f}}$ is marked at zero on the energy scale.

Figure 2

(a) Magnetic exchange paths connecting different Os sites (brown spheres) in the monoclinic unit cell of $\mathrm{S}{\mathrm{r}}_2\mathrm{BOs}{\mathrm{O}}_6$ ($B=Y,\mathrm{In}$, Sc). Sr and O atoms are omitted from the structure for clarity. The five interaction paths between different Os sites are denoted by $J_1-J_5$. The two lowest magnetic spin structures, (b) experimental spin structure AFM-I and (c) second lowest spin structure AFM-II.

Figure 3

The Wannier functions of Os-$t_{2\mathrm{g}}$'s for SYOO and SIOO calculated with the GGA prescription are shown in the top [(a) and (b)] and bottom [(c) and (d)] panels, respectively. The central part of the Os Wannier functions comprises Os-$5d_{\mathrm{yz}}$ and Os-$5d_{\mathrm{xy}}$ characters for (a) and (c) and (b) and (d), respectively. The exchange interactions $J_2-J_3-J_5$ and $J_1-J_2-J_4$ are shown in (a) and (b), respectively. The green and yellow colors represent surfaces with isovalues of 0.18 and $-0.18$, respectively. The red spheres represent O atoms, whereas the other color symbols are the same as those in Fig. 2.