Ab initio study of electronic, magnetic, and spectroscopic properties in $A$- and $B$-site-ordered perovskite $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Fe}}_2{\mathrm{Sb}}_2{\mathrm{O}}_{12}$

Electronic structure, magnetism, x-ray absorption spectroscopy (XAS), and x-ray magnetic circular dichroism (XMCD) spectra of $A$- and $B$-site-ordered quadruple perovskite $B$-site-ordered perovskite $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Fe}}_2{\mathrm{Sb}}_2{\mathrm{O}}_{12}$ (CCFSO) were studied using first-principles calculations with inclusion of spin-orbit coupling. The calculated XAS and XMCD spectra for Cu and Fe at the $L_{3,2}$ edges were consistent with a recent experiment and indicate ferrimagnetic ordering with antiparallel magnetic moments between Cu and Fe. The magnetic exchange coupling constants were also calculated to clarify the detailed mechanism of the ferrimagnetic ordering in CCFSO. The coupling constants for Cu-Cu, Fe-Fe, and Cu-Fe pairs were found to be moderate ferromagnetic, weak antiferromagnetic, and strong antiferromagnetic, respectively. From the analysis of the calculated density of states and magnetization density, the microscopic origin of the strong antiferromagnetic coupling between Cu and Fe was successfully elucidated by the superexchange mechanism via the $\mathrm{Cu}\left(d_{x^2-y^2}\right)-\mathrm{O}\left(p_x\right)-\mathrm{Fe}\left(t_{2g}\right)$ exchange path.

Figure 1

(a) Crystal structure of CaCu${}_3$Fe${}_2$Sb${}_2$O${}_{12}$ (CCFSO). CCFSO is a ferrimagnetic insulator with $Pn\overline{3}$ cubic symmetry consisting of CuO${}_4$ square planes and largely tilted FeO${}_6$ and SbO${}_6$ octahedra with Fe-O-Sb angle of 138.5${}^{\circ }$. (b) Nonequivalent CuO${}_4$ square planes under magnetization along the [001] direction. Cu1 (Cu2) indicates Cu in perpendicular (parallel) plane to magnetization axis.

Figure 2

Total and site-decomposed density of states of CaCu${}_3$Fe${}_2$Sb${}_2$O${}_{12}$: (a) GGA and (b) GGA + $U$ + SOC ($U_{\mathrm{eff}}=7$ eV for Cu and $U_{\mathrm{eff}}=4$ eV for Fe) with quantization axis [001].

Figure 3

Calculated XAS and XMCD spectra at (a) Cu $L_{3,2}$, (b) Fe $L_{3,2}$, and (c) O $K$ edges with Lorentzian function with widths of 0.4, 0.4, and 0.14 eV, respectively. Red solid (green dashed) lines denote XAS spectra for helicity +(−). Blue dotted lines represent the XMCD spectrum.

Figure 4

Magnetic structures in unit cells of CCFSO. Short (long) arrows indicate local spin magnetic moment of Cu${}^{2+}$ (Fe${}^{3+}$).

Figure 5

Orbital-decomposed partial density of states of (a) O($p_x,p_y,p_z$) and Cu($d_{x^2-y^2}$) and (b) Fe($t_{2g},e_g$). Positions of ions and principal axes of orbitals are shown in (c) for O and Cu and (d) for Fe.

Figure 6

Magnetization density of CCFSO for the Cu($d_{x^2-y^2}$)-O($p_x$)-Fe($t_{2g}$) band within an energy range from about $E_{\mathrm{VBM}}+2$ to $E_{\mathrm{VBM}}+3$ eV in Fig. 2. Spin magnetization is described by surface coloring; blue and red regions present up- and down-spin polarized charge density, respectively, and the green region indicates spin-compensated charge density.