Superexchange interaction in the $A$-site ordered perovskite ${\mathrm{YMn}}_3{\mathrm{Al}}_4{\mathrm{O}}_{12}$

Crystal structure and magnetic ordering in ${\mathrm{YMn}}_3{\mathrm{Al}}_4{\mathrm{O}}_{12}$ are determined by neutron powder diffraction measurement, indicating that $S=2$ spins of the $A^{\prime }$-site ${\mathrm{Mn}}^{3+}$ ions are ordered in G-type antiferromagnetic (AFM) arrangement in the $Im\overline{3}$ cubic crystal structure. Using the first-principles electronic structure calculations, it is found that the AFM spin structure is stabilized by the nearest-neighbour (NN) exchange interaction. The underlying mechanism of the NN exchange is revealed to be the antiferromagnetic Mn-O-Mn superexchange interaction from the calculations of electronic transfer integrals.

Figure 1

Crystal structure of ${\mathrm{YMn}}_3{\mathrm{Al}}_4{\mathrm{O}}_{12}$.

Figure 2

Temperature evolution of the neutron diffraction patterns of ${\mathrm{YMn}}_3{\mathrm{Al}}_4{\mathrm{O}}_{12}$ from 5–300 K.

Figure 3

Rietveld plots of neutron powder diffraction patterns at (a) 300 K and (b) 5 K. The observed (+), calculated (solid line) and differences (bottom) patterns are shown. The ticks indicate the allowed Bragg reflections for nuclear lattice (above), magnetic (middle, 5 K), and ${\mathrm{Al}}_2{\mathrm{O}}_3$ impurity (below).

Figure 4

Experimental temperature dependence of the refined magnetic moment at the Mn site.

Figure 5

Density of states (DOS) of ${\mathrm{YMn}}_3{\mathrm{Al}}_4{\mathrm{O}}_{12}$ calculated in GGA+$U$ ($U_{\mathrm{eff}}=4.5$ eV). In (a), the total DOS and Mn partial DOS are shown by the gray and red area, respectively. In (b) and (c), the orbital-decomposed DOS is shown for $\mathrm{Mn}-d_{3z^2-r^2}$, $\mathrm{Mn}-d_{xy}$, and $\mathrm{O}-p_y$ orbitals that are related to Mn-O-Mn AFM superexchange interaction (see text). The vertical dashed line shows the center of gravity of the upper Hubbard band, lower Hubbard band, and the $\mathrm{O}-p$ main peak.

Figure 6

Absolute values of calculated exchange interaction energies for direct exchange, superexchange, and super-superexchange based on the tight-binding Hubbard model. Note that the horizontal axis is in logarithmic scale. The transfer integrals were numerically calculated using the MLWFs. The Hubbard parameters (${\mathrm{\Delta }}_{pd}=4.5$ eV and $J_{dd}=7.5$ eV) were taken from the experimental values for ${\mathrm{LaMnO}}_3$ [28].