Electronic and magnetic properties of the candidate magnetocaloric-material double perovskites ${\mathrm{La}}_2{\mathrm{MnCoO}}_6$, ${\mathrm{La}}_2{\mathrm{MnNiO}}_6$, and ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$

The search for room-temperature magnetocaloric materials for refrigeration has led to investigations of double perovskites. In particular, a puzzle has appeared in the ${\mathrm{La}}_2{\mathrm{MnNiO}}_6$, ${\mathrm{La}}_2{\mathrm{MnCoO}}_6$, and ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$ family of compounds. They share the same crystal structure, but while ${\mathrm{La}}_2{\mathrm{MnNiO}}_6$ and ${\mathrm{La}}_2{\mathrm{MnCoO}}_6$ are ferromagnets below room temperature, ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$, contrary to simple expectations, is a ferrimagnet. To solve this puzzle, we use density functional theory calculations to investigate the electronic structure and magnetic exchange interactions of the ordered double perovskites. Our study reveals the critical role played by local electron-electron interaction in the Fe-$d$ orbital to promote the ${\mathrm{Fe}}^{3+}$ valence state with half-filled $d$ shell over ${\mathrm{Fe}}^{2+}$ and to establish a ferrimagnetic ground state for ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$. The importance of Hund's coupling and Jahn-Teller distortion on the ${\mathrm{Mn}}^{4+}$ ion is also pointed out. Exchange constants are extracted by comparing different magnetically ordered states. Mean field and classical Monte Carlo calculations on the resulting model give trends in $T_C$ that are in agreement with experiments on this family of materials.

Figure 1

Magnetization as a function of temperature in bulk ${\mathrm{La}}_2{\mathrm{MnCoO}}_6$ (black circles), ${\mathrm{La}}_2{\mathrm{MnNiO}}_6$ (blue squares), and ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$ (green triangles). Inset: zoom on the magnetic transition in LMFO.

Figure 2

Spin-resolved partial density of states for Mn-$e_g$, Mn-$t_{2}g$, Ni (Co, Fe)-$e_g$, Ni (Co, Fe)-$t_{2g}$, and O-$p$ from GGA calculations (top row) and $\mathrm{GGA}+U$ (middle row) calculations. $\mathrm{GGA}+U$ calculations are performed with $U_{eff}=3\mathrm{eV}$. The upper part in each panel is majority-spin DOS result, and the lower the minority-spin one. GGA calculations predict an insulating ferromagnetic ground state for (a) LMNO and (b) LMCO, and a metallic ferromagnetic ground state for (c) LMFO. $\mathrm{GGA}+U$ calculations predict an insulating ferromagnetic ground state for (d) LMNO and (e) LMCO, and an insulating ferrimagnetic ground state for (f) LMFO. Bottom row: schematic representation of the superexchange interaction in (g) LMNO, (h) LMCO, and (i) LMFO. The figures represent schematically the weight of each orbital with respect to the others and are derived from the partial DOS plots and partial charge data. In LMFO, $e_g$ electrons are more itinerant than the $t_{2g}$ electrons and therefore repulsion $U$ has a smaller impact on them. This leads to a smaller energy splitting between up- and down-spin states of $e_g$ electrons and in turn to positioning of $e_g$ states between $t_{2g}$ states.

Figure 3

Top panel: (a) reduced supercell with the four nonequivalent Mn (blue) and Ni(Co, Fe) (red) atoms. The gray atoms are on the Mn sublattice and the black ones on the Ni(Co, Fe) sublattice. The lattice vector $\mathbf{a}$ denotes the out-of-plane direction, while the lattice vectors $\mathbf{b}$ and $\mathbf{c}$ generate the plane. Bottom panel: spin configuration for Mn (blue) and Ni(Co, Fe) (red) sublattices in (b) AFM4, (c) AFM5, (d) AFM6, and (e) FiM phases.