Electronic and magnetic properties of the double perovskites ${\mathrm{La}}_2{\mathrm{MnRuO}}_6$ and $\mathrm{LaA}{\mathrm{MnFeO}}_6(A=\mathrm{Ba},\text{Sr},\text{Ca})$ and their potential for magnetic refrigeration

Magnetic refrigeration at room-temperature is a technology that could potentially be more environmentally friendly, efficient, and affordable than traditional refrigeration. The search for suitable materials for magnetocaloric refrigeration led to the study of double-perovskites ${\mathrm{La}}_2{\mathrm{MnNiO}}_6,{\mathrm{La}}_2{\mathrm{MnCoO}}_6$, and ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$. While ${\mathrm{La}}_2{\mathrm{MnNiO}}_6$ and ${\mathrm{La}}_2{\mathrm{MnCoO}}_6$ are ferromagnets with near room-temperature $T_C\mathrm{s}$, a previous theoretical study of double-perovskite ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$ revealed that this material is a ferrimagnet due to strong electronic interactions in $\mathrm{Fe}\text{−}d$ orbitals. Here we investigate the double-perovskites ${\mathrm{La}}_2{\mathrm{MnRuO}}_6$ and $\mathrm{La}A{\mathrm{MnFeO}}_6(A$ = Ba, Ca, and Sr) with density functional theory (DFT) as materials that can counteract the effects the strong repulsion present in the in $\mathrm{Fe}\text{−}d$ shells of ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$ and lead to a ferromagnetic state. Our study reveals that while ${\mathrm{La}}_2{\mathrm{MnRuO}}_6$ is also a ferrimagnet, but with a higher net magnetic moment per formula than ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$, doubly ordered $\mathrm{La}A{\mathrm{MnFeO}}_6$ are ferromagnets. By mapping the total energy of the $\mathrm{La}A{\mathrm{MnFeO}}_6$ compounds obtained from DFT calculations to the Ising model, we also calculate their magnetic exchange couplings. This allows us to estimate the trend in $T_C$ of the three doped ${\mathrm{La}}_2{\mathrm{MnFeO}}_6$ materials with classical Monte Carlo calculations and predict that doubly ordered ${\mathrm{LaBaMnFeO}}_6$ and ${\mathrm{LaSrMnFeO}}_6$ could be suitable materials for room-temperature magnetic refrigeration.

Figure 1

Spin-resolved partial density of states for $\mathrm{Mn}\text{−}{e}_g,\mathrm{Mn}\text{−}{t}_{2}g,\mathrm{Ru}\text{−}{e}_g,\mathrm{Ru}\text{−}{t}_{2g}$, and O-$p$ from (a) GGA calculations and (b) GGA + U calculations. GGA + U calculations are performed with $U_{\mathrm{eff}}=3\mathrm{eV}$ for $\mathrm{Mn}\text{−}d$ orbitals and $U_{\mathrm{eff}}=1.09\mathrm{eV}$ for $\mathrm{Ru}\text{−}d$ orbitals. The upper part in each panel is majority-spin DOS result, and the lower the minority-spin one. GGA(+U) calculations predict a metallic (insulating) ferrimagnetic ground state for LMRO. (c) Schematic representation of the superexchange interaction in ferrimagnetic LMRO. The figure represents schematically the weight of each orbital with respect to the others and is derived from the partial DOS plots and partial charge data.

Figure 2

Top (middle) panel: Partial density of states for O-$p,\mathrm{Fe}\text{−}{e}_g$, and $\mathrm{Mn}\text{−}{e}_g$, and $\mathrm{Fe}\text{−}{t}_{2g}$ and $\mathrm{Mn}\text{−}{t}_{2g}$ orbitals from GGA (GGA + U) calculations. Positive DOS corresponds to the majority-spin channel, while negative DOS corresponds to the minority-spin channel. GGA and GGA + U calculations predict a ferromagnetic insulating ground state in (a, d) LBMFO, (b, e) LSMFO, and (c, f) LCMFO. Bottom panel (g): Schematic representation of the ferromagnetic superexchange interaction between ${\mathrm{Mn}}^{4+}$ and ${\mathrm{Fe}}^{3+}$ in LBMFO, LSMFO, and LCMFO.

Figure 3

Reduced supercell with the four nonequivalent Mn (blue) and Fe (red) atoms. The lattice vector $\mathbf{a}$ denotes the out of plane direction, while the lattice vectors $\mathbf{b}$ and $\mathbf{c}$ generate the plane.

Figure 4

Comparison between the experimental maximal value of the isothermal entropy change of LMNO [2] (black empty squares), and the mean-field calculated values of $\mathrm{\Delta }{S}_{\max }$ of LMNO (dark blue filled squares), LBMFO (red circles), and LSMFO (green triangles). We used for the number of formulas per kilogram, $N=1.25\times {10}^{24}$ and $N=1.40\times {10}^{24}$ for LBMFO and LSMFO, respectively, to obtain the entropy change per kilogram of material from Eq. (A1).

Figure 5

Isothermal entropy change for an external field of $7\mathrm{T}$ in LMNO from our two-spin mean-field calculation (full red line), and from experimental (blue dots) and effective one-spin mean-field (dashed black line) data [2]. We plotted $\mathrm{\Delta }S$ as a function of $T-T_C$, where $T_C=280\mathrm{K}$ for the experimental and simple mean-field data, and $T_C=527\mathrm{K}$ for our mean-field results.