Charge Order and the Origin of Giant Magnetocapacitance in ${\mathrm{LuFe}}_2{\mathrm{O}}_4$

The nature of the charge order in the charge frustrated compound ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ and its effect on magnetocapacitance were examined on the basis of first-principles electronic structure calculations and Monte Carlo simulations of electrostatic energy. Our work shows that two different types of charge order of almost equal stability (i.e., $\sqrt{3}\times \sqrt{3}$ and chain types) occur in the ${\mathrm{Fe}}_2{\mathrm{O}}_4$ layers of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$, and that the ground state of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ has a ferrielectric arrangement of the ${\mathrm{Fe}}_2{\mathrm{O}}_4$ layers with $\sqrt{3}\times \sqrt{3}$ charge order. The giant magnetocapacitance effect of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ at room temperature is accounted for in terms of charge fluctuations arising from the interconversion between the two types of charge order, that becomes hindered by an applied magnetic field.

Figure 1

(a) Hexagonal unit cell structure of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$, where large gray, medium white, and small red circles represent the Lu, Fe, and O atoms, respectively. Schematic representations of the (b) CO-I, (c) CO-II, and (d) CO-III structures, where the small and large circles refer to the Fe ions in the upper and lower triangular sheets of a $\mathsf{W}$ layer, respectively. The ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions are represented by open and closed circles, respectively. Schematic representations of the (e) ferroelectric and (f) ferrielectric arrangements of the dipoles of the $\mathsf{W}$ layers in the CO-I structure.

Figure 2

Density of states of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ calculated for the room-temperature structure without CO. The DOS was calculated with 0.1 eV broadening.

Figure 3

DOS of ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ calculated for (a) the relaxed CO-I and (b) the relaxed CO-III structures. The blue regions highlight the PDOS of the ${\mathrm{Fe}}^{2+}$ ion. The inset shows the charge density plot calculated for the occupied down-spin $d$ states. The DOS was calculated with 0.1 eV broadening.