Verwey transition in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ investigated using $\mathrm{LDA}+\mathrm{DMFT}$

Motivated by recent structural data questioning the adequacy of the charge order (CO) or disorder picture for the Verwey transition (at $T=T_V$) in magnetite, we reinvestigate this issue within a new theoretical picture. Using the local density $\text{approximation}+\text{dynamical}$ mean-field theory ($\mathrm{LDA}+\mathrm{DMFT}$) method, we show that the nontrivial interplay between octahedral distortions and strong, multiorbital electronic correlations in the half-metallic state is a necessary ingredient for a proper quantitative understanding of the physical responses across $T_V$. While weak CO is found to have very small effects on the low-$T$ spectral function, the low-$T$ charge gap and the resistivity jump across $T_V$ are quantitatively reproduced only upon inclusion of CO in the local spin density $\text{approximation}+\mathrm{DMFT}$ scheme. Our results strongly suggest that the Verwey transition is dominantly driven by multiorbital electronic correlations with associated Jahn-Teller distortions on the $B$ sublattice, and constitutes a nontrivial advance in attempts to understand the physics of ${\mathrm{Fe}}_3{\mathrm{O}}_4$.

Figure 1

(Color online) Orbital-resolved (upper panels) and total (lower panel) one-electron spectral functions for the low temperature (LT) and high temperature (HT) insulating phases of ${\mathrm{Fe}}_3{\mathrm{O}}_4$. Notice the changes in the $A_{1g}$ orbital DOS; the $E_{g1}$ orbitals show small changes, demonstrating the nearly two-fluid character of the Verwey-transition.

Figure 2

(Color online) Comparison of theoretical $\mathrm{LSDA}+\mathrm{DMFT}$ results for the total spectral function in HT and LT phases of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ with experimental results taken from Ref. 5 (for PES) and from Ref. 4 (for BIS). Inset: The tin lines indicate the extrapolated Mott-Hubbard gap.

Figure 3

(Color online) Effect of the $t_{2g}$ level splitting $\Delta$ on the total one-electron spectral function across the Verwey transition in ${\mathrm{Fe}}_3{\mathrm{O}}_4$. The inset shows the effect of charge order (dashed line) in the low-T phase with $\Delta =0.04\mathrm{eV}$. Inset: The tin lines indicate the extrapolated Mott-Hubbard gap.