Origin of Insulating Ferromagnetism in Iron Oxychalcogenide ${\mathrm{Ce}}_2{\mathrm{O}}_2{\mathrm{FeSe}}_2$

An insulating ferromagnetic (FM) phase exists in the quasi-one-dimensional iron oxychalcogenide ${\mathrm{Ce}}_2{\mathrm{O}}_2{\mathrm{FeSe}}_2$, but its origin is unknown. To understand the FM mechanism, here a systematic investigation of this material is provided, analyzing the competition between ferromagnetic and antiferromagnetic tendencies and the interplay of hoppings, Coulomb interactions, Hund’s coupling, and crystal-field splittings. Our intuitive analysis based on second-order perturbation theory shows that large entanglements between doubly occupied and half filled orbitals play a key role in stabilizing the FM order in ${\mathrm{Ce}}_2{\mathrm{O}}_2{\mathrm{FeSe}}_2$. In addition, via many-body computational techniques applied to a multiorbital Hubbard model, the phase diagram confirms the proposed FM mechanism.

Figure 1

Sketch of the basic superexchange cases known (a)–(c). Blue lines and black arrows represent the orbitals and electrons with spin up or down, respectively. The two-way thin arrows indicate the overlap between intersite orbitals. Gray thick arrows in the green dashed circles indicate virtual hopping processes. Real materials might host more than one exchange, introducing competition between them [6].

Figure 2

(a) DFT iron $3d$ orbital-resolved band structure. (b) Sketches of bonding and antibonding states at small $U$ and $J_H$ and their close relation with the band structure in (a). The total population of electrons considered is six electrons to fill the energy levels (thick arrows). (c) DOS, from DFT calculations, for the nonmagnetic phase. (d) Crude sketches of the crystal-field splitting and dominant NN hopping parameters for the five orbitals. (e) Orbitals and their population at large $U$ and $J_H$. The spin down marked with a dashed oval plays a key role in the FM mechanism described in this Letter. (f),(g) Effective Wannier functions (WFs) of orbital ${\gamma }_1$ for Fe1 (in pink and purple) and ${\gamma }_2$ for Fe2 (in blue and yellow). The robust overlap between these two WFs, related to the amplitude of hoppings $t_{12}$, are indicated by the dashed red ovals.

Figure 3

Sketches of unperturbed and excited states for diagonal and off-diagonal hoppings. Both (a) FM and (b) AFM cases are considered. For the FM case, the diagonal hopping is forbidden (red ovals) due to the Pauli exclusion principle.

Figure 4

dmrg phase diagram of the three-orbital Hubbard model varying $U/W$ and $J_H/U$, using an $L=16$ chain. Different phases are indicated, with the conventions metal (M), Hund metal (HM), orbital-selective Mott phase (OSMP), Mott insulator (MI), paramagnetic (PM), AFM, and FM phases. Small circles indicate specific values of data points that were investigated with dmrg. The phase boundaries should only be considered crude approximations because a mixture of competing states as well as incommensurate phases were detected near those boundaries. However, the existence of the four phases shown was clearly established, even if the boundaries are only crude estimations.

Figure 5

(a) Orbital-resolved occupation number $n_{\gamma }$, mean value of the total spin squared $⟨{\mathbf{S}}^2⟩$ (in maroon color) and (b) charge fluctuations vs $U/W$ at $J_H/U=1/4$. Inset: spin structure factor for $U/W=2$ and 10. Similarly, as in Fig. 4, at the boundaries phase competition renders some results slightly inaccurate. For example, the first two black points in (a) from the left in the OSMP regime are not exactly 1. Yet because their state is FM, we believe they are part of the OSMP FM rather than a new phase.