Magnetic coupling parameters at an oxide-oxide interface from first principles: ${\text{Fe}}_2{\text{O}}_3{\text{-FeTiO}}_3$

Charge mismatch at the interface between canted antiferromagnetic hematite $\left(\alpha {\text{-Fe}}_2{\text{O}}_3\right)$ and antiferromagnetic ilmenite $\left({\text{FeTiO}}_3\right)$ is accommodated by the formation of mixed ${\text{Fe}}^{2+}$ and ${\text{Fe}}^{3+}$ contact layers, leading to uncompensated magnetic moments in the system. To derive the magnetic exchange interaction parameters of the end members and interface, we map total-energy differences of collinear spin arrangements obtained from density-functional theory calculations to a Heisenberg Hamiltonian using the least-squares method. Parameters for the end members, hematite $\left(J_m^{3+,3+}\right)$ and ilmenite $\left(J_m^{2+,2+}\right)$ are in good agreement with the values obtained from inelastic neutron-scattering data. The magnetic interaction parameters between ${\text{Fe}}^{2+}$ and ${\text{Fe}}^{3+}$ $\left(J_m^{2+,3+}\right)$ in the contact layer show a strong antiferromagnetic coupling to the adjacent hematite layers and thus explain the ferrimagnetism in the system.

Figure 1

(Color online) Side view of the corundum structure showing only the cation positions with alternating cationic layers denoted by light and dark atoms. Additionally, the pair magnetic exchange parameters $J_1$ to $J_8$ between the cations are defined.

Figure 2

(Color online) The magnetic pair interaction parameters $\left[J_m^q\left(K\right)\right]$ up to eighth neighbor are shown in (a) for hematite $\left(J_m^{3+,3+}\right)$, (b) for ilmenite $\left(J_m^{2+,2+}\right)$, and (c) for the interface $\left(J_m^{2+,3+}\right)$. Results for $U=6$ and 8 eV are marked by filled and open squares, respectively. The experimental values for hematite (open red/gray circle) are taken from Ref. 13 and for ilmenite (open red/gray circles and stars) are taken from Refs. 15, 16. The parameters for the interface in panel (c) are calculated for the configuration shown in Fig. 3b.

Figure 3

(Color online) Side view of the configurations with 60 atoms in the unit cell chosen for the calculations of interface magnetic interaction parameters: (a) represents an ilmenite block (three ${\text{Ti}}^{4+}$ layers separated by ${\text{Fe}}^{2+}$ layers) within a hematite host and (b) contains additionally mixed Fe-Ti layers in the hematite part. The red, gray, and black spheres are showing Fe, Ti, and oxygen atoms, respectively. The positions of ${\text{Fe}}^{2+}$ are marked with pink/gray circles and the rest of the iron are ${\text{Fe}}^{3+}$.