Confinement-driven electronic and topological phases in corundum-derived $3d$-oxide honeycomb lattices

Using density functional theory calculations including an on-site Coulomb term, we explore electronic and possibly topologically nontrivial phases in $3d$ transition-metal oxide honeycomb layers confined in the corundum structure ($\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$) along the [0001] direction. In most cases the ground state is a trivial antiferromagnetic Mott insulator, often with distinct orbital or spin states compared to the bulk phases. With imposed symmetry of the two sublattices the ferromagnetic phases of ($X_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) with $X=$ Ti, Mn, Co, and Ni exhibit a characteristic set of four bands, two that are relatively flat and two with a Dirac crossing at $K$, associated with the single-electron occupation of $e_g^{\prime }$ (Ti) or $e_g$ (Mn, Co, Ni) orbitals. Our results indicate that the Dirac point can be tuned to the Fermi level using strain. Applying spin-orbit coupling (SOC) leads to a substantial anomalous Hall conductivity with values up to 0.94 $e^2/h$. Moreover, at $a_{{\mathrm{Al}}_2{\mathrm{O}}_3}=4.81$ Å we identify a particularly strong effect of SOC with an out-of-plane easy axis for (${\mathrm{Ti}}_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) which stabilizes the system dynamically. Due to the unusually high orbital moment of $-0.88{\mu }_{\mathrm{B}}$ that nearly compensates the spin moment of $1.01{\mu }_{\mathrm{B}}$, this system emerges as a candidate for the realization of the topological Haldane model of spinless fermions. Parallels to the perovskite analogs ($\mathrm{La}X{\mathrm{O}}_3$)${}_2$/(${\mathrm{LaAlO}}_3$)${}_4$(111) are discussed.

Figure 1

(a) Side view of the ($X_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) superlattice where one metal ion bilayer in the corundum structure is exchanged with a $X=3d$ ion. (b) Top view of the buckled honeycomb lattice in the $a\text{−}b$ plane; solid and dashed lines connect the next-nearest TM-ion neighbors residing on the two sublattices.

Figure 2

Band structures and spin-density distributions of ($X_2{\mathrm{O}}_3{)}_1/{\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)}_5\left(0001\right)$, with $X$ = Ti, Mn, Co, Ni, for FM and AFM coupling. The spin density is integrated in the energy range from $-8$ eV to $E_{\mathrm{F}}$, except in (d)–(f) and (j), where the integration interval is $-0.6$ eV to $E_{\mathrm{F}}$. In the band structure blue (orange) denotes majority (minority) bands, and the Fermi level is set to zero. In the isosurfaces of the spin density blue (red) shows the majority (minority) contributions. The energy differences between the metastable and ground states are given in red; also the magnitude of the spin moments of the $X$ ions are displayed in the spin densities.

Figure 3

Band structures and spin-density distributions integrated in the energy range from $-8$ eV and $E_{\mathrm{F}}$ for $X$ = V, Cr and from $-0.6$ eV to $E_{\mathrm{F}}$ for Fe with FM and AFM coupling. The same color coding as in Fig. 2 is used.

Figure 4

Energy difference per u.c. with respect to the symmetric FM state at $a_{{\mathrm{Al}}_2{\mathrm{O}}_3}$. For each value of the lateral strain, the out-of-plane lattice constant was optimized within GGA+$U$. Additionally, the band structure is shown prior to and after the switching of orbital polarization from $e_g^{\prime }$ to $a_{1g}$ at $a=5.11$ Å.

Figure 5

Energy difference per u.c. with respect to (a) the AFM ground state of $X$ = Mn or (c) the symmetric FM state at $a_{{\mathrm{Al}}_2{\mathrm{O}}_3}$ for $X=\mathrm{Co}$. For each value of the lateral strain, the out-of-plane lattice constant was optimized within GGA+$U$. (b) and (d) The respective band structures at the optimum lattice parameters with the DP tuned to $E_{\mathrm{F}}$.

Figure 6

GGA + $U$ + SOC band structures for ($X_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) with $X$ = Ti, Mn, Co, Ni at the optimum lateral lattice constant and with magnetization along the [0001] direction. SOC opens a small gap at the DP at $K$. With the exception of $X$ = Ti and Ni, the $E_{\mathrm{F}}$ is found to be located within the gap, resulting in a topologically nontrivial gapped state.

Figure 7

AHC ${\sigma }_{xy}$ in units of $e^2/h$ as a function of the chemical potential for the corundum bilayers ($X_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) ($X$ = Ti, Mn, Co, Ni).

Figure 8

Side and top views of the Berry curvature distribution ${\mathrm{\Omega }}_z(k_x,k_y)$ for (${\mathrm{Co}}_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) (left) and (${\mathrm{Mn}}_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) (right). Note the opposite signs of ${\mathrm{\Omega }}_z(k_x,k_y)$ for the two cases.

Figure 9

Strong effect of SOC for (${\mathrm{Ti}}_2{\mathrm{O}}_3$)${}_1$/(${\mathrm{Al}}_2{\mathrm{O}}_3$)${}_5$(0001) at $a_{{\mathrm{Al}}_2{\mathrm{O}}_3}$: (a) band structure and (b) AHC plotted vs the chemical potential.