Insulating Ferromagnetic ${\mathrm{LaCoO}}_{3-\delta }$ Films: A Phase Induced by Ordering of Oxygen Vacancies

The origin of ferromagnetism in strained epitaxial ${\mathrm{LaCoO}}_3$ films has been a long-standing mystery. Here, we combine atomically resolved $Z$-contrast imaging, electron-energy-loss spectroscopy, and density-functional calculations to demonstrate that, in epitaxial ${\mathrm{LaCoO}}_3$ films, oxygen-vacancy superstructures release strain, control the film’s electronic properties, and produce the observed ferromagnetism via the excess electrons in the Co $d$ states. Although oxygen vacancies typically dope a material $n$-type, we find that ordered vacancies induce Peierls-like minigaps which, combined with strain relaxation, trigger a nonlinear rupture of the energy bands, resulting in insulating behavior.

Figure 1

(a) High resolution, high angle annular dark field (HAADF) image of a LCO thin film 15 nm thick, grown on a (001) oriented STO substrate, showing the contrast resulting from the O-vacancy ordering. The direction of the modulation vector, $q$, is marked with an arrow. (b) Map of the in-plane distance between first La neighbors ($\Delta x$) in (a), along the direction parallel to q. O-deficient planes are characterized by enlarged La-La distances. (c) Histogram of $\Delta x$ values across the image. Three peaks are clearly observed: the one corresponding to the lattice parameter of the STO substrate (black arrow), the one from the LCO fully stoichiometric planes (red arrow), and the lattice distance corresponding to the O-deficient ${\mathrm{CoO}}_x$ planes (blue arrow). Inset: 2D projection of the structure along the [011] direction ([100] in the pseudocubic setting), marking oxygen-deficient (shaded blue) and stoichiometric (red) planes. Blue, red, and green spheres are Co, O, and La atoms, respectively.

Figure 2

Top: high resolution $Z$-contrast image of the LCO film showing an average modulation length of three perovskite blocks. The inset shows the Co $L_3/L_2$ intensity ratio map for a spectrum image acquired in the area marked with a green rectangle. A schematic shows the pseudocubic unit cell ($\text{blue}=\mathrm{Co}$; $\text{green}=\mathrm{La}$; $\text{red}=\mathrm{O}$). Bottom left: elemental chemical maps constructed by integrating the corresponding EEL spectra: O $K$ edge (red), Co $L_3$ edge (blue), and La $M_5$ edge (green). Bottom right: normalized intensity across the O $K$, Co $L_3$, and the La $M_5$ images on the left, vertically averaged across the whole images. Fully stoichiometric ${\mathrm{CoO}}_2$ planes are indicated with red dashed lines in the background (through all three profiles), and O-deficient ${\mathrm{CoO}}_x$ planes are marked with blue dashed lines. The O intensity decreases on the latter planes as a result of the lower O content, which makes the La atoms move further apart from each other, giving rise to the dark stripes in the $Z$-contrast images.

Figure 3

EELS fine structures across the O-vacancy superlattice. (a) $L_3/L_2$ intensity ratio for an EELS line scan across the stripes, calculated by using a Hartree-Slater cross-section step function [27] (dark blue points), after deconvolution with the zero loss to remove multiple scattering, and also using the second derivative method [32] (cyan dots, same vertical scale). The top HAADF image in a matching scale shows the area where the line scan was acquired. Blue arrows mark the position of the O-deficient planes. (b) Theoretical O $K$ absorption edge along with experimental O $K$ and Co $L_{2,3}$ edges [averaged from the line scan in (a)] for the fully oxygenated ${\mathrm{CoO}}_2$ planes (red) and the O-deficient planes (blue).

Figure 4

The 3D model of the structure, and oxidation and spin states. Oxygen ions (red spheres) form distorted tetrahedra (blue) around Co ions (dark blue spheres) in vacancy-rich planes and bulklike octahedra (red) around Co atoms in fully oxygenized planes. Large green arrows indicate a high spin state and its relative direction (up or down). (b) Calculated density of states projected over different Co ions: high spin ${\mathrm{Co}}^{2+}$ in tetrahedral environment (top); high spin ${\mathrm{Co}}^{2+}$ in octahedral environment (middle); low spin ${\mathrm{Co}}^{3+}$ in a similar octahedral environment (bottom). Calculation details are in the Supplemental Material [28] (see also Refs. [40, 41, 42, 43]).

Figure 5

Origin of the energy gap. (a) Peierls mechanism. In a metallic 1D undistorted system (left), a distortion with a periodicity equal to half the Fermi wavelength ($\lambda =\pi /k_F$) opens a gap, marked by the arrow (right). (b) Atomic structure of ${\mathrm{LaCoO}}_{3-\delta }$ thin films on ${\mathrm{SrTiO}}_3$ substrates. ${\lambda }_{1,2}$ indicate periodicities induced by the O-vacancy ordering. (c),(d) Band diagram of the majority spin states, projected into the ${\mathrm{LaCoO}}_3$, reduced Brillouin zone: ferromagnetic undistorted material (c) and magnetic and structurally relaxed system (d). Colors indicate orbital character: $s$ and $p$ (light brown), $t_{2g}$ (red), $e_g$ (green), and $f$ (blue). Arrows mark Peierls-like gaps.