Strain-induced majority carrier inversion in ferromagnetic epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ thin films

Tensile-strained $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ thin films are ferromagnetic, in sharp contrast to the zero-spin bulk, although no clear consensus has emerged as to the origin of this phenomenon. While magnetism has been heavily studied, relatively little attention has been paid to electronic transport, due to the insulating nature of the strain-stabilized ferromagnetic state. Here, structure, magnetism, and transport are studied in epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films (10–22-nm thick) on various substrates (from 1.4% compressive to 2.5% tensile strain), using synchrotron x-ray diffraction, scanning probe and transmission electron microscopy, magnetometry, polarized neutron reflectometry, resistivity, and Hall effect. High quality, smooth films are obtained, exhibiting superstructures associated with both oxygen vacancy ordering and periodic in-plane ferroelastic domains. Consistent with prior work, ferromagnetism with an approximately 80–85 K Curie temperature is observed under tension; polarized neutron reflectometry confirms a relatively uniform magnetization depth profile, albeit with interfacial dead layer formation. Electrical transport is found to have similar semiconducting nature to bulk, but with reduced resistivity and activation energy. Hall effect measurements, however, reveal a striking inversion of the majority carrier type, from $p$-type in the bulk and under compression to n-type under tension. While thus far overlooked, ferromagnetism in epitaxial $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films is thus directly correlated with $n$-type behavior, providing important insight into the ferromagnetic state in this system. Aided by density functional theory calculations, these results are interpreted in terms of tensile-strain-induced orbital occupation and band structure changes, including a rapid decrease in effective mass at the $e_g$-derived conduction band minimum, and corresponding increase at the valence band maximum.

Figure 1

Specular synchrotron x-ray diffraction scans around the film 002 reflections of 190-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ (LCO) films on (a) SLAO, (b) LAO, (c) LSAT, and (d) STO substrates. In-plane strains $\left({\varepsilon }_{xx}\right)$ are labeled. (e)–(h) Corresponding synchrotron x-ray reciprocal space maps around the asymmetric $\overline{1}03$ film reflections ($\overline{1}011$ for SLAO) for the same films shown in (a)–(d). “r.l.u.” is used for (substrate) reciprocal lattice units.

Figure 2

(a) Out-of-plane strain $\left({\varepsilon }_{zz}\right)$ vs in-plane strain $\left({\varepsilon }_{xx}\right)$ for 130-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films, assuming various values [35, 36, 52] for the bulk pseudocubic lattice parameter ($a_{\mathrm{pc}}$). The dashed lines are straight-line fits with unity slope, corresponding to Poisson ratio 1/3. (b) Contact mode atomic force microscopy image (2.5×2.5 μm) of a 220-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ film on LAO, showing the extracted RMS roughness. HAADF-STEM images of 100-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films on (c) LAO and (d) LSAT. Yellow horizontal or vertical lines highlight the oxygen vacancy ordering orientation.

Figure 3

(a) Temperature ($T$) dependence of magnetization ($M$) of 150-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films on various substrates at 1 kOe $(8\times {10}^4\mathrm{A}{\mathrm{m}}^{-1})$ in-plane measuring and cooling field. (b) $M$ vs in-plane magnetic field ($H$) at 5 K for $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films on LSAT and STO. For reference, $1\mathrm{Oe}=79.58\mathrm{A}{\mathrm{m}}^{-1}$.

Figure 4

Neutron reflectivity ($R$, top panel) and spin asymmetry (SA, bottom panel) vs scattering vector ($Q$) at 5 K in a 30 kOe $(2.4\times {10}^6\mathrm{A}{\mathrm{m}}^{-1})$ in-plane magnetic field for (a), (b) a 200-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ film on STO, and (d), (e) a 140-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ film on LSAT. In (a) and (d), black and red points are nonspin-flip $R$ values ($R^{--}$ and $R^{++}$), respectively. The solid lines are fits to the model discussed in the text, with parameters shown in Table 1. (c), (f) Corresponding nuclear scattering length density $\left(\mathrm{SL}{\mathrm{D}}_{\mathrm{nuc}}\right)$, magnetic scattering length density $\left(\mathrm{SL}{\mathrm{D}}_{\mathrm{mag}}\right)$, and magnetization ($M$) vs depth ($z$). Unless otherwise noted, all uncertainties and error bars represent ±1 standard deviation.

Figure 5

(a) Temperature ($T$) dependence of zero magnetic field resistivity (ρ, on a $\mathrm{lo}{\mathrm{g}}_{10}$ scale) for 130-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films on various substrates. (b) Corresponding $\mathrm{lo}{\mathrm{g}}_{10}\left(\rho \right)$ vs $1/T$ plot, along with low $T$ straight-line fits yielding the activation energies shown. Bulk polycrystalline data are shown for comparison [20].

Figure 6

Magnetic field ($H$) dependence of the 225 K Hall resistivity $\left({\rho }_{xy}\right)$ of 130-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films under (a) compressive strain on SLAO and LAO, and (b) tensile strain on LSAT and STO. As is typical, a zero field background has been subtracted.

Figure 7

(a) Hall electron or hole density (${log}_{10}$ scale, solid symbols for electrons, open symbols for holes) vs inverse temperature ($T$) for 130-Å-thick $\mathrm{LaCo}{\mathrm{O}}_{3-\delta }$ films on various substrates. Solid lines are straight line (Arrhenius) fits. (b) Corresponding Hall mobility (μ, $\mathrm{lo}{\mathrm{g}}_{10}$ scale) vs $T$.

Figure 8

Density functional theory electronic band structure for $\mathrm{LaCo}{\mathrm{O}}_3$ films under (a) 1.5% compressive strain and (b) 2.5% tensile strain. (c) Electron and hole (black and red symbols) effective masses ($m^{*}/m_e$, where $m_e$ is the free electron mass, computed along the Γ-$X$ direction) vs in-plane strain $\left({\varepsilon }_{xx}\right)$. (d) Energy Splitting between the cobalt $e_g$-like Wannier orbitals $(\mathrm{\Delta }E=E_{z^2}–E_{x^2-y^2})$ vs biaxial strain $\left({\varepsilon }_{xx}\right)$. The two insets show the $d_{x^2-y^2}$ (top left) and $d_{z^2}$ (bottom right) Wannier orbitals.