Understanding the metal-to-insulator transition in La_1−xSr_xCoO_3−δ and its applications for neuromorphic computing

The search for computing architectures with low-power consumption is an active field of research, and neuromorphic architectures, which aspire to mimic the human brain, have attracted much attention lately. The realization of neuromorphic devices imposes specific requirements on the materials to be used: the response to an input signal should be dependent on the signal’s intensity, frequency and the previous status of the material, in a way similar to neurons and synapses in the brain, which combine computation and memory in one unit. In addition, the energy consumption to transmit and process signals should be extremely low to be affordable on a large scale; remarkably there are ~10^11 neurons and ~10^14 synapses in the brain, with a power consumption of ~10W for daily cognitive tasks. In the last decades, several transition metal oxides (TMO) have been proposed as promising resistive switching materials, i.e. systems showing tunable resistance states, induced by an external electrical bias. These TMO exhibit a metal-to-insulator transition (MIT) as a function of pressure, temperature, or doping, which may be designed to mimic the behavior of neurons and synapses in the presence of stimuli. One of such TMO is La1−xSrxCoO3−δ (LSCO), for which a resistivity change on the order of 10^4 was shown with increasing pressure for x < 0.5. This MIT process is tunable by dopants, e.g. Sr, with a change in resistivity of ~10^5 for x between 0 and 0.8. Recently, an experimental study suggested to control the MIT by tuning the oxygen vacancy concentration in LSCO, and a topotactic transition was realized from a paramagnetic metallic perovskite (δ≈0) to an antiferromagnetic (AFM) semiconducting brownmillerite (BM) structure (δ = 0.5). A similar transition was also observed between SrCoO3 and SrCoO2.5 and oxygen vacancy concentrations have been varied in multiple ways in cobaltites, e.g. by depositing oxygen-scavenging metals, annealing in reducing environment, using electric fields and with epitaxial strain. In spite of extensive work, the mechanisms underlying the MIT in cobaltites remain elusive, thus hampering the control of the properties of these materials to design efficient neuromorphic devices. Here we report an investigation of the MIT in LSCO (and the semiconductor-to-insulator transition in LCO) using first principles calculations; we unravel the complex interplay between structural, electronic, and magnetic properties of the material as the transition is driven from a perovskite to a BM phase, as a function of oxygen vacancies. Our calculations show that cooperative, global structural distortions leading to a decrease of the elastic energy of the solid, which in turn are accompanied by changes in the magnetic state of the material, are the main factors driving the MIT. Our results allow for the identification of general descriptors to design materials for neuromorphic computing applications, including multiple resistive states. Finally, we present a model based on first principles to predict the electric bias necessary to drive the MIT, which shows good agreement with experiment, and is general and applicable to broad classes of TMO.

- Prior studies have shown MITs in La1−xSrxCoO3 as a function of pressure (resistivity change ~10^4 for x < 0.5) and Sr doping (resistivity change ~10^5 for 0 ≤ x ≤ 0.8). - Experiments demonstrated control of MIT via oxygen vacancy concentration, with a topotactic transition from metallic perovskite (δ≈0) to AFM semiconducting brownmillerite (δ=0.5). Similar behavior observed in SrCoO3/SrCoO2.5. - Oxygen vacancy concentrations in cobaltites can be tuned by oxygen-scavenging metals, reducing anneals, electric fields (ion-gel gating), and epitaxial strain. - In situ TEM and diffraction studies reported layer-by-layer nucleation of oxygen vacancies in LCO and related perovskites. - Previous theoretical/experimental works reported vacancy-induced changes in magnetic order and spin states in cobaltites and related perovskites; correlations between Jahn-Teller distortions and magnetic/conductive states have been discussed in earlier literature. These works motivate a microscopic, first-principles understanding of how structural, magnetic, and electronic changes with vacancy concentration drive the MIT relevant to neuromorphic device operation.

- Electronic structure: Density Functional Theory (DFT) with PBE generalized gradient approximation plus Hubbard U (DFT+U). Tested LDA, PBE, SCAN functionals and U from 3–7 eV; chose PBE+U with U=3 eV as optimal to reproduce structural, electronic, and magnetic properties of perovskite LaCoO3 (LCO) and brownmillerite SrCoO2.5. - Supercell/modeling: √2 × 4 × √2 perovskite supercell (La(Sr)Co8O24, 40 atoms), four octahedral layers. Considered oxygen vacancy concentrations V_O = 4.2%, 8.3%, 12.5%, 16.7% (δ where V_O = δ/3 × 100%), sampling symmetry-inequivalent vacancy configurations (2 at 4.2%, 12 at 8.3%, 1 at 12.5%). - Magnetism: Explored multiple magnetic states at each V_O, including ferromagnetic (FM) and antiferromagnetic (G-AFM, A-AFM, C-AFM), as well as non-magnetic constraints for comparison; analyzed local/FM-AFM mixed states near vacancies. - Structural optimization: Orthorhombic symmetry; plane-wave cutoff 90 Ry; 6×3×6 Monkhorst-Pack k-point grid; PAW pseudopotentials (PSlibrary). Sampled symmetry-inequivalent Sr A-site positions; assessed variability of lattice parameters and magnetic moments with Sr distribution. - Lattice dynamics and coupling model: Performed phonon calculations (DFPT in Quantum ESPRESSO) to obtain vibrational frequencies and estimate stiffness parameters for Jahn-Teller (JT), breathing, and rotation modes. Built a harmonic Hamiltonian H = Σ α_T T_r^2 + Σ α_D D_r^2 + Σ α_R R_r^2 with constraints (corner-sharing octahedra, maintained parallelogram) to include cooperative coupling between JT/breathing and rotations; analyzed stiffness in momentum space versus rotation angle Φ_0. - Electronic structure analysis: Total and projected DOS (O 2p; Co 3d separated by coordination: octahedral, pyramidal, tetrahedral; spin-resolved). Born effective charges and dielectric constants; Berry-phase polarization P^polar. - Vacancy thermodynamics and bias estimation: Computed oxygen vacancy free energy of formation F_vac including vibrational contributions from phonons. Determined electrochemical potential η such that F_vac/n = 0 at spontaneous formation; estimated required applied electric field E_0 via E_0 = E + (2ε_∞ − 1) E_∞ P^polar / (2 ε_0 ε_∞), where E = η/d along lattice directions; averaged voltages over axes; compared LCO and LSCO. Considered vacancy migration enthalpy from literature/DFT+U (~0.7 eV) for diffusion context.

- Structural pathway and cooperativity: - Vacancies order within layers and transform CoO6 octahedra to CoO5 pyramids and then CoO4 tetrahedra within a layer; transformation proceeds in alternating layers, yielding the brownmillerite (BM) phase. - Lattice expands with increasing V_O; Co–O–Co tilt angle decreases substantially with V_O (rotation distortion). Sr doping attenuates expansion and rotations due to increased Co oxidation state and reduced JT distortion. - Cooperative coupling: Rotations (low stiffness) reduce the elastic cost of JT/breathing distortions (high stiffness ~10^4 meV Å^-2), enabling a cooperative structural response that stabilizes the BM structure. Increasing rotation angle Φ_0 lowers JT/breathing stiffness, more in BM than perovskite. - Magnetic transitions: - With increasing V_O, LCO evolves from non-magnetic to FM-local AFM to AFM; LSCO evolves from FM to FM-local AFM to AFM. - Spin polarization and near-180° Co–O–Co superexchange favor AFM ordering with reduced Co–O hybridization and longer Co–O bonds. Constraining to non-magnetic suppresses lattice expansion and rotations, demonstrating magnetism-structure interdependence. - Electronic transition (MIT): - Band gap opens in concert with FM-to-AFM transition; in LSCO the gap opens at higher V_O than in LCO. Gap first appears between states in oxygen-deficient layers; with increasing V_O, localization and correlation increase at both oxygen-deficient and neighboring octahedral Co sites. - Band-edge contributions evolve from octahedral Co e_g (majority) at V_O ≤ 8.3% to pyramidal Co e_g (majority) at 12.5%, and to minority-spin Co at 16.7%, reflecting configurational and valence changes. - Non-magnetic constraint closes the gap; FM retains a smaller gap than AFM—highlighting the crucial role of spin order and rotations (not volume expansion alone) for gap opening. - Energetics and kinetics: - Lowest-energy structural transition pathway is ~0.8 eV per vacancy lower than metastable pathways. - Vacancy formation free energy per vacancy F_vac/n peaks leading to η ≈ 0.6 V (LCO) and 0.4 V (LSCO); Sr doping lowers F_vac/n by ~0.4–0.5 eV. - Vacancy migration enthalpy in LCO ~0.7 eV, implying formation, not diffusion, dominates the energetic cost. - Device-relevant bias estimates: - Estimated applied voltage to trigger phase transition (averaged over axes): ~1.2 V for LCO (at ~8.3% V_O) and ~0.8 V for LSCO (at ~12.5% V_O, approximate due to polarization assumption). Near-threshold partial transitions would require ~0.14 V less in LCO; Sr=37.5% lowers the upper bound by ~0.4 V. In SCO the transition may require ~30 mV. - Distinction from nickelates: Unlike defective nickelates where local electronic changes suffice, in cobaltites cooperative structural distortions and magnetic transitions are essential for the MIT.

The study addresses the central question of what microscopic mechanisms drive the oxygen-vacancy–induced MIT in La1−xSrxCoO3−δ relevant to neuromorphic devices. The results demonstrate that cooperative structural distortions—especially rotations of Co–O units—coupled to Jahn-Teller/breathing distortions and concurrent magnetic transitions are requisite for band-gap opening. The MIT is not governed by purely local bonding changes at vacancy sites but by global, layer-by-layer structural transformations that reduce elastic energy and modify crystal-field environments and correlation. This intertwined structural–magnetic–electronic response explains experimental observations: lattice expansion, resistivity increase with V_O, and magnetic moment reduction. The findings are significant for neuromorphic computing: vacancy concentration can tune the band gap and thus multiple resistive states; Sr doping reduces the energetic cost, enabling lower-bias operation. The first-principles-informed electrochemical model predicts applied biases in line with experiments, offering design rules for low-energy devices. The identification of cooperative rotations as a key enabler suggests experimental probes (X-ray, TEM) focused on octahedral tilts and layer-specific vacancy ordering, and engineering strategies using strain, interfaces, and A-site composition to tailor rotation magnitudes and magnetic order. The mechanism contrasts with nickelates, underscoring material-specific pathways to programmable resistive behavior.

This work provides a microscopic, first-principles characterization of the oxygen-vacancy–driven transition from perovskite to brownmillerite in LaCoO3 and La1−xSrxCoO3, revealing that cooperative structural distortions (rotations coupled to JT/breathing) and concomitant magnetic transitions are essential for the MIT and resistive-state formation. The study maps the structural pathway, quantifies the role of magnetism in enabling gap opening, and shows that gap magnitude and localization evolve with coordination changes (octahedral → pyramidal → tetrahedral) as vacancies increase. A general electrochemical model grounded in computed vacancy formation free energies and dielectric/polarization properties estimates operating voltages (~0.8–1.2 V; even lower with higher Sr or partial transitions), in agreement with experimental trends, and provides a framework to design low-energy neuromorphic devices. Future research directions include: experimental validation of predicted cooperative rotations and layer-resolved vacancy ordering; optical spectroscopy to quantify band-gap evolution; systematic strain/interface engineering to control rotations and magnetic order; exploration of broader TMO families using the same modeling framework; and dynamic studies of vacancy creation/annihilation to optimize switching speed and endurance.

- Approximate parameters: The estimated LSCO voltage at 12.5% V_O assumes polarization values similar to LCO, introducing uncertainty in the applied-bias prediction. - Experimental validation gaps: Direct measurements of Co–O–Co tilt angles during vacancy-driven transitions are lacking; current validation relies on indirect structural metrics (e.g., La(Sr)–La spacing) and qualitative agreement with volume expansion. - DFT+U sensitivity: Although PBE+U (U=3 eV) was benchmarked, results may show quantitative dependence on functional/U choice for correlated Co 3d states. - Sr-distribution effects: While computed lattice/magnetic variability with Sr-site configurations is small, real films may exhibit inhomogeneities and segregation that could locally affect pathways. - Constrained-state analyses: Non-magnetic and FM constraints used to dissect mechanisms are not ground states and serve as comparative probes; quantitative values under these constraints may not be realized experimentally.