High-entropy alloys are solid solutions of multiple principal elements that are capable of reaching composition and property regimes inaccessible for dilute materials. Discovering those with valuable properties, however, too often relies on serendipity, because thermodynamic alloy design rules alone often fail in high-dimensional composition spaces. We propose an active learning strategy to accelerate the design of high-entropy Invar alloys in a practically infinite compositional space based on very sparse data. Our approach works as a closed-loop, integrating machine learning with density-functional theory, thermodynamic calculations, and experiments. After processing and characterizing 17 new alloys out of millions of possible compositions, we identified two high-entropy Invar alloys with extremely low thermal expansion coefficients around 2 × 10 ⁻⁶ per degree kelvin at 300 kelvin. We believe this to be a suitable pathway for the fast and automated discovery of high-entropy alloys with optimal thermal, magnetic, and electrical properties.

Based on first-principles calculations, we predict that 5d transition metals on graphene present a unique class of hybrid systems exhibiting topological transport effects that can be manipulated effectively by external electric fields. The origin of this phenomenon lies in the exceptional magnetic properties and the large spin-orbit interaction of the 5d metals leading to significant magnetic moments accompanied with colossal magnetocrystalline anisotropy energies. A strong magnetoelectric response is predicted that offers the possibility to switch the spontaneous magnetization direction by moderate electric fields, enabling an electrically tunable quantum anomalous Hall effect.

Autonomous materials discovery with desired properties is one of the ultimate goals for materials science, and the current studies have been focusing mostly on high-throughput screening based on density functional theory calculations and forward modeling of physical properties using machine learning. Applying the deep learning techniques, we have developed a generative model, which can predict distinct stable crystal structures by optimizing the formation energy in the latent space. It is demonstrated that the optimization of physical properties can be integrated into the generative model as on-top screening or backward propagator, both with their own advantages. Applying the generative models on the binary Bi-Se system reveals that distinct crystal structures can be obtained covering the whole composition range, and the phases on the convex hull can be reproduced after the generated structures are fully relaxed to the equilibrium. The method can be extended to multicomponent systems for multi-objective optimization, which paves the way to achieve the inverse design of materials with optimal properties.

Using ab initio methods for correlated electrons in solids, we investigate the metal-insulator transition across the Ruddlesden-Popper (RP) series of iridates and explore the robustness of the ${J}_{\mathrm{eff}}=1/2$ state against band effects due to itineracy, tetragonal distortion, octahedral rotation, and Coulomb interaction. We predict the effects of epitaxial strain on the optical conductivity, magnetic moments, and ${J}_{\mathrm{eff}}=1/2$ ground-state wave functions in the RP series. To describe the solution of the many-body problem in an intuitive picture, we introduce a concept of energy-dependent atomic states, which strongly resemble the atomic ${J}_{\mathrm{eff}}=1/2$ states but with coefficients that are energy or time dependent. We demonstrate that the deviation from the ideal ${J}_{\mathrm{eff}}=1/2$ state is negligible at short time scales for both single- and double-layer iridates, while it becomes quite significant for ${\mathrm{Sr}}_{3}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7}$ at long times and low energy. Interestingly, ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ is positioned very close to the $SU(2)$ limit, with only $$\sim${}3%$ deviation from the ideal ${J}_{\mathrm{eff}}=1/2$ situation.

We address the importance of the modern theory of orbital magnetization for spintronics. Based on an all-electron first-principles approach, we demonstrate that the predictive power of the routinely employed “atom-centered” approximation is limited to materials like elemental bulk ferromagnets, while the application of the modern theory of orbital magnetization is crucial in chemically or structurally inhomogeneous systems such as magnetic thin films, and materials exhibiting nontrivial topology in reciprocal and real space, e.g., Chern insulators or noncollinear systems. We find that the modern theory is particularly crucial for describing magnetism in a class of materials that we suggest here—topological orbital ferromagnets.

By combining first-principles calculations with Wannier-based tight-binding modeling, we demonstrate that a ${\text{TiO}}_2/{\text{VO}}_2$ heterostructure that was previously proposed as a prototypical semi-Dirac system becomes a Chern insulator (quantum anomalous Hall insulator) in the presence of spin-orbit coupling. We show that this occurs only when the semi-Dirac structure is of a special type that can be formed by the merging of three conventional Dirac points. Our results reveal how the nontrivial topology with a nonzero Chern number emerges naturally from this kind of semi-Dirac structure, establishing a general scenario that provides a different route to the formation of Chern-insulating states in practical materials systems.