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First-principles calculations based on density functional theory (DFT) solve the forward problem of predicting properties from a given crystal structure and composition. Designing materials with given properties is the corresponding inverse problem. Data-driven approaches such as surrogate-model optimization and generative models have been actively applied to this inverse problem, but they involve training-data costs, unreliable extrapolation, and components outside the first-principles framework. Gradient-based optimization of the elemental composition avoids these issues by directly exploring the optimization parameter space. In most first-principles calculations, however, composition enters through discrete choices of atomic species, precluding the direct application of gradient methods. Moreover, computing gradients by finite differences requires a separate first-principles calculation for each composition variable and becomes impractical in high dimensions.

The Korringa-Kohn-Rostoker method combined with the coherent potential approximation (KKR-CPA) [1] is a first-principles DFT approach that treats composition as a continuous variable, enabling gradient-based composition search. Reverse-mode automatic differentiation (AD) computes gradients at a cost independent of the number of optimization parameters, making gradient-based search feasible in high dimensions [2]. In this talk, I introduce a gradient-based materials-design framework combining KKR-CPA and reverse-mode AD [3]. Applications to several magnetic materials are presented, including the rediscovery of the peak of the Slater-Pauling curve, the automatic discovery of new magnetic compounds, and the design of a half-metal via density-of-states optimization.

[1] H. Akai, J. Phys.: Condens. Matter 1, 8045 (1989).

[2] K. Inui and Y. Motome, Commun. Phys. 6, 37 (2023).

[3] K. Ishii, H. Akai, T. Fukushima, H. Shinya, and K. Inui, in preparation.

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