Scalable higher-order finite-element-based methods for non-collinear magnetism and spin-orbit coupling in real-space density functional theory*

We introduce a systematically convergent and scalable higher-order finite-element-based real-space methodology for first-principles calculations of non-collinear magnetic phenomena and spin-orbit coupling effects within pseudopotential Kohn-Sham Density Functional Theory (KS-DFT). Our proposed methodology is compatible with semi-local GGA functionals and utilizes Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials, and accommodates generic boundary conditions, enabling its application to non-periodic, semi-periodic, and fully-periodic systems. Furthermore, we present a generalized configurational force approach for computing atomic forces and periodic cell stresses within the above framework. We subsequently demonstrate the precision and performance of our methodology across diverse benchmark systems involving up to tens of thousands of electrons on multi-node CPU and GPU architectures. Our proposed approach has been integrated into DFT-FE, a massively parallel finite-element-based DFT code.