Spin-orbit coupling is a fundamental and complex relativistic effect that plays a crucial role in a wide range of experimental phenomena, including magnetic anisotropy, phosphorescence, and spin-orbit torque. This effect is important in various active research areas, such as spintronics, low-dimensional materials, topological insulators, materials for quantum computing. The utilization of pseudopotential DFT has been shown to be effective in predicting various material properties when extended to account for non-collinear magnetism and spin-orbit coupling. To this end, we have derived a real-space formulation for non-collinear magnetism with spin-orbit coupling using ONCV (Optimised Norm Conserving Vanderbilt) pseudopotentials and developed an efficient, scalable finite-element-based methodology, tailored for both multinode CPU and GPU architectures. The proposed method utilizes the FE cell-matrix approach to evaluate the matrix multi-vector products encountered during the iterative solution of the Kohn-Sham eigenproblem to increase the arithmetic intensity of the underlying computations. We further intend to develop hardware-aware strategies to accelerate further the underlying iterative eigensolver used to solve the FE discretized Kohn-Sham eigenproblem by employing a matrix-free approach to compute these matrix multi-vector products. Furthermore, we aim to derive and implement a generalized force approach for evaluating atomic forces and unit-cell stresses in a unified computational framework for geometry optimization involving non-collinear magnetism with spin-orbit coupling.
References
2024
Under Review
Finite-element methods for noncollinear magnetism and spin-orbit coupling in real-space pseudopotential density functional theory
We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the open-source DFT-FE computational framework, fills a significant gap in real-space DFT calculations using finite element basis sets, which offer several advantages over traditional DFT basis sets. In particular, we leverage the local reformulation of DFT electrostatics to derive the finite-element (FE) discretized governing equations involving two-component spinors. We subsequently utilize an efficient self-consistent field iteration approach based on Chebyshev filtered subspace iteration procedure exploiting the sparsity of local and non-local parts of FE discretized Hamiltonian to solve the underlying nonlinear eigenvalue problem based on a two-grid strategy. Furthermore, we propose using a generalized functional within the framework of noncollinear magnetism and spin-orbit coupling with a stationary point at the minima of the Kohn-Sham DFT energy functional to develop a unified framework for computing atomic forces and periodic unit-cell stresses. Validation studies against plane-wave implementations show excellent agreement in ground-state energetics, vertical ionization potentials, magnetic anisotropy energies, band structures, and spin textures. The proposed method achieves up to 8x-11x speed-ups for semi-periodic and non-periodic systems with ~5000-7000 electrons in terms of minimum wall times compared to widely used plane-wave implementations on CPUs in addition to exhibiting significant computational advantage on GPUs.
@misc{kodali2024finiteelementmethodsnoncollinearmagnetism,title={Finite-element methods for noncollinear magnetism and spin-orbit coupling in real-space pseudopotential density functional theory},author={Kodali, Nikhil and Motamarri, Phani},url={https://arxiv.org/abs/2410.02754},doi={10.48550/arXiv.2410.02754},language={en},year={2024},month=oct,eprint={2410.02754},dimensions={true},ownpub={true}}