a scalable finite-element framework for ab-initio modelling of Non-Collinear Magnetism and Spin-Orbit Coupling in pseudopotential DFT
collaborators: Dr. Phani Motamarri
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
2018
PhysRevB
Configurational forces in electronic structure calculations using Kohn-Sham density functional theory
We derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of a material point {}textbf{x}\. These configurational forces that result from the inner variations of the Kohn-Sham energy functional provide a unified framework to compute atomic forces as well as stress tensor for geometry optimization. Importantly, owing to the variational nature of the formulation, these configurational forces inherently account for the Pulay corrections. The formulation presented in this work treats both pseudopotential and all-electron calculations in single framework, and employs a local variational real-space formulation of Kohn-Sham DFT expressed in terms of the non-orthogonal wavefunctions that is amenable to reduced-order scaling techniques. We demonstrate the accuracy and performance of the proposed configurational force approach on benchmark all-electron and pseudopotential calculations conducted using higher-order finite-element discretization. To this end, we examine the rates of convergence of the finite-element discretization in the computed forces and stresses for various materials systems, and, further, verify the accuracy from finite-differencing the energy. Wherever applicable, we also compare the forces and stresses with those obtained from Kohn-Sham DFT calculations employing plane-wave basis (pseudopotential calculations) and Gaussian basis (all-electron calculations). Finally, we verify the accuracy of the forces on large materials systems involving a metallic aluminum nanocluster containing 666 atoms and an alkane chain containing 902 atoms, where the Kohn-Sham electronic ground state is computed using a reduced-order scaling subspace projection technique (P. Motamarri and V. Gavini, Phys. Rev. B 90, 115127).
@article{motamarri_configurational_2018,title={Configurational forces in electronic structure calculations using {Kohn}-{Sham} density functional theory},volume={97},issn={2469-9950},url={https://link.aps.org/doi/10.1103/PhysRevB.97.165132},doi={10.1103/PhysRevB.97.165132},number={16},urldate={2023-07-03},journal={Physical Review B},author={Motamarri, Phani and Gavini, Vikram},month=apr,year={2018},note={Publisher: American Physical Society},pages={165132},dimensions={true}}
We describe the implementation of total angular momentum dependent pseudopotentials in a plane wave formulation of density functional theory. Our approach thus goes beyond the scalar-relativistic approximation usually made in ab initio pseudopotential calculations and explicitly includes spin-orbit coupling. We outline the necessary extensions and compare the results to available all-electron calculations and experimental data.
@article{theurich_self-consistent_2001,title={Self-consistent treatment of spin-orbit coupling in solids using relativistic fully separable ab initio pseudopotentials},volume={64},issn={0163-1829},url={https://link.aps.org/doi/10.1103/PhysRevB.64.073106},doi={10.1103/PhysRevB.64.073106},number={7},journal={Physical Review B},author={Theurich, Gerhard and Hill, Nicola A.},month=jul,year={2001},pages={073106},dimensions={true}}