[论文解读] High-throughput determination of Hubbard U and Hund J values for transition metal oxides via linear response formalism

Guy C. Moore, Matthew K. Horton+5 more|arXiv (Cornell University)|Jan 11, 2022

Magnetic and transport properties of perovskites and related materials被引用 36

一句话总结

该论文开发了一个完全自动化、高通量的工作流，利用线性响应在现场计算超过2000个过渡金属氧化物的Hubbard U和Hund J参数，并演示对非共线磁结构（LiNiPO4）及晶格参数的影响。

ABSTRACT

DFT+U provides a convenient, cost-effective correction for the self-interaction error (SIE) that arises when describing correlated electronic states using conventional approximate density functional theory (DFT). The success of a DFT+U(+J) calculation hinges on the accurate determination of its Hubbard U and Hund's J parameters, and the linear response (LR) methodology has proven to be computationally effective and accurate for calculating these parameters. This study provides a high-throughput computational analysis of the U and J values for transition metal d-electron states in a representative set of over 2000 magnetic transition metal oxides (TMOs), providing a frame of reference for researchers who use DFT+U to study transition metal oxides. In order to perform this high-throughput study, an atomate workflow is developed for calculating U and J values automatically on massively parallel supercomputing architectures. To demonstrate an application of this workflow, the spin-canting magnetic structure and unit cell parameters of the multiferroic olivine LiNiPO4 are calculated using the computed Hubbard U and Hund J values for Ni-d and O-p states, and are compared with experiment. Both the Ni-d U and J corrections have a strong effect on the Ni-moment canting angle. Additionally, including a O-p U value results in a significantly improved agreement between the computed lattice parameters and experiment.

研究动机与目标

• Motivate the need for first-principles, environment-sensitive Hubbard U and Hund J values to correct self-interaction errors in DFT.
• Provide a systematic, predictive, and transferable method to compute U and J via linear response for a large materials set.
• Develop and deploy an automated, parallelized workflow (atomate/VASP) to obtain U and J for d- and O-p states.
• Analyze the distribution and environmental dependence of U and J across transition metals and oxygen in oxides.
• Demonstrate the physical impact of these parameters on a case study (LiNiPO4) and compare with experimental data.

提出的方法

• Use the linear-response (LR) formulation to determine U and J by measuring the curvature of total energy as a function of site occupation via on-site potential perturbations.
• Compute interacting and non-interacting response matrices chi and chi0 to obtain U and J through mappings (e.g., U = (chi0^-1 - chi^-1) for spin-agnostic cases; extensions to spin-resolved chi and mappings to U and J discussed).
• Implement a spin-polarized LR workflow within the atomate framework to enable spin-channel screening and inter-site/spin-channel screening analyses.
• Carry out DFT+U+J corrections using VASP with PAW/PBE pseudopotentials, 520 eV cutoff, and 50 k-points per reciprocal angstrom, across over 2000 TM oxides.
• Provide a focused analysis of Mn-d, Fe-d, Ni-d, and O-p sites to interpret trends in U and J, including the unusually large U for O- p states (≈10 eV).
• Compare computed U_eff = U − J values with Materials Project (MP) benchmarks and analyze differences when re-relaxing formation energies (notably for W).

实验结果

研究问题

• RQ1 What are the distributions and environmental dependences of Hubbard U and Hund J across d-block transition metals and O-2p states in transition metal oxides?
• RQ2 How do LR-derived U and J values influence magnetic properties and structural parameters in real materials, including noncollinear spin states?
• RQ3 How do LR-derived U and J compare with empirically fitted MP values, and what are the implications for high-throughput predictions?
• RQ4 What is the impact of including O- p corrections on lattice parameters and magnetic interactions in TMOs?
• RQ5 Can the LR workflow be scaled to robustly generate U and J for large materials datasets in a high-throughput setting?

主要发现

• U values show element- and environment-dependent distributions with notable differences across Mn- d, Fe- d, Ni- d, and O- p sites.
• O- p states exhibit large U values (≈10 eV), reflecting higher energy curvature and chemical hardness aspects of oxygen compared to transition metals.
• The computed U_eff values differ from MP’s empirical values for several elements (e.g., Co, Cr, Fe, Ni, W), with substantial adjustments in some cases (e.g., W showing a large discrepancy).
• Including the LR-derived U and J corrections significantly affects Mn and Ni moments and spin canting in LiNiPO4, and adding O- p U improves agreement of lattice parameters with experiment.
• A high-throughput, automated LR workflow was implemented in atomate and applied to over 2000 TM-oxide compounds, providing a broad reference for U and J across the period.