[Paper Review] Combining Quasiparticle Self-Consistent $GW$ and Machine-Learned DFT+$U$ in Search of Half-Metallic Heuslers

Zefeng Cai, Malcolm J. A. Jardine+7 more|arXiv (Cornell University)|Feb 24, 2026

Heusler alloys: electronic and magnetic properties0 citations

TL;DR

This study compares QPGW band structures with DFT variants (PBE, HSE) and DFT+U(BO) with Bayesian-optimized U values to assess half-metallicity in Co- and Ni-based Heuslers lattice-matched to InAs, highlighting method-dependent spin polarization outcomes.

ABSTRACT

Half-metallic Heusler compounds are of significant interest for spintronics. For device fabrication, compounds that can be epitaxially grown on III-V semiconductors are particularly attractive. We present a first-principles investigation of four Co-based and two Ni-based Heusler compounds that are lattice-matched to InAs. The results of density functional theory (DFT) using semi-local and hybrid functionals are compared to quasiparticle self-consistent $GW$ (QPGW). We also consider DFT with machine-learned Hubbard $U$ corrections [npj Computational Materials 6, 180 (2020)] with a new Bayesian optimization (BO) objective function to determine the $U$ values that yield the closest agreement with the QPGW band structure and magnetic moments. We find that DFT+U(BO) can adequately reproduce the key QPGW features in most cases. Our results reveal a strong method dependence of the degree of spin polarization at the Fermi level and, in some cases, even the dominant spin channel (majority or minority). Of the materials studied here, Co$_2$TiSn and Co$_2$ZrAl are the most likely to be half-metals, and Co$_2$MnIn is likely to be a near-half-metal.

Motivation & Objective

• Motivate search for lattice-matched half-metallic Heuslers suitable for spintronic integration with InAs/GaSb substrates.
• Evaluate how different electronic structure methods (PBE, HSE, QPGW, DFT+U(BO)) predict magnetism and spin polarization in six Heuslers.
• Develop and apply Bayesian optimization to determine U values that best reproduce QPGW band structures and magnetic moments.

Proposed method

• Perform fully self-consistent QPGW calculations starting from HSE for six lattice-matched Heuslers using SOC.
• Conduct PBE and HSE calculations, plus PBE+U with U-values optimized by Bayesian optimization to fit QPGW references.
• Introduce a BO objective function that includes band structure, magnetic moments, and, for metals, spin polarization to guide U optimization.
• Apply DFT+U(BO) with U corrections on X and Y site d-orbitals while excluding the Z main-group element.
• Compute spin polarization at the Fermi level from DOS and band structure, and compare across methods.
• Analyze orbital-resolved DOS and compare with experimental RPES/ARPES data where available.

Figure 1: Band structure and element-resolved DOS of Co 2 MnSn calculated using (a) PBE, (b) HSE, (c) QPGW, and (d) PBE+U(BO). In the band-structure panels, the majority and minority spin channels are shown in blue and red, respectively. In the DOS panels, the majority and minority spin components a

Experimental results

Research questions

• RQ1 How do QPGW and DFT-based methods (PBE, HSE, PBE+U) differ in predicting half-metallicity and the dominant spin channel for each Heusler?
• RQ2 Can Bayesian-optimized DFT+U reproduce key QPGW electronic structure features (band gaps, magnetic moments) for these materials?
• RQ3 Which Co-based/Ni-based Heuslers are most likely to be half-metallic when lattice-matched to InAs, and how sensitive is this to the chosen method?
• RQ4 What are the implications of method dependence for high-throughput screening of Heuslers for spintronic interfaces with III–V semiconductors?

Key findings

• Only Co2TiSn is unanimously predicted as a half-metal by all methods studied.
• Spin polarization at the Fermi level and even the dominant spin channel can be method-dependent and qualitatively different across PBE, HSE, QPGW, and PBE+U(BO).
• Co2MnSn and Co2MnIn show strong method-dependent behavior with notable discrepancies between PBE, HSE, QPGW, and PBE+U(BO) on gaps and spin polarization.
• QPGW results often lie between PBE and HSE, and PBE+U(BO) can reproduce key QPGW features for many cases.
• Co2TiSn remains robustly half-metallic across methods, with 100% spin polarization at the Fermi level.
• PBE+U(BO) can closely match QPGW band structures and magnetic moments, though not universally across all materials.

Figure 2: Orbital-resolved DOS of Co 2 MnSn calculated using (a) PBE, (b) HSE, (c) QPGW, and (d) PBE+U(BO), compared to the resonant photoemission spectroscopy (RPES) spectra of Co-3 $d$ and Mn-3 $d$ , reproduced with permission from Ref. [ 123 ] . The computed spectra are broadened by a Gaussian wi