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

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.

Figures (5)

• 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 are plotted on the left and right sides, respectively. The rightmost panels present a magnified view of the DOS around the Fermi level. The total magnetic moment (MM, in $\mu B$) and spin polarization percentage at the Fermi level (SP%) are listed for each method. Negative spin polarization indicates that the minority spin channel is dominant around the Fermi level. The dashed box in (c) highlights the flat minority-spin band near the Fermi level that gives rise to the minority-dominated spin polarization in the QPGW results.
• 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. 2015_Baral_ExpCo2MnSbPESDFT_JournAlloyComp. The computed spectra are broadened by a Gaussian with $\sigma = 0.77\,\mathrm{eV}$ to simulate the resolution of the experiment. All spectra are normalized to the same maximum intensity. The satellite features between $-6\,\mathrm{eV}$ and $-2\,\mathrm{eV}$ in the experimental spectrum of Co-3$d$ are attributed in Ref. 2015_Baral_ExpCo2MnSbPESDFT_JournAlloyComp to excitation effects that are not captured by the electronic structure methods used here.
• Figure 3: Band structure and element-resolved DOS of Co$_2$MnIn 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 are plotted on the left and right sides, respectively. The rightmost panels present a magnified view of the DOS around the Fermi level. The total magnetic moment (MM, in $\mu B$) and spin polarization percentage at the Fermi level (SP%) are listed for each method. Negative spin polarization indicates that the minority spin channel is dominant around the Fermi level.
• Figure 4: Band structure and element-resolved DOS of Co$_2$TiSn 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 are plotted on the left and right sides, respectively. The rightmost panels present a magnified view of the DOS around the Fermi level. The total magnetic moment (MM, in $\mu B$) and spin polarization percentage at the Fermi level (SP%) are listed for each method.
• Figure 5: Band structure and element-resolved DOS of Co$_2$ZrAl 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 are plotted on the left and right sides, respectively. The rightmost panels present a magnified view of the DOS around the Fermi level. The total magnetic moment (MM, in $\mu B$) and spin polarization percentage at the Fermi level (SP%) are listed for each method. Negative spin polarization indicates that the minority spin channel is dominant around the Fermi level.