Spin polarization of graphene on ${\mathrm{Co}}_2{\mathrm{FeGe}}_{0.5}{\mathrm{Ga}}_{0.5}\left(001\right)$ observed by spin-polarized surface positronium spectroscopy

Following previous work on graphene on Ni(111) and Co(0001) surfaces [Phys. Rev. B 97, 195405 (2018)], the spin polarization of graphene on a ${\mathrm{Co}}_2{\mathrm{FeGe}}_{0.5}{\mathrm{Ga}}_{0.5}$ (CFGG) (001) surface was examined using spin-polarized surface positronium spectroscopy. The graphene was found to be magnetically insulated from the CFGG(001) even after heat treatment, which increased the spin polarizations of graphene on Ni(111) and Co(0001). First-principles calculations indicated that graphene is weakly bound to the CFGG(001) surface mainly through the van der Waals interaction, and consequently the interlayer distance between graphene and the CFGG(001) surface is greater ($\sim 3$ Å) than that between graphene and Ni(111) or Co(0001) ($\sim 2$ Å). The weak hybridization between graphene and CFGG(001) sufficiently reduces the spin polarization in graphene, which enables the magnetic insulation of graphene from CFGG.

Figure 1

Positronium fractions obtained for graphene-CFGG(001) and graphene-Co(0001) surfaces in their as-prepared states and after annealing up to $700{}^{\circ }\mathrm{C}$ and 1 keV Ar ion sputtering.

Figure 2

Spin polarizations obtained for graphene-CFGG(001) surface in its as-prepared state and after annealing up to $700{}^{\circ }\mathrm{C}$ and 1 keV Ar ion sputtering. The vertical axis is the shift of the spin polarization for positive ($+M$) and negative ($-M$) magnetizations (see text). The net spin polarization $[\mathrm{\Delta }{P}_{-}(-M)-\mathrm{\Delta }{P}_{-}(+M)]$ is indicated in each panel. The numbers in parentheses indicate errors.

Figure 3

Cross-sectional distributions of (a) positron density in $a_B^{-3}$ and (b) electron-positron density in $a_B^{-6}$ calculated for graphene-CFGG(001) on the (010) plane. The red, green, and gray circles denote C, Fe, and Ga atoms, respectively.

Figure 4

(a) Electron density of states around graphene layer on CFGG(001). (b) Electron-positron density of states (e-p DOS) calculated for graphene-CFGG(001) (red) and CFGG(001) (black). (c) Electron spin polarizations calculated from the above e-p DOS as a function of the lower level of integration in e-p DOS. The Fermi level corresponds to $E=0$. The broken line denotes the position of the calculated positronium work function of CFGG.