Spin polarization of graphene and $h-\mathbf{BN}$ on Co(0001) and Ni(111) observed by spin-polarized surface positronium spectroscopy

In spin-polarized surface positronium annihilation measurements, the spin polarizations of graphene and $h$-BN on Co(0001) were higher than those on Ni(111), while no significant differences were seen between graphene and $h$-BN on the same metal. The obtained spin polarizations agreed with those expected from first-principles calculations considering the positron wave function and the electron density of states from the first surface layer to the vacuum region. The higher spin polarizations of graphene and $h$-BN on Co(0001) as compared to Ni(111) simply reflect the spin polarizations of these metals. The comparable spin polarizations of graphene and $h$-BN on the same metal are attributed to the creation of similar electronic states due to the strong influence of the metals: the Dirac cone of graphene and the band gap of $h$-BN disappear as a consequence of $d-\pi$ hybridization.

Figure 1

(a) Schematic diagram of the experimental setup. A positron beam with an energy of 12 keV is decelerated to 200 eV and injected into the sample. Some of the positrons reach the sample surface and are emitted as positronium into the vacuum. Annihilation photons are observed by a Ge detector. The positron beam is transversely spin polarized with $P_{+}=0.3$. The sample is in-plane magnetized by a Helmholtz coil with a field strength of 30 mT. (b) Energy spectra of annihilation photons for 0% (mica at room temperature) and 100% (Ge at 1000 K) positronium formation. The intensities are normalized to the 511 keV peak intensity. The shaded areas define the intensities $R$ and $P$ in Eq. (1).

Figure 2

Spin polarizations obtained for all the samples. The vertical axis is the shift of spin polarizations for positive ($+M$) and negative ($-M$) magnetizations (see text). The net spin polarizations $[\mathrm{\Delta }{P}_{-}(-M)-\mathrm{\Delta }{P}_{-}(+M)]$ are indicated below each panel.

Figure 3

Temperature dependence of spin polarizations obtained for graphene and $h$-BN on Co(0001) and Ni(111). The broken lines are guides for the eye.

Figure 4

Electron density of states (DOS) profiles calculated for graphene and $h$-BN in isolated form, on Co(0001) and on Ni(111).

Figure 5

Cross-sectional electron-positron density distributions calculated for Co, graphene/Co, and $h$-BN/Co on the ($1\overline{1}00$) plane and Ni, graphene/Ni, and h-BN/Ni on the ($11\overline{2}$) plane. The unit of the color bar is $a_B^{-6}$. White circles are Co and Ni atoms and gray and blue circles are C and N atoms, respectively. B atoms are not shown on these planes.

Figure 6

(a) Electron-positron density of states ($e-p$ DOS) calculated for graphene/Co(0001), $h$-BN/Co(0001), graphene/Ni(111), and $h$-BN/Ni(111). (b) Electron spin polarization calculated from Eq. (3) and the above electron-positron densities of states as a function of the lower energy of integration. The inset is a magnification of the region around the positronium work function.