Giant magneto-optical Faraday effect of graphene on Co in the soft x-ray range

Abstract

Using polarization analysis of linearly polarized synchrotron radiation we demonstrate the existence of a giant magneto-optical Faraday effect at the carbon $1s$ edge of single-layer graphene on Co, reaching Faraday rotation angles of $2.9\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{0.16em}{0ex}}\mathrm{deg}/\mathrm{mm}$. This value is of the order of those observed at the Co $3p$ and $2p$ edges. Using element-selective magnetic hysteresis curves we find that graphene on Co exhibits ferromagnetic order. The magnetism in graphene is found to be carried by and be strongly enhanced by aligned \ensuremath{\pi} orbitals of carbon atoms. It is induced by hybridization with the Co $3{d}_{z}2$ orbitals while carbon \ensuremath{\sigma} bonds show negligible magnetism due to insignificant hybridization with Co. From additional x-ray magnetic circular dichroism and transversal magneto-optical Kerr effect spectra a magnetic moment of $0.14\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ is estimated for graphene. From Faraday spectra the complete set of x-ray magneto-optical constants of graphene has been deduced which allows for future modeling of magneto-optical devices based on graphene. The strong magnetism in graphene results from hybridization of carbon ${p}_{\mathrm{z}}$ and metal $3d$ orbitals. Atoms of the graphene sublattice A, placed on top of Co, lead to strongest hybridization with Co $3{{d}_{z}}^{2}$ orbitals. Carbon atoms of sublattice B, and those of rotated graphene domains without Co atoms beneath, hybridize with each other and with $3{d}_{\mathrm{xz}}$ and $3{d}_{\mathrm{yz}}$ orbitals of neighboring Co atoms forming tilted ${p}_{\mathrm{z}}$ bonds. We show that the related reduction of A-B symmetry leads to a splitting of the spin-polarized density of conduction-band states which is responsible for the strong magneto-optical Faraday effect.