Femtomagnetism in graphene induced by core level excitation of organic adsorbates

We predict the induction or suppression of magnetism in the valence shell of physisorbed and chemisorbed organic molecules on graphene occurring on the femtosecond time scale as a result of core level excitations. For physisorbed molecules, where the interaction with graphene is dominated by van der Waals forces and the system is non-magnetic in the ground state, numerical simulations based on density functional theory show that the valence electrons relax towards a spin polarized configuration upon excitation of a core-level electron. The magnetism depends on efficient electron transfer from graphene on the femtosecond time scale. On the other hand, when graphene is covalently functionalized, the system is magnetic in the ground state showing two spin dependent mid gap states localized around the adsorption site. At variance with the physisorbed case upon core-level excitation, the LUMO of the molecule and the mid gap states of graphene hybridize and the relaxed valence shell is not magnetic anymore.


Evaluation of the molecular orbital projected density of states
We describe here the procedure to compute the Molecular Orbital Projected Density of States (MOPDOS) that we have recently implemented in the molecularpdos.x code within the Quantum ESPRESSO distribution [1]. As we used in the current framework, the aim is to single out the contributions to the density of states of an adsorbed system coming from the orbitals of the free molecule. In more general terms, one can analyze the electronic structure of a given system named "A" (here, the molecule/graphene interface) in terms of the energy levels of a part of it named "B" (here, the molecule).
This approach may also be used to analyze a complex molecule in terms of its subunits, or a different electronic configuration (say, A is the molecule with a core-level excitation while B is the same but in the ground state as we did to study excitations of pentacene [2]).
If we indicate by |ψ A nak the eigenvectors of system A and by A nak its eigenvalues (same for system B), where k is the k-vector in the Brillouin zone with weight ω k , the MOPDOS of system A, projected onto the n b -th orbital of system B and evaluated at the energy E reads: The eigenstates are computed by separate pw.x calculations for A and B; for consistency, the same unit cell and k sampling should be used.
A shortcoming of the plane wave representation is that direct evaluation of the overlap integral | ψ B n b k |ψ A nak | 2 requires handling the full states for the two systems, which can be computationally demanding already for a moderately large unit cell (of the order of 10 6 plane waves or real space points in the case presented here, for each k and orbital). Our implementation instead goes through a more efficient local basis set representation of the system. Let us indicate by |φ nlm I ≡ |φ ν , with ν = (I, n, l, m), the atomic wavefunction of atom I with quantum numbers n, l, and m. The number of such states, N φ , is generally much smaller than that of plane waves making the calculations more manageable (here, N φ ≈ 300). Hence we can approximate the eigenfunctions in terms of this local basis set: where the coefficients P are the complex projections of the Kohn-Sham eigenstates onto the local basis, P A nak,ν = φ ν |ψ A nak and similarly for B. The above expressions are approximate since the local basis set does not span completely the original Hilbert space (see, e.g., the "spilling" [3]) but this is often of no concern to a qualitative analysis. Within Quantum ESPRESSO, the coefficients P are computed by the projwfc.x code in a standard calculation of the DOS projected onto atomic orbitals and are stored in the file atomic_proj.xml. The execution of projwfc.x has to be performed for systems A and B separately.
The orbital overlaps in Eq. (1) are eventually computed from Eqs. (2) and (3) as: Notice that the index ν in the summation should identify the same atomic state in the two systems for the local orbitals which are common for the two systems only. So, if system B is a subsystem of A, we have N A φ > N B φ and the summation runs over N B φ states. We remark that, for an adsorbed radical, where the dangling bond is saturated by the surface, system B is most effectively taken as the radical saturated by an hydrogen atom whose atomic state should not be included in Eq. (4). In all cases, the fraction of atomic states to be used can be specified in input by appropriate variables (i_atmwfc_beg_full/part and i_atmwfc_end_full/part), as illustrateed by the following sample input for a pyridine radical adsorbed on 5 × 7 graphene: orbitals for a total of N A φ = 75 × 4 + 1 × 4 + 4 × 1 = 308, 280 from graphene and 28 from the radical. The saturated molecule (B) has one H atom more hence N B φ = 29 atomic orbitals. In the above example we project all states of the full system onto the molecular HOMO and LUMO (orbitals 15 and 16), assuming that the graphene atoms are listed last in system A and that the H atom saturating the dangling bond (to be neglected) is given first in system B. Had we saturated the radical with a methyl group, 7 atomic orbitals should have been neglected from system B.