Vacancy-induced magnetism in graphene and graphene ribbons

We address the electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons. By using a mean-field Hubbard model, we study the appearance of magnetic textures associated with removing a single atom (vacancy) and multiple adjacent atoms (voids) as well as the magnetic interactions between them. A simple set of rules, based on the Lieb theorem, link the atomic structure and the spatial arrangement of the defects to the emerging magnetic order. The total spin S of a given defect depends on its sublattice imbalance, but some defects with S=0 can still have local magnetic moments. The sublattice imbalance also determines whether the defects interact ferromagnetically or antiferromagnetically with one another and the range of these magnetic interactions is studied in some simple cases. We find that in semiconducting armchair ribbons and two-dimensional graphene without global sublattice imbalance, there is a maximum defect density above which local magnetization disappears. Interestingly, the electronic properties of semiconducting graphene ribbons with uncoupled local moments are very similar to those of diluted magnetic semiconductors, presenting giant Zeeman splitting.

Magnetization reversal of ferromagnetic nanowires studied by magnetic force microscopy

The magnetization reversal of two-dimensional arrays of parallel ferromagnetic Fe nanowires embedded in nanoporous alumina templates has been studied. By combining bulk magnetization measurements (superconducting quantum interference device magnetometry) with field-dependent magnetic force microscopy (MFM), we have been able to decompose the macroscopic hysteresis loop in terms of the irreversible magnetic responses of individual nanowires. The latter are found to behave as monodomain ferromagnetic needles, with hysteresis loops displaced (asymmetric) as a consequence of the strong dipolar interactions between them. The application of field-dependent MFM provides a microscopic method to obtain the hysteresis curve of the array, by simply registering the fraction of up and down magnetized wires as a function of applied field. The observed deviations from the rectangular shape of the macroscopic hysteresis loop of the array can be ascribed to the spatial variation of the dipolar field through the inhomogeneously filled membrane. The system studied proves to be an excellent example of the two-dimensional classical Preisach model, well known from the field of hysteresis modeling and micromagnetism.

Magnetic Edge Anisotropy in Graphenelike Honeycomb Crystals

The independent predictions of edge ferromagnetism and the quantum spin Hall phase in graphene have inspired the quest of other two-dimensional honeycomb systems, such as silicene, germanene, stanene, iridates, and organometallic lattices, as well as artificial superlattices, all of them with electronic properties analogous to those of graphene, but a larger spin-orbit coupling. Here, we study the interplay of ferromagnetic order and spin-orbit interactions at the zigzag edges of these graphenelike systems. We find an in-plane magnetic anisotropy that opens a gap in the otherwise conducting edge channels that should result in large changes of electronic properties upon rotation of the magnetization.

Topological spin waves in the atomic-scale magnetic skyrmion crystal

We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.