Effect of uniaxial strain on ferromagnetic instability and formation of localized magnetic states on adatoms in graphene

We investigate the effect of an applied uniaxial strain on the ferromagnetic instability due to long-range Coulomb interaction between Dirac fermions in graphene. In the case of undeformed graphene the ferromagnetic exchange instability occurs at sufficiently strong interaction within the Hartree-Fock approximation. In this work we show that using the same theoretical framework but with an additional applied uniaxial strain, the transition can occur for much weaker interaction, within the range in suspended graphene. We also study the consequence of strain on the formation of localized magnetic states on adatoms in graphene. We systematically analyze the interplay between the anisotropic (strain-induced) nature of the Dirac fermions in graphene, onsite Hubbard interaction at the impurity, and the hybridization between the graphene and impurity electrons. The polarization of the electrons in the localized orbital is numerically calculated within the mean-field self-consistent scheme. We obtain a complete phase diagram containing nonmagnetic as well as magnetic regions, and our results can find prospective application in the field of carbon-based spintronics.

Figure 1

Left: Undeformed graphene honeycomb lattice structure showing two sublattices A and B with t${}_1$, t${}_2$, and t${}_3$ as the nearest neighbor hopping parameters. Right: Uniaxially strained along the armchair, $y$ direction.

Figure 2

Boundary separating the paramagnetic and ferromagnetic regions indicating the onset of an exchange instability in deformed graphene. The value of the critical coupling constant ${\alpha }_x^c$ decreases as a function of applied uniaxial strain.

Figure 3

Schematic of (a) a uniaxially strained graphene with an adatom (in green) sitting on top of one of the two sublattices (red or blue) and (b) the corresponding anisotropic dispersion of the Dirac fermions near one of the Dirac points along with flat dispersionless level of the localized adatom which can be moved in the conduction (as shown in the figure) or in the valence band.

Figure 4

Phase diagram showing the magnetic regions signaling the onset of formation of localized magnetic states on the adatom (impurity) in graphene for various values of applied uniaxial strain. The $x$ and the $y$ axes of the phase diagram are scaled model parameters. Each phase plot is for a fixed value of localized impurity energy level ($E_0$) and the strength of bare hybridization ($V$) in units of eV. The plots in the upper (lower) panels are for positive (negative) values of $E_0$.