Graphene nanoflakes in external electric and magnetic in-plane fields

• Magnetic ground-state phase diagram of graphene nanoflakes was constructed.
• The combined effect of in-plane electric and magnetic fields on total spin was studied.
• A rich phase diagram with both disordered and ordered (nonzero spin) phases was found.
• The importance of size and edge geometry of the nanostructure was emphasized.

The paper discusses the influence of the external in-plane electric and magnetic fields on the ground state spin phase diagram of selected monolayer graphene nanostructures. The calculations are performed for triangular graphene nanoflakes with armchair edges as well as for short pieces of armchair graphene nanoribbons with zigzag terminations. The mean field approximation (MFA) is employed to solve the Hubbard model. The total spin for both classes of nanostructures is discussed as a function of external fields for various structure sizes, for charge neutrality conditions as well as for weak charge doping. The variety of nonzero spin states is found and their stability ranges are determined. For some structures, the presence of antiferromagnetic orderings is predicted within the zero-spin phase. The process of magnetization of nanoflakes with magnetic field at constant electric field is also investigated, showing opposite effect of electric field at low and at high magnetic fields.