# Ferrimagnetic and antiferromagnetic phase in bilayer graphene nanoflake controlled with external electric fields

## TL;DR

This study computationally explores how external electric and magnetic fields influence the magnetic phases of bilayer graphene nanoflakes, revealing controllable transitions between nonmagnetic, antiferromagnetic, and ferrimagnetic states.

## Contribution

It introduces a detailed phase diagram for bilayer graphene nanoflakes under combined electric and magnetic fields, highlighting electric field control of magnetic phases.

## Key findings

- Antiferromagnetic phases are stable over significant parameter ranges.
- Electric fields can switch magnetic phases, demonstrating a magnetoelectric effect.
- Magnetic field influences the stability and transitions of magnetic phases.

## Abstract

The paper presents a computational study of the ground-state magnetic phases of a selected bilayer graphene nanoflake in external electric field and magnetic field. The electric field has parallel and perpendicular component while the magnetic field is oriented in plane. The system consists of two rectangular layers having armchair edges and zigzag terminations with Bernal stacking. The theoretical model is based on a tight binding Hamiltonian with Hubbard term. The magnetic phase diagram involving the total spin is constructed, showing the stability areas of phases with total spin values equal to 0 and 1. A significant stability range of antiferromagnetic, layer-like arrangements is found and extensively discussed. The possibility of switching between nonmagnetic, antiferromagnetic and ferrimagnetic phases with both components of external electric field is demonstrated, being a manifestation of a magnetoelectric effect. The influence of magnetic field on the phase diagrams is analysed.