[Paper Review] Magnetic-field tunable antiferromagnetism of vacancies in graphene nanoflakes

Matthias Droth, Guido Burkard|arXiv (Cornell University)|May 21, 2014

Graphene research and applications1 citations

TL;DR

This study uses a tight-binding model with Peierls' phase to show that a perpendicular magnetic field can tune the exchange coupling J between spin states localized at two vacancies in graphene nanoflakes. By controlling the field, J can be switched in situ from positive (antiferromagnetic ground state) to zero, enabling field-tunable spintronics with experimentally accessible Néel temperatures.

ABSTRACT

Graphene nanoflakes are interesting because electrons are naturally confined in these quasi zerodimensional structures, whereas confinement in bulk graphene would require a bandgap. Vacancies inside the graphene lattice lead to localized states and the spins of such localized states may be used for spintronics. We perform a tight-binding description of a nanoflake with two vacancies and include a perpendicular magnetic field via Peierls’ phase. The tunnel coupling strength and from it the exchange coupling between the localized states can be obtained from the energy splitting between numerically calculated bonding and antibonding energy levels. This allows us to estimate the exchange coupling J , which governs the dynamics of coupled spins. We predict the possibility of switching in-situ from J > 0 to J = 0 by tuning the magnetic field. In the former case, the ground state will be antiferromagnetic with Neel temperatures accessible by experiment.

Motivation & Objective

• To investigate how magnetic fields influence the exchange coupling between localized spins at vacancies in graphene nanoflakes.
• To explore the potential for in-situ electrical or magnetic control of spin states in zero-dimensional graphene systems.
• To determine whether the exchange coupling J can be tuned from antiferromagnetic (J > 0) to non-interacting (J = 0) via an external magnetic field.
• To assess the feasibility of achieving experimentally accessible Néel temperatures in such systems for spintronic applications.

Proposed method

• A tight-binding model is applied to a graphene nanoflake containing two vacancies to describe localized electronic states.
• The Peierls' phase is introduced to incorporate the effect of a perpendicular magnetic field on electron hopping between atoms.
• The tunnel coupling strength between the localized states is extracted from the energy splitting between bonding and antibonding molecular states.
• The exchange coupling J is calculated from the tunnel coupling, governing the spin dynamics of the two-site system.
• Numerical diagonalization of the Hamiltonian is used to compute energy levels and extract the splitting under varying magnetic fields.
• The dependence of J on magnetic field strength is analyzed to identify field-tunable transitions in spin coupling.

Experimental results

Research questions

• RQ1 Can an external magnetic field tune the exchange coupling J between two vacancy-induced localized spins in a graphene nanoflake?
• RQ2 What is the magnetic field dependence of the energy splitting between bonding and antibonding states in the two-vacancy system?
• RQ3 At what magnetic field strength does the exchange coupling J transition from J > 0 to J = 0?
• RQ4 Is the Néel temperature of the antiferromagnetic ground state accessible under experimentally feasible conditions?
• RQ5 Can the system be used for in-situ switching of spin coupling for spintronic applications?

Key findings

• The exchange coupling J between two vacancy-induced localized spins in a graphene nanoflake can be tuned by applying a perpendicular magnetic field.
• The energy splitting between bonding and antibonding states provides a direct measure of the tunnel coupling, which determines J.
• A transition from J > 0 (antiferromagnetic) to J = 0 (non-interacting) is predicted as the magnetic field is increased.
• The antiferromagnetic ground state has a Néel temperature that is experimentally accessible under realistic conditions.
• The system enables in-situ, reversible switching of spin coupling via magnetic field control, offering a route to tunable spin qubits.
• The predicted field-tunable behavior arises from the interplay between Peierls phases and the localized electronic structure at vacancies.