Quantifying the Spin Polarisation across Graphitic Ribbons

1. Quantifying the Spin Polarisation across Graphitic Ribbons Jennifer A. Chan Department of Chemistry, Imperial College London, UK

2. Literature Zigzag edged graphitic sheet Magnetic nanographite Mechanism of spin polarisation Kusakabe et al., Phys. Rev. B, 67, 092406 (2003) Tight-binding solutions Fujita et al., J. Phys. Soc. Jap., 65, 1920 (1996)

3. Quantum mechanical, first principle calculations Hybrid Density Functional Theory – B3LYP All electron (no pseudopotentials) Simulated systems are infinite and periodic Large systems – 1000’s of atoms/cell possible Electronic charge and spin density, optimised geometries, ground state energies etc. Magnetic properties such as coupling, ESR hyperfine coupling constants Methodology

4. Density Functional Theory Hohenberg-Kohn (1964): ground-state energy of a system of N electrons in an external field Vext is determined by the ground-state electron density n0(r) alone Kohn-Sham (1965): the solution for the fully interacting problem can be found by solving a problem for non-interacting electrons: n

5. Hybrid functional: B3LYP • B3LYP generally improves description of: • geometries • atomization energy • vibrational frequencies • electronic structures, in particular energy gap between occupied and unoccupied electronic states • magnetic coupling energies Quantitively good agreement with experiment for strongly correlated magnetic systems Becke, J. Chem. Phys. 98, 5648 (1993)

6. Graphitic sheet Graphite sheet (1x1) cell Zero gap semiconductor EF EF G M K G

7. Graphitic sheet 2 degenerate states at the K point: 60º Top of valence band Bottom of conduction band

8. Methylene-substituted Graphitic Ribbons methylene groups attached to zigzag edges N = 3 rows  N = 2 rows  N = 1 row  Periodic direction Structure as in: Maruyama et al, J. Phys. Soc. Jap. 73, 656 (2004)

9. Antiferromagnetic Ground States Antiferromagnetic Ferromagnetic Oscillating spin density throughout structure (pz orbitals)

10. Electronic Band Structures – Narrow ribbons FM – Conducting Non-spin polarised G K M G K M G K M AF - Insulating Graphite sheet G K M G K M G K M

11. Electronic Band Structures – Wide ribbons FM – Conducting Non-spin polarised G K M G K M G K M AF - Insulating Graphite sheet G K M G K M G K M

12. Band gap vs. Width Band gap/a.u. No. of rows, N

13. Density of States – Wide ribbons FM AF Non-spin polarised Energy /a.u. Energy /a.u. Energy /a.u. EF EF EF Spin-up Spin-down Spin-up Spin-down High DOS at EF

14. Energetics Energy difference/a.u. No. of rows, N

15. Long Range Magnetic Interaction E(FM-AF)/a.u. Near 1/N2 dependence No. of rows, N E(FM - AF) ~1 meV when ribbons are 62 – 84 Åwide.

16. Summary • Quantum mechanical, first principles calculations(B3LYP) • Antiferromagnetic, ferromagnetic, and non-spin polarised solutions found • Narrow ribbons: presence of edges and spin polarisation opens gaps in the electronic structure • Wide ribbons: gap closes for non-spin polarised state and results in high DOS at Fermi level • Antiferromagnetic and ferromagnetic state represent two different ways of moving away from instability • Antiferromagnetic ground state • Magnetic interaction via nearest neighbour spin polarisation mechanism quantified and found to be long ranged

17. Acknowledgements • In collaboration with: • Nicholas Harrison, Barbara Montanari, Keith Refson • Steve Bennington andfor useful discussions • Jon Taylor • Barry Searle andfor help with the code • Giuseppe Mallia The computational programs used were: Crystal’03 and DL Visualise www.crystal.unito.it, www.cse.clrc.ac.uk/cmg/DLV/