Possible origins of defect-induced magnetic ordering in carbon-irradiated graphite

We investigated possible sources of defect-induced magnetic ordering in carbon-irradiated graphite from first-principles calculations. Among candidate structures with interstitial defect configurations that could be generated during carbon irradiation processes, two metastable configurations with finite magnetic moments were identified. They are coupled ferromagnetically to their neighboring defects, thereby enabling them to contribute to the observed macroscopic magnetic ordering. The Ruderman-Kittel-Kasuya-Yosida interaction is considered as a possible mechanism for the ferromagnetic ordering.

Figure 1

(Color online) Four interstitial-defect configurations in graphite. Spiro, bridge, on-top, and vertical link structures are shown. Only local structures near the interstitial defects are shown in (black) circles to emphasize them. Configurations in red boxes exhibit magnetic moments. The eV unit shows relative energies to the total energies of the spiro structure.

Figure 2

(Color online) Spin-density plots of paramagnetic and ferromagnetic structures. Red (dark gray) balloons show majority-spin isosurfaces and white (lighter) balloons show minority-spin isosurfaces. The exchange energies at the bottom are defined as spin-unpolarized energy minus spin-polarized energy for the given structures.

Figure 3

(Color online) Electronic band structures of majority and minority spins and charge densities. Red (solid) and blue (dashed) rectangles indicate localized unpaired $p_x$ and $p_y$ states and delocalized $\pi$ states, respectively. (b) and (c) show the charge densities corresponding the states marked by rectangles in (a) for majority and minority spins, respectively. Schematic of the electronic and the magnetic structures is illustrated in (d).

Figure 4

(Color online) Spin-density plots and corresponding energies of ferro- and antiferromagnetic configurations of the VL structures. Those for the in-plane and out-of-plane orderings are shown in (a) and (b), respectively. The upper and lower parts of each configuration correspond to the top view and side views, respectively. Red (Dark gray) and white (lighter) balloons correspond to the spin-up and spin-down isosurfaces, respectively.