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(Color online) Spin-polarization energy as a function of the distance between the adjacent vacancies. ΔEsp increases with the increasing separation and the critical distance is 7.38 Å. The corresponding supercell structures (the numbers with multiply signs represent the size with one vacancy and additional 2VN in brackets means two defects within one supercell) and the corresponding defect density are also marked.
(Color online) (a) Spin-resolved DOS of a VN in a 72-atom AlN supercell. The spin polarization leads to a splitting between majority- and minority-spin states. (b) Isosurface charge density plot (isovalue is 0.008 e/Å3) of the net spin states associated with a VN in a 72-atom AlN supercell, showing both the localized nature and the tails of the defect wave functions extending well beyond the size of the 72-atom supercell. Al atoms are shown in pink and N atoms in blue. A black arrow indicates the location of VN.
(Color online) (a) The PXRD pattern of S2. (b) The typical low-magnification scanning electron microscope image of AlN whiskers ranged from several hundred nanometers to several micrometers of S1. (c) and (d) The typical SAED pattern and corresponding HRTEM image of S1.
(Color online) (a) RTPL spectra of the as-grown AlN whiskers. The defects are confirmed to be VNs and the VN concentration increases from S2 to S1. (b) and (c) The magnetization (in units of 1 emu = 10−3 Am2) measured at T = 5 K as a function of magnetic field (1 Oe = 103/4π Am−1) by cycling the field from 5000 Oe to − 5000 Oe, and back to 5000 Oe for AlN whiskers before and after removing the intrinsic DM contribution. The magnetization of polycrystalline AlN after removing the DM contribution is magnified 50 times.
Magnetic coupling between VN-induced local moments in AlN. The coupling is ferromagnetic between two VNs with a separation of adjacent vacancies 7.38 Å and 9.39 Å. Upon the distance of 10.05 Å, J 0 is believed to be zero and the coupling prefers PM.
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