The magnetic anisotropy energy for a single Co atom on CuN/Cu(001) surface is investigated making use of the first-principles relativistic local spin density approximation (LSDA) calculations and the torque method. A single-ion character of the magnetic anisotropy is revealed, which originates mainly from the local magnetic moment of the Co atom. The effect of the orbital polarization beyond that given by the LSDA is studied making use of the different flavors of the LDA+U method. It is shown that the LDA+U induced orbital polarization affects the orbital component of the magnetic moment for different directions of the Co-atom magnetization and can modify substantially the magnetic anisotropy energy. Comparison with the available experimental data is discussed. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3072475]
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