Effect of substrate strain on calculated magnetic properties and magnetic anisotropy energy of CoO

The electronic structure, magnetic properties, and magnetic anisotropy energy (MAE) of the insulating antiferromagnetic bulk CoO and CoO strained by silver or MnO substrates have been studied by means of three different methods: (1) a simple model based on the crystal-field approach, (2) the full-potential linear augmented plane-waves method within the generalized gradient approximation (GGA), and (3) the so-called GGA+U method. In all methods the spin-orbit coupling is included. In the third method, the Hubbard interaction U is used to treat the strong electron-electron interaction due to the cobalt localized open d shell. The results of the various calculations for bulk CoO and those of CoO strained by silver or MnO substrates are discussed and compared with available experimental data and other calculations. The GGA predicts incorrectly that bulk CoO is a metallic oxide and its spin magnetic moment is oriented along the inclination angle theta of 66 degrees and the azimuth angle phi of 45 degrees and the hard axis along the c direction. The orbital magnetic moment is also much smaller compared to experiment. On the contrary, within the GGA+U bulk CoO becomes an insulator as expected and the spin magnetic moment is oriented along the tetragonal c axis; it rotates in plane when CoO is strained by a silver substrate, and out of plane when strained by an MnO substrate. Within the GGA+U an unquenched orbital magnetic moment on the order of 1 mu(B) is obtained in both bulk CoO and CoO strained by MnO substrate but is much smaller (0.45 mu(B)) when CoO is strained by silver. All these results together with the values of MAE are in good agreement with experiment and our crystal-field analysis.