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Using first-principles density functional calculations, electronic and optical properties of ferromagnetic semiconductor EuO are investigated. In particular, we have developed a way to obtain the spin-dependent optical response of the magnetic materi als, which is helpful to verify the spin-dependent band structure of EuO. Significantly different optical responses from spin-up and spin-down channels are obtained in both linear and nonlinear cases, making it possible to distinguish contributions from different spin-channels in the optical absorption spectra if spin-flip process can be neglected. In addition, the red-shift of the absorption edge from paramagnetic to ferromagnetic ordering is explained by exchange interactions. Using such method, we have also compared the optical properties of multiferroic EuO which is induced by strong epitaxial strain. Our results show that from tensile to compressive strain, the blue-shift of the leading absorption peaks in the optical spectra, the red-shift of the optical band gap in spin-up state can be observed, consistent to the energy difference between spin-splitting orbits. The spin-dependent nonlinear optical properties reveal that in the infrared and visible light region, the contributions to second-harmonic generation (SHG) susceptibilities are mainly from spin-majority channels. In addition, the strain effect is also discussed. With the increase of epitaxial strain, the larger energy shift of the leading absorption peaks, and the more remarkable nonlinear optical response can be obtained.
We propose a way to use electric-field to control the magnetic ordering of the tetragonal BiFeO3. Based on systematic first-principles studies of the epitaxial strain effect on the ferroelectric and magnetic properties of the tetragonal BiFeO3, we fi nd that there exists a transition from C-type to G-type antiferromagnetic (AFM) phase at in-plane constant a ~ 3.905 {AA} when the ferroelectric polarization is along [001] direction. Such magnetic phase transition can be explained by the competition between the Heisenberg exchange constant J1c and J2c under the influence of biaxial strain. Interestingly, when the in-plane lattice constant enlarges, the preferred ferroelectric polarization tends to be canted and eventually lies in the plane (along [110] direction). It is found that the orientation change of ferroelectric polarization, which can be realized by applying external electric-field, has significant impact on the Heisenberg exchange parameters and therefore the magnetic orderings of tetragonal BiFeO3. For example, at a ~ 3.79 {AA}, an electric field along [111] direction with magnitude of 2 MV/cm could change the magnetic ordering from C-AFM to G-AFM. As the magnetic ordering affects many physical properties of the magnetic material, e.g. magnetoresistance, we expect such strategy would provide a new avenue to the application of multiferroic materials.
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