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Magnetic ordering, as one of the most important characteristics in magneticmaterials, could have significant influence on the band structure, spindependent transport, and other important properties of materials. Itsmeasurement, especially for the case of antiferromagnetic ordering, however, isgenerally difficult to be achieved. Here we demonstrate the feasibility ofmagnetic ordering detection using a noncontact and nondestructive opticalmethod. Taking the compressive strained tetragonal BiFeO3 (BFO) as an exampleand combining density functional theory calculations with the minimal one-bandtight-binding models, we find that when BFO changes from C1-typeantiferromagnetic (AFM) phase to G-type AFM phase, the top of valance bandshifts from the Z point to {\Gamma} point, which makes the original direct bandgap become indirect. This can be explained by the two-center Slater-Kosterparameters using the Harrison approach. The impact of magnetic ordering onenergy band dispersion dramatically changes the optical properties oftetragonal BFO. For the linear ones, the energy shift of the optical band gapcould be as large as 0.4 eV. As for the nonlinear ones, the change is evenlarger. The second-harmonic generation coefficient d33 of G-AFM becomes morethan 13 times smaller than that of C1-type AFM case. Finally, we propose apractical way to distin-guish the C1- and G-type AFM of BFO using the opticalmethod, which might be of great importance in next-generation informationstorage technologies and widens the potential application of BFO to opticalswitch.

Magnetic Ordering Induced Giant Optical Property Change in Tetragonal BiFeO3