Barium magnesium fluoride crystal features nonlinear and electro-optic effects, making it a highly promising deep-ultraviolet nonlinear and electro-optic crystal. Boasting extremely high transmittance and a broad transmission spectrum, BaMgF4 serves as an outstanding optical window material. Its electro-optic coefficient gamma13 exceeds the maximum electro-optic coefficient gamma51 (32.6 pm/V) of LiNbO3 crystal, is comparable to gamma33 of KTP crystal, and is more than ten times gamma11 of BBO crystal. Furthermore, it has a low absorption coefficient and a high laser-induced damage threshold, enabling electro-optic applications from the deep-ultraviolet to the mid-infrared range.