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We propose an optical-acoustic means to excite broadband terahertz antiferromagnetic (AFM) spin wave in a metal/insulator/antiferromagnet heterostructure. The AFM spin wave is excited by an ultrafast strain wave triggered by a femtosecond pulsed laser based on photoacoustic conversion. This spin wave comprises an AFM exchange spin wave and a magnetoelastic spin wave. Their dispersion curves are overlapped in a wide frequency range by manipulating the Dzyaloshinskii–Moriya interaction, which is accompanied by lifting the degeneration of the spin-wave modes with opposite chirality. This optical-acoustic excitation of spin waves exploits the laser-induced ultrafast strain waves and avoids the thermal effect from the laser. It paves a way to develop novel AFM devices that can apply for ultrafast information processing and communication.