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In the probe limit, we investigate the effects of the Born–Infeld electrodynamics on the holographic paramagnetism–ferromagnetism phase transition in the background of a Schwarzschild–AdS black hole spacetime. We find that the presence of Born–Infeld scale parameter b decreases the critical temperature and makes the magnetic moment harder to form in the case of without external field. Furthermore, the increase of b will result in extending the period of the external magnetic field.