Critical dimension of the transition from single switching to an exchange spring process in hard/soft exchange-coupled bilayers

Hard/soft exchange-coupled (formula presented) bilayers with well-defined induced in-plane uniaxial anisotropy were deposited on (100) Si and glass substrates by dc magnetron sputtering. The magnetization-reversal process was systematically studied by analyzing the magnetic hysteresis loops measured by the alternating-gradient magnetometer and surface-sensitive magneto-optic Kerr effect. The coercivity in the single-switching process and the nucleation field in the exchange spring process are quantitatively described by theoretical models. As a result, a critical dimension equation describing the transition from a single-switching process to an exchange spring process is developed. Different magnetization-reversal processes are essentially determined by the exchange length (or domain wall width) of the soft layer under an external field and the pinning energy exerted on the domain wall of the hard layer near the interface.