exchange constant at the interface, S refers to the spin vector, M refers to the magnetization, t refers to film thickness and H is the external field. The subscript F describes the properties of the ferromagnet and AF to the antiferromagnet. The expression omits magnetocrystalline anisotropy, which is unaffected by the presence of the antiferromagnet. At the switching field of the ferromagnet, the pinning energy represented by the first term and the Zeeman dipole coupling represented by the second term will exactly balance. The equation then predicts that the exchange bias shift Hb will be given by the expression Many experimental findings regarding the exchange bias contradict this simple model. For example, the magnitude of measured Hb values is typically 100 times less than that predicted by the equation for reasonable values of the parameters. The amount of hysteresis shift Hb is not correlated with the density n of uncompensated spins in the plane of the antiferromagnet that appears at the interface. In addition, the exchange bias effect tends to be smaller in epitaxial bilayers than in polycrystalline ones, suggesting an important role for defects. In recent years progress in fundamental understanding has been made via synchrotron radiation based element-specific magnetic linear dichroism experiments that can image antiferromagnetic domains and frequency-dependent magnetic susceptibility measurements that can probe the dynamics. Experiments on the Fe/FeF2 and Fe/MnF2 model systems have been particularly fruitful. Technological impact Exchange bias was initially used to stabilize the magnetization of soft ferromagnetic layers in readback heads based on the anisotropic magnetoresistance (AMR) effect. Without the stabilization, the magnetic domain state of the head could be unpredictable, leading to reliability problems. Currently, exchange bias is used to pin the harder reference layer in spin valve readback heads and MRAM memory circuits that utilize the giant magnetoresistance or magnetic tunneling effect. Similarly, the most advanced disk media are antiferromagnetically coupled, making use of interfacial exchange to effectively increase the stability of small magnetic particles whose behavior would otherwise be superparamagnetic. Desirable properties for an exchange bias material include a high Néel temperature, a large magnetocrystalline anisotropy and good chemical and structural compatibility with NiFe and Co, the most important ferromagnetic films. The most technologically significant exchange bias materials have been the rocksalt-structure antiferromagnetic oxides like NiO, CoO and their alloys and the rocksalt-structure intermetallics like FeMn, NiMn, IrMn and their alloys. History Exchange anisotropy was discovered by Meiklejohn and