Exchange Bias - Fundamental Science

Fundamental Science

The essential physics underlying the phenomenon is the exchange interaction between the antiferromagnet and ferromagnet at their interface. Since antiferromagnets have a small or no net magnetization, their spin orientation is only weakly influenced by an externally applied magnetic field. A soft ferromagnetic film which is strongly exchange-coupled to the antiferromagnet will have its interfacial spins pinned. Reversal of the ferromagnet's moment will have an added energetic cost corresponding to the energy necessary to create a Néel domain wall within the ferromagnetic film. The added energy term implies a shift in the switching field of the ferromagnet. Thus the magnetization curve of an exchange-biased ferromagnetic film looks like that of the normal ferromagnet except that is shifted away from the H=0 axis by an amount H_b.

In most well-studied ferromagnet/antiferromagnet bilayers, the Curie temperature of the ferromagnet is larger than the Néel temperature T_N of the antiferromagnet. This inequality means that the direction of the exchange bias can be set by cooling through T_N in the presence of an applied magnetic field. The moment of the magnetically ordered ferromagnet will apply an effective field to the antiferromagnet as it orders, breaking the symmetry and influencing the formation of domains.

Exchange anisotropy has long been poorly understood due to the difficulty of studying the dynamics of domain walls in thin antiferromagnetic films. A naive approach to the problem would suggest the following expression for energy per unit area:

where n is the number of interfacial spins interactions per unit area, J_ex is the 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 H_b will be given by the expression

Many experimental findings regarding the exchange bias contradict this simple model. For example, the magnitude of measured H_b values is typically 100 times less than that predicted by the equation for reasonable values of the parameters. The amount of hysteresis shift H_b 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.