On the microscopic theory of the magnetoelectric effect

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Abstract
This is a tutorial paper. We first consider why one should be interested in the origin of the magnetoelectric effect in ordered magnetic compounds. The non-zero elements of the tensor may be deduced from group theory arguments alone. A microscopic understanding is important if one wishes to learn which systems are likely to have large effects and possibly to design new combinations of materials which should show strong or unusual effects. It also contributes to the overall understanding of the materials involved. Another important feature is that different microscopic origins do give rise to very different behaviour with temperature and hence a microscopic understanding of a particular material is essential to understand the temperature dependence of the magnetoelectric tensor. This is particularly important if one actually has the situation in which the magnetoelectric effect may be used to measure a critical exponent just below the transition temperature. A final reason for being interested in the quantum-mechanical details is the frequency dependence of the effect. It is important to know if the effect will still be there at optical frequencies. The different ways in which the magnetic interactions can be involved will be summarised. We discuss the factors which effect the magnitude of these contributions.