Ferromagnetism of an Ideal System
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In an ideal system of magnetic moments, three types of interaction coexist: exchange interactions favouring -as far as this chapter is concerned- ferromagnetic or ferrimagnetic order, interactions with the lattice which give rise to a magnetocrystalline anisotropy, and magnetic dipolar interactions. The impossibility of simultaneously satisfying the requirements associated with ali these interactions frequently leads to the establishment of magnetic domain structures. The configuration of the moments thus obtained results from a compromise, and can, for this reason, be easily perturbed. The size, and relative dimensions ofthe system under consideration have a radical effect on the equilibrium configuration obtained as well as on the strength of perturbations capable of modifying it. In a perfect, anisotropic system, large enough to feature a multidomain structure in the demagnetised state, ali the magnetization processes starting from this state are perfectly reversible. By contrast, magnetization reversal starting from the fully saturated state implies crossing an energy barrier. In the presence of magnetocrystalline anisotropy, this reversal takes place only for applied reverse fields in excess of the anisotropy field (Brown 's theorem). In the absence of magnetocrystalline anisotropy, configurations of non-uniform magnetization allow reversal in weaker fields.
1. INTRODUCTION When the temperature of a ferromagnetic system is maintained below Tc. the exchange interactions become preponderant, and lead to a parallel ordering of the individual moments. All ferromagnetic materials whose Curie temperature is above room temperature should, therefore, appear as spontaneously magnetised. Experience teaches us that this is, in fact, not the case, and the magnetization of many ferromagnetic systems (iron, nickel, sheets of iron-silicon for example) becomes manifest only in an applied field. However, it is also known that a toroid of any ferromagnetic substance, once saturated by an applied field, retains a remanent
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MAGNETISM- FUNDAMENTALS
magnetization close to M8 even after the inducing field has been brought to zero. This magnetization disappears when a slit or air-gap, however narrow, is introduced into the toroid (fig. 5.1). Remagnetising to saturation a toroid thus sectioned requires the application of a much larger field than that which was necessary to magnetise it without the slit. Furthermore, this magnetization retums to a value close to zero the moment the applied field is suppressed. M,MA . m- 1
10 H,A . m- 1
-10
H, A . m- 1
-1
Figure 5.1 - The influence of a slit on the magnetiza/ion curve of a toroid of soft iron as a function of the applied externa/ magnetic jield This observation shows that the absence of spontaneous magnetization in most ferromagnetic materials is a response to the need to prevent the formation of poles on the surface of a sample. Exchange interactions, which favour the parallel alignment of the moments, tend to generate such poles while, by contrast, the dipolar interaction
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