Field Dependence of Order Parameter Hysteresis Loops

1 Field Dependence of Order Parameter. Hysteresis Loops 

In low-temperature phase, the order parameter is a sum of field-induced and spontaneous parts so that it becomes nonlinear function of external field due to domain structure influence. As a result, the field dependence of order parameters in the ferroics is described by hysteresis loops, schematically depicted in Fig. 1.1. The shape of these loops is close to those observed in specially prepared (e.g. by application of external field during the crystal growth) monodomain ferroics. One can see from Fig. 1.1 that order parameter in the ferroics contains spontaneous part (at zero field, where two opposite values of order parameter exist) and field-induced one, that saturates at large fields. Under the field decrease, order parameter first decreases and at some field called coercive, it becomes zero and then changes sign (so-called switching phenomenon) accompanied by strong nonlinearity. 

To illustrate the peculiarities of hysteresis loops in multidomain ferroics, we show the hysteresis loop for soft iron [8] on Fig. 1.2. It is seen that at the initial stages of switching the increase of magnetic induction B = H follows 

The absence of order parameter at zero fields in ferroics stems from the fact that in multidomain samples the order parameter is the sum of contributions from 

M H = 0) = Msj 0 due to residual field-induced domain orientation. The shape of the rest of the loop (curves b, c) is similar to that of single-domain ferroics (see Fig. 1.1). This shows the possibility of transformation of multidomain ferroic into single-domain one by the external field. One can see from Fig. 1.2, that for soft iron the coercive field is about 1 Gs, the saturation induction is Bs = 15,000 Gs and spontaneous magnetization is about two times smaller. In general case these parameters depend essentially on the specific material properties. 

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