The dependence of the state of a system on its previous history, generally in the form of a lagging of a physical effect behind its cause.
A phenomenon wherein two (or more) physical quantities bear a relationship which depends on prior history. More specifically, the response Y takes on different values for an increasing input X than for a decreasing X .
If one cycles X over an appropriate range, the plot of Y versus X gives a closed curve which is referred to as the hysteresis loop. The response Y appears to be lagging the input X .
Hysteresis occurs in many fields of science. Perhaps the primary example is of magnetic materials where the input variable H (magnetic field) and response variable B (magnetic induction) are traditionally chosen. For such a choice of conjugate variables, the area of the hysteresis loop takes on a special significance, namely the conversion of energy per unit volume to heat per cycle. For mechanical hysteresis, it is customary to take the variables stress and strain, where the energy density loss per cycle is related to the internal friction. Thermal hysteresis is characteristic of many systems, particularly those involving phase changes, but here the hysteresis loops are not usually related to energy loss. See Ferroelectrics
a phenomenon that consists in the fact that a physical quantity that characterizes the state of a body (for example, magnetization) depends nonuniquely on the physical quantity that characterizes external conditions (for example, a magnetic field). Hysteresis is observed in cases in which the state of a body at a given instant is determined by external conditions not only at that instant but also at preceding instants. The nonunique dependence of quantities is observed in any process, since a certain amount of time (the relaxation time) is always required for a change in the state of a body, and the reaction of the body lags behind the factors responsible for the change. The slower the change in external conditions, the smaller the lag. However, for some processes the lag does not diminish as the change in external conditions becomes slower. In these cases the nonunique dependence of the quantities is called a hysteretic relationship, and the phenomenon itself is called hysteresis.
Hysteresis is observed in various substances and physical processes. Of greatest interest are magnetic, dielectric, and elastic hysteresis.
Magnetic hysteresis Magnetic hysteresis is observed in magnetic materials, such as ferromagnets. The main feature of ferromagnets is the presence of spontaneous magnetization. A ferromagnet usually is not uniformly magnetized but is divided into domains—regions of uniform spontaneous magnetization whose degree of magnetization (the magnetic moment per unit volume) is identical, although the directions are different. Under the effect of an external magnetic field the number and size of the domains magnetized along the field increase at the expense of other domains. Moreover, the magnetic moments of certain domains may rotate in the direction of the field. As a result the magnetic moment of the sample increases.
The dependence of the magnetic moment M of a ferromagnetic sample on the intensity H of the external magnetic field (the magnetization curve) is shown in Figure 1. In a sufficiently strong magnetic field the sample is magnetized to saturation (as the field increases further, the value of M remains virtually unchanged—point A). Here the sample consists of one domain with a magnetic moment of saturation Ms oriented along the field. As the intensity H of the external magnetic field is reduced, the magnetic moment M of the sample will decline along curve I primarily because of the appearance and growth of domains whose magnetic moment is oriented against the field. The growth of the domains is due to the movement of the domain walls. This movement is hindered by the presence in the sample of various defects (such as impurities or inhomogeneities) that strengthen the domain walls at some points; very strong magnetic fields are required to displace them. Therefore as the field H drops to zero, the so-called residual magnetic moment Mr (point B ) is retained. A sample can be completely demagnetized only in a sufficiently strong field of opposite direction, which is called a
coercive field (coercive force) Hc (point C). As the magnetic field of reverse orientation is further increased, the sample is once again magnetized along the field to saturation (point D ). Magnetic reversal (from point D to point A) takes place along curve II. Thus, as the field undergoes a cyclical change, the curve characterizing the change in the magnetic moment of the sample forms a magnetic hysteresis loop. If the field H changes cyclically with such limits that magnetization does not reach saturation, a nonlimiting magnetic hysteresis loop is produced (curve III). By reducing the extent of the change in field H to zero, the sample can be completely demagnetized (point O can be reached). The magnetization of the sample from point O proceeds along curve IV.
Figure 1. Magnetic hysteresis loop for a ferromagnet: H is the intensity of the magnetic field, M is the magnetic moment of the sample, Hc is the coercive field, Mr is the residual magnetic moment, and Ms is the saturation magnetic moment. The nonlimiting hysteresis loop is shown by the dotted line. The domain structure of the sample for certain points on the loop is shown schematically.
In magnetic hysteresis different values of the magnetic moment M correspond to the same value of the external magnetic field intensity H. This nonuniqueness is due to the influence of the states of the sample that precede the given state (that is, to the magnetic prehistory of the sample).
The shape and size of magnetic hysteresis loops and the quantity Hc may range within wide limits in various ferromagnets. For example, in pure iron, Hc = 1 oersted, and in a magnico alloy Hc = 580 oersteds. A magnetic hysteresis loop is strongly affected by processing of the material, during which the number of defects is changed (Figure 2).
The area of a magnetic hysteresis loop is equal to the energy lost in the sample in one cycle of field change. This energy ultimately is used to heat the sample. Such energy losses are called hysteresis losses. In cases when losses to hysteresis are undesirable (for example, in transformer cores and in the stators and rotors of electrical machinery), magnetically soft materials with a low Hc and a small hysteresis loop area are used. On the other hand, magnetically hard materials with a high Hc are required to manufacture permanent magnets.
As the frequency of the alternating magnetic field (the number of magnetic reversal cycles per unit time) increases, other losses caused by eddy currents and magnetic viscosity are added to hysteresis losses. At high frequencies the area of the hysteresis loop increases correspondingly. Such a loop is sometimes called a dynamic loop, in contrast to the static loop described above.
Many other properties of a ferromagnet, such as electrical resistance and mechanical deformation, depend on the magnetic moment. A change in magnetic moment also brings about a change in these properties—for example, gal-vanomagnetic and magnetostrictive hysteresis, respectively, are observed.
Dielectric hysteresis. Dielectric hysteresis is usually observed in ferroelectrics such as barium titanate. The dependence of the polarization P on the electrical field intensity E in ferroelectrics (Figure 3) is similar to the dependence of M on H in ferromagnets and is due to the presence of spontaneous electrical polarization and electrical domains and to the difficulty of rearranging the domain structure. Hysteresis losses make up a large part of dielectric losses in ferroelectrics.
Insofar as other characteristics of ferroelectrics such as deformation are associated with polarization, other types of hysteresis, such as piezoelectric hysteresis (Figure 4) and the hysteresis of the electrooptical effect, are related to dielectric hysteresis. In some cases double dielectric hysteresis loops are observed (Figure 5). This is due to the fact that a phase transition involving rearrangement of the crystalline structure takes place in the sample under the influence of the electrical field. This type of dielectric hysteresis is closely related to the hysteresis during phase transitions.
Figure 2. Effect of mechanical and thermal treatment on the form of the magnetic hysteresis loop for permalloy: (1) after cold hardening, (2) after annealing, (3) curve for soft iron (for comparison)