In this article we will discuss about the phenomenon of magnetic hysteresis and why it occurs in ferromagnetic materials.
The transition metals Fe, Co, and Ni, rare earth metals such as Gd, and a few oxides such as CrO2 and ErO display very large and permanent magnetization. In fact, these substances remain magnetized even when the field is removed. Their magnetization is not reversible; that is, it depends on how the field is applied. The magnetization curve for a ferromagnetic material is shown schematically in Fig. 4.2.
As the applied field H is increased, B begins to increase slowly. Then, the slope rises sharply and B rapidly increases until the saturation induction, Bs, is attained. With further increase in the field, the slope levels off. Upon decreasing the field, the original curve is not retraced. At H equal to zero, the specimen is still magnetized and B = Br, the remanent induction.
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This lagging of the flux density B with respect to the magnetizing field H is called hysteresis. If the magnetizing field H is now increased further in the reverse direction, the value of B decreases further and becomes zero when H reaches Hc. Hc, is known as coercive Field or coercivity of the specimen. Thus, coercivity is a measure of magnetic field required to destroy completely the residual magnetism of the specimen.
If H is now made negative and the specimen saturated in the reverse direction before returning to zero field, the symmetric curve shown in Fig. 4.2 is obtained with a saturation, coercive force, and remanence equal to those on the positive side. Such irreversible, double-valued hysteresis behavior is characteristic of the magnetic behavior of ferromagnetic materials and is known as hysteresis loop or B-H curve.
The work required to go around the hysteresis loop once is proportional to the area enclosed by the curve. If H is brought back to zero and the cycle repeated at less than saturation, a similar hysteresis curve of smaller area is obtained.
When successive loops retrace preceding ones, the material is said to be in a cyclically magnetized condition. For electromagnet core materials, values of Br and Hc are determined from a hysteresis loop taken when material is cyclically magnetized. Permanent values, however, are taken from the first hysteresis loop, since permanent magnets need to be magnetized only once.
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The hysteresis loop equals the work which is necessary to reverse the direction of magnetization. The actual shape and area of the loop depend on the internal structure and composition of the ferromagnetic substance. Thus, work done (W) = (area of B-H loop) J/m3/cycle. It may be noted that while calculating the actual area, scales of B and H should be taken into consideration e.g., if scales are-
1 cm = x amp turn/m and 1 cm = y wb/m2 for H and B respectively, then
W = xy (area of B-H) J/m3/cycle
Steinmetz developed an empirical relationship to express this loss in following terms:
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Ph = KhBlmax f
where, Ph = hysteresis loss in watt/m3,
Bmax = maximum flux density in wb/m2,
Kh = hysteresis co-efficient,
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l = Steinmetz co-efficient and
f = frequency of magnetization in Hz.
The value of Steinmetz co-efficient ‘l’ is approximately 2 for all magnetic materials. The transformer, generator cores and armatures of the electric motors etc. which are subjected to rapid reversals of magnetization should be made of such substances which have low co-efficient in order to reduce the hysteresis loss.
Weiss Field:
The first questions one might ask about ferromagnetic materials is the source of the large magnetization. The saturation magnetization is so large that virtually all of the magnetic dipoles in a ferromagnetic material must be lined up with the field. Paramagnetism indicated that such behavior would not occur, due to the disruption of the alignments by the thermal energy, if pm.
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H were the total energy of the dipole. To make our model fit the facts, it is necessary to add a term to the energy which will make the dipoles all line up. By adding a new energy term we are actually making the same assumption as Weiss since he was the first to postulate the existence of such a field. It is given by-
Hw = λM … (6)
The constant λ is called the Weiss constant. For applied fields below saturation, we can add the Weiss field to H, in Equation 5,
and solve for (M/H)
The above equation is known as Curie-Weiss law. It clearly indicates that at Curie temperature, the susceptibility tends to be infinite i.e. the interaction of the individual magnetic moments reinforce each other causing them to align parallel at T = TC. Below Curie temperature TC, the material is spontaneously magnetized to a degree depending upon the temperature. The magnetization approaches saturation value as the temperature reaches absolute zero.
Above TC, spontaneous magnetization ceases and the ferromagnetic material transform to paramagnetic material. The Weiss constant λ is usually of the order of 103, which is very large as compared to the theoretically calculated value which considers that the field is arising due to the interaction of atomic dipoles. This discrepancy can be overcome by considering the quantum mechanical.
A quantum mechanical explanation for the Weiss field, proposed by Heisenberg, involves an exchange interaction between neighbouring electron spins. Overlapping wave functions can lead to a decrease in over-all energy in certain cases, and therefore favour, in this case, a parallel alignment of spins. In some materials (antiferromagnetic) the exchange energy leads to an opposite or antiparallel spin alignment.
The energy of interaction which causes adjacent dipoles to line up is called the exchange interaction energy and is the function of the ratio of the atomic diameter to the 3d orbital diameter.
For ferromagnetic materials, this ratio lies in the range 1.4 to 2.7 and for these materials (e.g. Fe, Co, Ni) the exchange interaction energy is positive. For antiferromagnetic materials (anti parallel alignment of magnetic dipoles as in Mn and Cr), the exchange energy is negative.
Having explained the magnitude of xm for ferromagnetic materials, we can now consider the hysteresis curve (Fig. 4.2). The question arises as to why a ferromagnetic material may be magnetized, or demagnetized at zero fields. It is necessary to explain why B and M depend on how H is applied (for any value of H up to saturation, B and, therefore, M may have one of many values, depending on how we have gone around the curve).
Magnetic Domains:
To provide an explanation for the hysteresis effects observed in ferromagnetic materials. Weiss offered a second novel idea- magnetic domains. A ferromagnetic material is divided up into small regions, known as domain which acquires a net magnetic moment due to exchange interaction among large number of atomic/molecular dipoles.
A domain has a volume of the order of 10-8 m3 to 10-12 m3 and may contain about 1015 or more atomic/molecular dipoles. Each domain is magnetized to the maximum possible value. The direction of magnetization of each of the domain depends upon the crystalline state of the substance.
It is found that ferromagnetism is exhibited only by crystalline substances and the magnetization of the domain is parallel to the axis of symmetry of the crystal. Thus, the ferromagnetic substances are intrinsically magnetized even in the absence of external magnetic field. However, the net magnetic moment of the sample is zero, because the domains within the sample are randomly aligned and the material as a whole has zero magnetization.
To give the material a net magnetization, one direction must predominate in the domains. There are two possible ways to magnetize a domain structure. The most obvious is to permit rotation of the individual domain magnetization. However, less energy is required if domains initially parallel to the applied field grow at the expense of their less favourably oriented neighbours.
Domain Motion:
In Fig. 4.5 the concept of domain growth and rotation is used to explain the magnetization curve. Initially, no domain growth occurs as the field H is increased. Then the favourably oriented domains grow and the magnetic induction B increases rapidly. Finally, domain growth stops as we enter the saturation region and rotation of the remaining unfavourably aligned domains occurs. Since domain rotation requires higher energy than domain growth the slope of the B versus H curve decreases.
When the field is removed, the specimen remains magnetized. Although the domains tend to rotate back, the large aligned domains do not easily revert to the original random arrangement. If a reverse field (-H) is applied, the domain structure may be changed to produce a resultant zero magnetic induction. The magnitude of the applied field required is equal to coercive force Hc. Once magnetized, the state H = 0, B = 0 is no longer attainable by simply changing the applied field.
In ferromagnetic materials thermal energy can overcome the Weiss field at some high temperatures called the Curie temperature. Above their Curie temperatures, ferromagnetic materials become paramagnetic.
Ferromagnetism is due to the mutual self-alignment of groups of atoms carrying permanent magnetic moments in same direction. These elementary permanent moments are also responsible for paramagnetism; hence the new aspect of a discussion of ferromagnetism is that of describing why the atomic moments should be self-aligning without the help of an outside field.
Before a study of the basis of the ferromagnetic interaction is begun, a review of some of the physical characteristics of the ferromagnetic elements is worthwhile. Some of these data are presented in Table 4.3.
An examination of these data shows that ferromagnetism is not exclusively characteristic of any particular crystal type, since all the simple metallic crystal types are represented. The elements have a wide variety of Curie temperatures and a considerable range in magnetic moment. The one common feature is the electronic structure. Three of these elements are found in the 3d transition group, the other in the 4f rare-earth transition group. The existence of partly filled d or f shells is essential in modern theories of ferromagnetism.
The Temperature Dependence of the Magnetization:
Thermal motion of the atoms affects ferromagnetic properties in several ways. One of the most important is the effect on the degree of magnetization. This effect is most pronounced in the vicinity of the Curie temperature, but it is also observable far below the Curie temperature.
The spontaneous magnetization of ferromagnets is caused, we have seen, by the interaction between neighbouring atoms which tends to align their spins. When this effect is so strong that all adjacent spins are aligned, the magnetization of the material has its maximum value.
The long-range alignment results from both the strong nearest neighbour interactions and the continuity of the crystal. Thermal vibrations of the atoms, however, tend to misalign the spins. Hence the maximum magnetization (which is characteristic of complete alignment of every spin) is observed only at the lowest possible temperature, i.e., absolute zero.
At every higher temperature the magnetization has a lower value, until it becomes zero at the Curie temperature. The magnetization as function of temperature for ferromagnetic materials is shown in Fig. 4.6. The magnetization decreases very slowly as the temperature is first raised above absolute zero. The curve drops more steeply at higher temperatures, until it finally falls precipitously to zero at the Curie temperature.
Above the Curie temperature the ferromagnetic solids exhibit paramagnetism. They have a large susceptibility just above Tc, but they do not all obey a Curie-Weiss law, Ni obeys a Curie-Weiss law best, but just above its Curie temperature its susceptibility deviates somewhat from exact agreement with this law. This behavior just above Tc has an interesting interpretation.
It shows that, although thermal motion of the atoms has destroyed long-range order of the spin moments, some spin order of a much weaker character still persists. It is a kind of short-range spin order in which a given atom is surrounded by a small island in which the spins are more or less aligned. This phenomenon presumably exists for all ferromagnetic solids just above Tc.
Effect of Alloying Element on Magnetization:
Alloying a ferromagnetic material with another element causes changes in the magnetic properties. One important change is that of the saturation magnetization; hence, with alloying, the number of Bohr magnetrons averaged over the entire number of lattice atoms changes.
The way in which alloying affects the saturation magnetization depends in part on the type of structure formed upon alloying; perhaps the simplest structure is the solid solution. Of these, the Ni-Cu solution has some of the most easily interpreted features. Ni has ten 3d + 4s electrons which are thought to fill the overlapping d and s bands in such a way that one of the half bands of the 3d state is completely full and the other lacks 0.6 of an electron per atom of being filled.
When an atom of Cu is substituted for an atom of Ni in the solid solution, eleven 3d + 4s electrons are substituted for the original ten; i.e., the solid has gained an extra electron by this substitution. This electron must go into the partially empty half band, filling it slightly. Hence the addition of Cu atoms ought to reduce the net magnetization.
In fact, when Cu atoms have been substituted for 60 per cent of the Ni atoms, both half bands ought to be just full and the magnetization should have dropped to zero. Adding divalent Zn causes the decreases to occur more rapidly, trivalent Al even more rapidly, etc. Pd, which has an electronic structure in the 4d series analogous to that of Ni in the 3d, causes no change in NB.
Similar changes for other alloys of Co, Fe, and Ni with each other and with other metals of the 3d transition series have been observed.