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A Closer Look at the Hysteresis Loop for Ferromagnets - a Survey of Misconceptions and Misinterpretations in Textbooks Hilda W

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A Closer Look at the Hysteresis Loop for Ferromagnets - a Survey of Misconceptions and Misinterpretations in Textbooks Hilda W A closer look at the hysteresis loop for ferromagnets - A survey of misconceptions and misinterpretations in textbooks Hilda W. F. Sung and Czeslaw Rudowicz Department of Physics and Materials Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong SAR, People’s Republic of China This article describes various misconceptions and misinterpretations concerning presentation of the hysteresis loop for ferromagnets occurring in undergraduate textbooks. These problems originate from our teaching a solid state / condensed matter physics (SSP/CMP) course. A closer look at the definition of the 'coercivity' reveals two distinct notions referred to the hysteresis loop: B vs H or M vs H, which can be easily confused and, in fact, are confused in several textbooks. The properties of the M vs H type hysteresis loop are often ascribed to the B vs H type loops, giving rise to various misconceptions. An extensive survey of textbooks at first in the SSP/CMP area and later extended into the areas of general physics, materials science and magnetism / electromagnetism has been carried out. Relevant encyclopedias and physics dictionaries have also been consulted. The survey has revealed various other substantial misconceptions and/or misinterpretations than those originally identified in the SSP/CMP area. The results are presented here to help clarifying the misconceptions and misinterpretations in question. The physics education aspects arising from the textbook survey are also discussed. Additionally, analysis of the CMP examination results concerning questions pertinent for the hysteresis loop is provided. Keywords: ferromagnetic materials; hysteresis loop; coercivity; remanence; saturation induction 1. Introduction presentation of the magnetic hysteresis loop for ferromagnetic materials. Having identified some During years of teaching the solid state physics misconceptions existing in several textbooks (SSP), which more recently become the condensed currently being used for our SSP/CMP course at matter physics (CMP) course, one of us (CZR), CityU, we have embarked on an extensive literature prompted by questions from curious students survey. Search of physics education journals have (among others, HWFS), has realized that textbooks revealed only a few articles dealing with magnetism, contain often not only common misprints but e.g. Hickey & Schibeci (1999), Hoon & Tanner sometimes more serious misconceptions. The latter (1985). Interestingly, a review of middle school occur mostly when the authors attempt to present a physical science texts by Hubisz (http://www.psrc- more advanced topic in a simpler way using online.org/curriculum/book.html), which has schematic diagrams. One such case concerns recently come to our attention, provides ample 1 examples of various errors and misconceptions loop for ferromagnets: (i) B vs H curve or (ii) M vs together with pertinent critical comments. However, H curve. In both cases, the ‘coercivity’ (‘coercive none of these sources have provided clarifications of force’) is defined as the point on the negative H- the problems in question. To find out the extent of axis, often using an identical symbol, most these misconceptions existing in other physics areas, commonly Hc. Yet it turns out that the two we have surveyed a large number of available meanings of ‘coercivity’ are not equivalent. In some textbooks pertinent for solid state / condensed textbooks the second notion of coercivity (M vs H) matter, general physics, materials science, and is distinguished from the first one (B vs H) as the magnetism / electromagnetism. Several pertinent ‘intrinsic’ coercivity Hci. An apparent identification encyclopedias and physics dictionaries have also of the two meanings of coercivity Hc (B vs H) and been consulted. The survey has given us more than Hci (M vs H) as well as of the properties of soft and we bargained for, namely, it has revealed various hard magnetic materials have lead to other substantial misconceptions than those misinterpretation of Hc as the point on the B vs H originally identified in the SSP/CMP area. The hysteresis loop where the magnetization is zero. results of this survey are presented here for the This is evident, for example, in the statements benefit of physics teachers (as well as researchers) referring to Hc as the point at which “the sample is and students. The textbooks, in which no relevant again unmagnetized” (Serway, 1990) or “the field misconceptions and/or confusions were identified, required to demagnetize the sample” (Rogalski & are not quoted in text, however, they are listed for Palmer, 2000). Other misconceptions identified in completeness in Appendix I in order to provide a our textbook survey concern: 'saturation induction comprehensive information on the scope of our Bsat’ and the inclination of the B vs H curve after survey. saturation, shape of the hysteresis loop for soft In order to provide the counterexamples for the magnetic materials, and presentation of the misconceptions identified in the textbooks, we have hysteresis loop for both soft and hard ferromagnets reviewed a sample of recent scientific journals in the same diagram. Minor problems concerning searching for real examples of the magnetic terminology and the drawbacks of using schematic hysteresis loop, beyond the schematic diagrams diagrams are also discussed. Analysis of the found in most textbooks. To our surprise a number condensed matter physics examination results of general misconceptions concerning magnetism concerning questions pertinent for the hysteresis have been identified in this review. The results of loop is provided to illustrate some popular this review are presented in a separate article, which misconceptions in students' understanding. focuses on the research aspects and provides recent literature data on soft and hard magnetic materials 2. Two notions of coercivity (Sung & Rudowicz, 2002; hereafter referred to as S & R, 2002). For a ferromagnetic material, the magnetic The root of the problem appears to be the induction (or the magnetic field intensity) inside the existence of two ways of presenting the hysteresis 2 sample, B, is defined as (see, e.g. any of the books In Fig. 1 we present schematically the hysteresis listed in References): curves for a ferromagnetic material together with B = H + 4πM (CGS); the definitions of the terms important for technological applications of magnetic materials. B = µo ( H + M ) (SI) (1) The two meanings of ‘coercivity’ Hci and Hc as where M is the magnetization induced inside the defined on the diagrams: (a) the magnetization M vs sample by the applied magnetic field H. In the free applied field H and (b) magnetic induction (or flux ≡ µ space: M = 0 and then in the SI units: B o H, density) B vs H, respectively, are clearly µ µ π where o is the permeability of free space ( o = 4 x distinguished. Both curves have a similar general -7 -2 -2 -1 10 [m kg A sec ]; note that the units [Hm ] and characteristic, except for one crucial point. After the -1 -1 [WbA m ] are also in use). The standard SI units saturation point is reached, the M curve becomes a are: B [tesla] = [T], H and M [A/m], whereas B straight line with exactly zero slope, whereas the [Gauss] = [G], H [Oersted] = [Oe], and M [emu/cc] slope of the B curve reflects the constant magnetic (see, e.g. Jiles, 1991; Anderson, 1989). Both the susceptibility and depends on the scale and units CGS units and the SI units are provided since the used to plot B vs H (see below). In other words, the CGS unit system is in use in some textbooks B vs H curve does not saturate by approaching a surveyed and comparisons of values need to be made later. Magnetic induction B = µo(H + M) (a) (b) Fig. 1. Hysteresis curves for a ferromagnetic material: (a) M vs H: Mr is the remanent magnetization at H = 0; Hci is the intrinsic coercivity, i.e. the reverse field that reduces M to zero; Ms is the saturation magnetization; (b) B vs H: Br is the remanent induction (or ‘remanence’) at H = 0; Hc is the coercivity, i.e. the reverse field required to reduce B to zero (adapted from Elliot, 1998). 3 limiting value as in the case of the M vs H curve. H reaches again zero, the sample still retains some For an initially unmagnetized sample, i.e. M ≡ 0 magnetization due to the existence of domains still at H = 0, as H increases from zero, M and B aligned in the original direction of the applied field increases as shown by the dashed curves in Fig. 1 Dalven (1990). The respective values at H = 0 are (a) and (b), respectively. This magnetization process defined (see, e.g. Kittel (1996), Elliott (1998), is due to the motion and growth of the magnetic Dalven (1990), Skomski & Coey (1999), Jiles domains, i.e. the areas with the same direction of (1991)) as the remnant magnetization Mr, Fig. 1 the local magnetization. For a full discussion of the (a), and the remnant induction Br, Fig. 1 (b). To formation of hysteresis loop and the nature of reduce the magnetization M and magnetic induction magnetic domains inside a ferromagnetic sample B to zero, a reverse field is required known as the one may refer to the specialized textbooks listed in coercive force or coercivity. The soft and hard the References, e.g. Kittel (1996), Elliott (1998), magnetic materials are distinguished by their small Dalven (1990), Skomski & Coey (1999). Here we and large area of the hysteresis loop, respectively. provide only a brief description of these aspects. A By definition, the coercive force (coercivity) distinction must be made at this point between the defined in Fig. 1 (a), and that in Fig. 1 (b) are two magnetically isotropic materials, for which the different notions, although their values may be very magnetization process does not depend on the close for some materials.
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