History of Magnetism and Basic Concepts

Abstract

Magnetism is a microcosm of the history of science over more than two millennia. The magnet allows us to manipulate a force field which has catalyzed an understanding of the natural world that launched three revolutions. First came the harnessing of the directional nature of the magnetic force in the compass that led to the exploration of the planet in the fifteenth century. Second was the discovery of the relation between electricity and magnetism that sparked the electromagnetic revolution of the nineteenth century. Third is the big data revolution that is currently redefining human experience while radically transforming social interactions and redistributing knowledge and power.

The emergence of magnetic science demanded imagination and observational acuity, which led to the theory of classical electrodynamics. The magnetic field is associated with electric currents and the angular momentum of charged particles in special materials. Our current understanding of the magnetism of electrons in solids is rooted in quantum mechanics and relativity. Yet only since about 1980 has fundamental theory underpinned rational design of new functional magnetic materials and the conception of new spin electronic devices that can be reproduced on ever smaller scales, leading most notably to the disruptive, 60-year exponential growth of magnetic information storage. The development of new magnetic concepts, coupled with novel materials, device and machine designs has become a rich source of technical innovation.

Appendix: Units

By the middle of the nineteenth century, it was becoming urgent to devise a standard set of units for electrical and magnetic quantities in order to exchange precise quantitative information. The burgeoning telegraph industry, for example, needed a standard of electrical resistance to control the quality of electrical cables. Separate electrostatic and electromagnetic unit systems based on the centimeter, the gram and the second had sprung into existence, and Maxwell and Jenkin proposed combining them in a coherent set of units in 1863. Their Gaussian cgs system was adopted internationally in 1881. Written in this unit system, Maxwell’s equations relating electric and magnetic fields contain explicit factors of c, the velocity of light. Maxwell also introduced the idea of dimensional analysis in terms of the three basic quantities of mass, length, and time. The magnetic field H and the induction B are measured, respectively, in the numerically identical but dimensionally different units of oersted (Oe) and gauss (G).

Another basic unit, this time of electric current, was adopted in the Système International d’Unités (SI) in 1948. The number of basic units and dimensions in any system is an arbitrary choice; the SI (International System of Units) uses four insofar as we are concerned, the meter, kilogram, second, and ampere (or five if we include the mole). The system has been adopted worldwide for the teaching of science and engineering at school and universities; it embodies the familiar electrical units of volt, ampere, and ohm for electrical potential, current, and resistance. Maxwell’s equations written in terms of two electric and two magnetic fields contain no factors of c or 4π in this system (Eq. 7), but they inevitably crop up elsewhere. B and H are obviously different quantities. The magnetic field strength H, like the magnetization M, has units of Am⁻¹. The magnetic induction B is measured in tesla (1 T ≡ 1 kgs²A⁻²). Magnetic moments have units of Am², clearly indicating the origin of magnetism in electric currents and the absence of magnetic poles as real physical entities. The velocity of light is defined to be exactly 299,792,458 ms⁻¹. The two constants μ₀ and ε₀, the permeability and permittivity of free space, are related by μ₀ε₀ = c², where μ₀ was 4π 10⁻⁷ kgs⁻²A⁻² according to the original definition of the ampere. However, in the new version of SI, which avoids the need for a physical standard kilogram, the equality of μ₀ and 4π 10⁻⁷ is not absolute, but it is valid to ten significant figures.

Only two of the three fields B, H, and M are independent (Fig. 4). The relation between them is Eq. 8, B = μ₀(H + M). This is the Sommerfeld convention for SI. The alternative Kenelly convention, often favored by electrical engineers, defines magnetic polarization as J = μ₀M, so that the relation becomes B = μ₀H + J. We follow the Sommerfeld convention in this Handbook. The magnetic field strength H is not measured in units of Tesla in any generally accepted convention, but it can be so expressed by multiplying by μ₀.

At the present time, Gaussian cgs units remain in widespread use in research publications, despite the obvious advantages of SI. The use of the cgs system in magnetism runs into the difficulty that units of B and H, G and Oe, are dimensionally different but numerically the same; μ₀ = 1, but it normally gets left out of the equations, which makes it impossible to check whether the dimensions balance. Table 1 lists the conversion factors and units in the two systems. The cgs equivalent of Eq. 8 is B = H + 4πM. The cgs unit of charge is defined in such a way that ε₀ = 1/4πc and μ₀ = 4π/c so factors of c appear in Maxwell’s equations in place of the electric and magnetic constants. Convenient numerical conversion factors between the two systems of units are provided in Table 1.

Table 1 Numerical conversion factors between SI and cgs units

Theoretical work in magnetism is sometimes presented in a set of units where c = ℏ = k_B = 1. This simplifies the equations, but does nothing to facilitate quantitative comparison with experimental measurements.