Magnetic Properties Of Solids

Type of physical science: Condensed matter physics

Field of study: Solids

The magnetic properties of solids are caused by electron and nuclear spins and motions and their interaction with specific chemical bonds and crystal structures. The magnetic properties include the bulk properties of diamagnetism, paramagnetism, and ferromagnetism, and spectroscopic interactions such as nuclear magnetic resonance.

Overview

The magnetic properties of all materials are caused by charged particles that move or rotate. The various magnetic properties depend on how these particles behave, the nature of their surroundings or chemical environment, and how they react to external magnetic fields in their particular chemical environments.

A free atom's reaction to a magnetic field is fairly simple. Within an atom, there are two sites of the magnetic properties, the electrons and the nucleus. Electrons have an orbital motion and a spin motion; both of these motions generate magnetic fields with a positive and a negative pole. The orbital motion of the electron constitutes a circulating electrical charge or current, which generates a magnetic field exactly as a current through a loop of wire generates a magnetic field. The magnetic fields generated by a large number of atoms packed together in a material usually tend to cancel one another; such material is termed nonmagnetic. If an external magnetic field is applied, there is a small bias toward aligning the orbital motions and their magnetic poles to oppose the applied field. This response is weak, for the natural randomizing of the orbital motions must be overcome by the applied field. The stronger the applied field, the greater the alignment of the orbitally induced magnets. The response is linear and is usually about one-millionth the strength of the imposed field. This behavior is termed "diamagnetism."

In addition to the orbital motion, each electron has a spin with a quantum value of +/-0.5. The spin also allows the electron to behave as a magnet. When there are two electrons within an orbital, the two have different spin quantum numbers and are magnetically opposed to each other, thereby canceling out each other. Whenever there is a single--and therefore unpaired--electron within the orbital, the electron spin results in an uncanceled contribution to the magnetic response of the atom. The strength of the magnetic field generated by spin is greater than that generated by orbital motion. The spin direction can give two orientations to this magnetic field--parallel to that of the orbital motion (and therefore strengthening it) or antiparallel to it (and therefore opposing or weakening it). The two spin directions have slightly different energy levels; the energy level with the spin direction antiparallel to the orbital motion is lower and therefore more stable. For a material with unpaired electrons, the response to an applied field involves the tendency to orient spins to reinforce the magnetic field. This behavior is termed "paramagnetism" and is also a linear function of the strength of the applied field. As is the case with diamagnetism, the constant of proportionality is on the order of one one-millionth.

Both diamagnetic and paramagnetic behavior involve orientation of orbital and spin motions, which are basically unaligned prior to the application of the applied field. In some solids, however, the density of atoms with unpaired electrons is great enough that there is a spontaneous ordering of the spin directions within the crystal. This behavior is termed "ferromagnetism," for it is found in natural solids that are very rich in iron. Ferromagnetism involves a consistent orientation of spin directions; frequently, one atom is canceled by another with respect to the spins. These latter types of ferromagnetic materials are referred to as being antiferromagnetic or ferrimagnetic. The character of the spin alignment depends on the character of chemical bonding and the nature of the crystal structure.

The principles of ferromagnetism and ferrimagnetism can be illustrated by looking at two of the most common iron oxide minerals: hematite (Fe₂O₃) and magnetite (Fe₃O₄). Both minerals are composed of closely packed oxygen ions. Between these anions (negatively charged ions) are two kinds of openings where the cations (positively charged ions) of iron may fit. One of these sites is surrounded equidistantly by four oxygen ions in the shape of a tetrahedron and is therefore called a tetrahedral site. The other site, called an octahedral site, is surrounded equidistantly by eight oxygen ions which correspond to the corners of an octahedron. Within the close-packed structure, both the oxygens and the cation sites occur in distinct layers. There are as many octahedral holes as there are oxygens and twice as many tetrahedral holes as there are oxygens.

In hematite, the iron ions occur only in the octahedral sites and fill only two-thirds of these sites. All the tetrahedral sites are empty. Within the layers of octahedral sites, the spin directions of adjacent iron ions are oriented antiparallel and therefore tend to cancel out each other. This internal cancellation of aligned spin directions is antiferromagnetic.

Within magnetite's unit cell (the fundamental repeating unit of the crystal), there are thirty-two oxygens, sixty-four tetrahedral sites, and thirty-two octahedral sites. The different sites occur as layers. In magnetite, there are twenty-four cations in the unit cell--sixteen Fe⁺³ ions and eight Fe⁺² ions. The Fe⁺³ ions are distributed equally among both octahedral and tetrahedral sites. Rather than canceling electron spin directions within each layer, all the spins of the Fe⁺³ ions in the octahedral layers are aligned together and oppose the uniformly aligned spin directions of the Fe⁺³ ions in the tetrahedral layers. Thus, the cancellation of Fe⁺³ ions in magnetite occurs between adjacent layers rather than within each layer as in hematite. The Fe⁺² ions still need to be accounted for, however; they all go into the tetrahedral sites and oppose the directions of the Fe⁺³ ions in those layers. Thus, magnetite has a lack of balance in the cancellation of spin directions and is highly magnetic. This structural situation is termed "ferrimagnetic."

The spontaneous ordering within ferromagnetic substances occurs only within a very small volume of a crystal called a domain. Crystals below 1 micron (10 ^-6 meters) in size may be composed of a single domain, but larger ferromagnetic crystals are multidomain, with adjacent domains tending to cancel out each other. Whereas single domain solids are often very stable permanent magnets, large multidomain solids may not show remanent magnetism because of the mutual cancellation of the magnetic moments of the individual domains.

When an external magnetic field is applied to a ferromagnetic solid, the response is similar to paramagnetism in character but is greater in strength. The applied field causes a slight reorientation of spin directions of the solid; if the field is removed quickly, however, the solid returns to its original state. If the ferromagnetic substance is subjected to a stronger magnetic field or to a low magnetic field for a long enough time, the resulting stress will result in recrystallization of the magnetic domains. In the original solid, the domains tended to cancel one another; recrystallization of the solid results in the growth of domains that are oriented parallel to the imposed magnetic field and the reduction in size of domains that are oriented antiparallel to the field. Since recrystallization involves breaking and rebuilding of chemical bonds, this magnetic response does not disappear instantly upon removal of the imposed magnetic field. The result is remanence, a magnetic record of the direction of the imposed field. Remanence may be removed by recrystallization and reordering of domains with or without the imposition of a new magnetic field.

The difficulty in removing the remanence is measured by the coercive force or coercivity, which is the strength of a reversed magnetic field necessary to remove the remanence rapidly. The coercive force is related to the strength of the chemical bonds in the solid and the activation energy necessary to initiate a structural reorganization in the crystal. If the activation energy is high, a strong magnetic field is necessary to effect the reordering of the magnetic spin directions. If the activation energy is low, the recrystallization and reordering can be accomplished even at low magnetic fields. If the coercive force is low enough, the internal drive for mutual cancellation of the domains will be enough to effect recrystallization and the loss of remanence, given enough time.

Magnetic effects in solids may also be caused by the nuclei of atoms. Although the electrons give the major response in magnetic materials, magnetic fields also induce weak responses in certain nuclei. These responses are caused by the spin motion of the nucleus. In a magnetic field, there is a tendency for the nuclear spin directions to align with the imposed field. Since the spinning nuclei have an angular momentum, they do not line up exactly with the field. Instead, they precess around an axis defined by the magnetic field direction, behaving like a child's top spinning in the earth's gravitational field. The rate of this precession is related to the strength of the imposed field.

The nuclear spin can align either with or against the imposed field. There is a very small difference in the energy of these two states, and this energy difference forms the basis for nuclear magnetic resonance (NMR) spectroscopy. When a beam of electromagnetic radiation is sent through the material, the wavelength comparable to the energy level of a quantized energy transition within the material will be absorbed. Since the difference in the energy levels of the two nuclear spin states is very small, this absorption occurs at radio wavelengths.

Applications

The atomic level controls on the magnetic properties of solids have allowed scientists to make major technological advances in understanding the nature of crystalline solids and the structures of a variety of complex organic compounds. Furthermore, nuclear magnetic resonance spectroscopy has provided methods of measuring magnetic fields and a system of imaging in addition to the classical X-ray technique.

Much effort has been spent on the synthesis of new materials with desirable magnetic properties. Among these materials are nonmagnetic ones that are composed of normally magnetic material. Nonmagnetic steel is strong and resilient but cannot be magnetized. Another application is the development of mu-metal, a material with such high permeability that it can screen out and remove magnetic fields. Perhaps the most important applications have been in the development of very strong and very high-coercivity magnets. These developments have been accomplished through the discovery of new alloys, which combine high coercivities and strong spin alignments.

The magnetic properties of solids depend on their crystalline structures. Like other crystalline materials, ferromagnetic materials respond to imposed mechanical stress. The general name for this response is piezomagnetism. When a ferromagnetic material is placed under pressure, elastic deformation within the solid may change the susceptibility of the material; in many ferromagnetic solids, this deformation can produce an imbalance in the domain structure, thereby creating a remanence related to the strain. This principle has been used in the laboratory and in field applications to monitor strain in rocks related to increased stress. Scientists have applied this research to detect local changes in the earth's magnetic field prior to rock failure in earthquakes or large mass movements. Conversely, the application of a strong magnetic field may cause a deformation and small change in the material's shape. This property has been used successfully to disaggregate very fine-grained iron ores: A rapidly alternating magnetic field causes crystal deformation sufficient to break the rock into individual minerals.

The interaction of matter with applied magnetic fields can also involve the nuclei of atoms. Perhaps the simplest example of this effect is the proton precession magnetometer, which is used to measure total magnetic fields. A proton- or hydrogen-rich material such as oil or kerosene is subjected to a strong magnetic field created by a current in a loop of wire. The imposed field causes an alignment in the proton spin directions. When the imposed field is removed, the proton spins will precess around the earth's magnetic field direction. This precession can be detected because the moving poles of the spinning protons induce an electrical current in a loop of wire around the material. Since the rate of precession is related to the magnitude of the earth's field, the magnetometer can rapidly measure the variations in the strength of the field that result from variations caused by latitude and longitude or from the presence of various rock types or ores.

The applications of nuclear magnetic properties to spectroscopy have depended on the technology to create strong magnetic fields and to monitor radio wavelength absorption through materials. Since the energy-level differences for the nuclear spin directions depend upon the strength of the imposed magnetic field, one can investigate the material by changing the field or by changing the radio frequency. The response of a "free" atom's nucleus to these factors depends on the structure of the nucleus. Since an atom within a chemical compound is surrounded by the electrical and magnetic fields of other atoms or ions, the exact behavior of the NMR spectra is related to the chemical environment of the nucleus. Thus, NMR spectroscopy has been used extensively to refine scientists' understanding of the chemical structures of many compounds. Moreover, since NMR can detect particular nuclei, it can define the presence or position of some materials that are nearly invisible to X rays. For example, NMR is used in medicine to detect the location and abnormalities of soft tissue.

Context

The study of the magnetic properties of matter spanned many centuries. Major advances were made after the discovery of the relationships between electrical and magnetic phenomena by Hans Christian Orsted in 1820. Chief among the early advances was the work of the great experimentalist Michael Faraday, who discovered electromagnetic induction, defined diamagnetic and paramagnetic behavior, developed the first electrical motor, demonstrated that magnetism could affect electromagnetic radiation, and initiated the idea that the effects of electrical charges and currents and of magnetic poles could be described in terms of an altered region of space defined by lines of force. This last idea was the basis for the development of the concept of the electromagnetic field of James Clerk Maxwell.

At this point, the bulk properties of materials were basically understood and the scene was set for the development of atomic and quantum theory and the definition of chemical bonding and crystalline structures, which revolutionized science at the beginning of the twentieth century. Research was guided by the assumption that the bulk physical properties of matter must reside in the smallest unit of the particular material. For elements, that unit is the atom; for chemical compounds, it is the molecule; for crystalline solids, it is the unit cell.

Advances in the fields of chemistry, physics, and mineralogy went hand in hand at the beginning of the twentieth century. An understanding of the nature of atomic structure was essential to explaining the fundamental magnetic properties of matter. Between 1900 and 1910, the conception that atoms could be considered as tiny permanent magnets was widely accepted, but the basic understanding of the atom began with the proposal by Ernest Rutherford that the electrons exist in orbits around the nucleus.

Soon thereafter, Niels Bohr developed the theory of the atomic structure of the hydrogen atom based on the idea of quantized energy levels. Over the next twenty years, the details of the quantum nature of atomic structure and the wavelike properties of particles were worked out. Among the discoveries was the orbital magnetic quantum number (m₁), whose quantized values are related to the orbital quantum number 1. This quantum property explains the splitting of the spectral lines by a strong magnetic field that was measured first by Pieter Zeeman in 1896. The existence of electron spin as the source of an additional magnetic field within the atom was suggested in 1925. The spin quantum number, s, was also verified by the detailed splitting of spectral lines.

The definition of four basic quantum numbers related to energy levels in the electrons surrounding the nucleus demonstrated that the orbital and spin motions of the electron were the most important sites where magnetism resides in matter. Work on the fundamental properties of protons and neutrons proved the existence of a potential magnetic moment in the nuclei of atoms as well, and again it was the quantized character of the interaction between electromagnetic radiation and matter that confirmed the theoretical ideas. At the same time that scientists were explaining the atom, others had defined the complex structures of crystalline solids and the interaction between the crystal field and the energy levels of electrons in the structure. This research helped to explain why different solids with nearly identical chemical compositions could have very different electrical and magnetic properties.

As soon as the magnetic nature of the atom was proposed, it was suggested that some solids have a molecular or crystal field that causes a spontaneous alignment of the "atomic magnets." Such an alignment was clearly required to create permanent magnets. In the light of the apparent tendency toward magnetic ordering, scientists needed to explain the existence of any unmagnetized iron or other ferromagnetic material. The explanation was offered by Pierre Weiss, who postulated the existence of the domains. The study of domains and domain boundaries is related to a variety of crystal chemical studies, and the recognition of the anisotropic character of the magnetic properties in solids is important in crystallographic studies.

Principal terms:

ACTIVATION ENERGY: the energy level that must be achieved to effect a change from one physically or chemically stable state to another

ANTIPARALLEL: the orientation of two vectors, which are parallel to each other but point in opposite directions

CRYSTAL FIELD: the sum total of the electrical and magnetic fields that exist within a particular crystal structure

CRYSTALLINE: referring to the existence of a long-range, regular, and internal ordering of atoms or ions within a solid

MAGNETIC DOMAIN: a small volume within a ferromagnetic or antiferromagnetic solid where there is a spontaneous alignment of electron spin direction

PRECESSION: the circular motion of the direction of the spin axis of a rotating body in a gravitational or magnetic field

RESONANCE: a periodic alternation between energy levels within a physical system, such as an atom, which has a natural frequency and is stimulated by an energy source operating at the same frequency

SPECTROSCOPY: the study of the interaction between electromagnetic radiation and various energy states in matter

SPIN: one of the four basic physical properties of subatomic particles (electrons, protons, and neutrons); related to the magnetic properties of subatomic particles

UNIT CELL: the smallest three-dimensional geometric unit of a crystal that can create the complete crystal structure through repetition

Bibliography

Collinson, D. W., K. M. Creer, and S. K. Runcorn. METHODS IN PALAEOMAGNETISM. New York: Elsevier, 1967. Presents the basic data on paleomagnetic and rock magnetic studies and discusses magnetic structure and domains in natural minerals and the instrumentation related to magnetic studies. Excellent drawings and graphs illustrate basic relationships.

Gadian, D. G. NUCLEAR MAGNETIC RESONANCE AND ITS APPLICATIONS TO LIVING SYSTEMS. New York: Oxford University Press, 1982. Contains a good introduction to the theory of magnetic resonance and a thorough discussion of its applications to living tissues. The coverage of NMR parameters and their measurement is straight-forward, well illustrated, and inclusive.

Mitchell, I. V. ND-FE PERMANENT MAGNETS: THEIR PRESENT AND FUTURE APPLICATIONS. New York: Elsevier Applied Science Publishers, 1985. A good discussion of permanent magnet technology with sections on the conditions of magnet fabrication, specific magnetic alloys, and crystal chemistry. An excellent overview of the properties and structures of the best modern permanent magnets.

Tebble, R. S. MAGNETIC DOMAINS. London: Methuen, 1969. Efficiently presents ferromagnetic materials and the nature of magnetic domains. Major sections deal with observations, including many diagrams and photographs; theory; and applications, including permanent magnets, recording tapes, and thin magnetic films.

Tebble, R. S., and D. J. Craik. MAGNETIC MATERIALS. New York: John Wiley & Sons, 1969. A general text on magnetic materials with detailed diagrams of the crystal structures of numerous ferromagnetic compounds. Includes information on the physical properties of these compounds and the methods of measurement.

Thompson, John Eaton. THE MAGNETIC PROPERTIES OF MATERIALS. Feltham, England: Hamlyn, 1968. A good text on magnetic materials with an excellent historical perspective on the development of the science of magnetics and the research into ferromagnetism. Many good illustrations of how experiment and theory combine to advance science.

Weidner, Richard T., and Robert L. Sells. ELEMENTARY MODERN PHYSICS. 3d ed. Boston: Allyn & Bacon, 1980. A straightforward elementary textbook that describes the foundations of atomic theory and the orbital and spin quantum numbers. Formulas and equations are clearly explained and ideas are well illustrated in numerous figures.

Wilson, Michael A. N.M.R. TECHNIQUES AND APPLICATIONS IN GEOCHEMISTRY AND SOIL CHEMISTRY. New York: Pergamon Press, 1987. A middle-level book that presents the basic principles of nuclear magnetic resonance spectroscopy and discusses many of the problems in its application. Examples include studies of a wide range of crystalline solids, soils, and natural organic substances such as oil shale and coal.

Deformation of Solids