Diamagnetism And Paramagnetism

Type of physical science: Diamagnetism and Paramagnetism, Magnetism, Electromagnetism, Classical physics

Field of study: Electromagnetism

Magnetic behaviors can be categorized as either diamagnetism, paramagnetism, or ferromagnetism. Only the first two types can be explained in terms of classical physics.

Overview

Magnetic behavior can be divided primarily into three principal varieties: diamagnetism, paramagnetism, and ferromagnetism. The first two varieties can be explained using classical physics, with the aid of the concept of electromagnetic induction in the case of diamagnetism, and with the use of the concept of an atomic magnetic moment arising from the orbital motion of electrons about the nucleus in the case of paramagnetism. Ferromagnetism, the most familiar type of magnetism, the class of so-called permanent magnets, cannot be described by classical physics. Rather, ferromagnetism must be explained in terms of the quantum-mechanical concept of electron spin and involves the spin-spin interaction between ferromagnetic atoms in a lattice structure.

An electron orbiting about its nucleus has orbital angular momentum. Since the electron is a charged particle, by virtue of its orbital motion, it constitutes an atomic current. Currents flowing in loops produce magnetic moments. It can be shown that an electron's orbital angular momentum and its magnetic moment, which is the product of its orbital area and equivalent atomic current, are directly proportional to each other. The direction of an electrical current is conventionally described in terms of the motion of positive charges. Since electrons are negatively charged, their atomic currents point in the opposite direction. As a result, the direction of the orbital angular momentum--which is independent of the sign of the moving charge--is opposite to the direction of the electron's magnetic moment. It can be shown that the ratio of the magnitude of an orbiting electron's magnetic moment to its angular momentum is one-half the ratio of the magnitude of the electron's charge to its mass, both fundamental constants of nature. If an atom has more than one electron in the electron cloud surrounding its nucleus, the atom's total magnetic moment is merely the vector sum of the individual electrons' magnetic moments. This sum can be zero in certain cases; otherwise the atom will have a net magnetic moment.

This behavior is atomic in nature, and although identical atoms in a bulk sample will have identically strong magnetic moments, they need not point in the same direction. The direction of the individual magnetic moments usually depends upon external influences, such as temperature and applied magnetic field. If the directions of the individual atomic magnetic moments are random, then the sample will have no net magnetization. If the directions essentially line up--although not necessarily completely, because of random thermal fluctuations--then the sample will have a net magnetization, which will be in direct proportion to the external field that causes the alignment. The ratio of the magnetization strength to the external magnetic field strength is a dimensionless quantity intrinsic to the identity of the atom or molecule composing the sample and is called "magnetic susceptibility." This property can be used as a means to distinguish between paramagnetic and diamagnetic materials.

A diamagnetic substance has atoms that have no permanent magnetic moment under ordinary circumstances. For example, consider an atom that has two electrons in the same orbital traveling about the nucleus in opposite directions. Each has the same magnitude of orbital angular momentum, but because one circulates about the nucleus in a clockwise fashion whereas the other circulates about the nucleus in a counterclockwise fashion, these angular momenta point in antiparallel directions and therefore add vectorially to zero. A similar statement can be made concerning the contribution of magnetic moment of each electron to the atom's total magnetic moment. Each electron has the same magnitude of magnetic moment, as a consequence of having the same angular momentum value, but these two moments point antiparallel to each other and therefore add vectorially to zero.

However, suppose that a material made of such a diamagnetic substance is placed within an external magnetic field. By Faraday's law of induction, a magnetic moment will be established in the substance while the external field's magnetic flux is time varying. This can result simply from the motion of the external magnetic field relative to the position of the diamagnetic substance, which is to say that the simple act of moving a magnet toward a diamagnetic material will induce a magnetic moment within the diamagnetic substance. This is accomplished in the following manner. The time-dependent magnetic flux intercepted throughout the diamagnetic material creates an induced electromotive force that circulates throughout the substance. Therefore, there is a potential difference across the material; or, in other words, an induced electric field is established within this diamagnetic material. Any charged particle placed within an electric field experiences an electric force of either attraction or repulsion depending upon the sign of the charge. In the case of diamagnetic materials, the point of interest is what happens to the electrons orbiting the nucleus in opposite directions. Each experiences the same electric force and therefore is subjected to the same external torque in its rotational motion. Yet because one electron is moving clockwise about the nucleus and the other is moving counterclockwise, one electron's angular velocity--and, hence, angular momentum--increase, while the other electron's angular velocity and angular momentum decrease. Since the electron's magnetic moment is directly proportional to its total angular momentum, and since the angular momenta of the two electrons are not equal, each electron has a different value of magnetic moment. The two moments are antiparallel to each other and no longer add vectorially to zero. Therefore, a net magnetic moment has been induced in the diamagnetic substance. This effect disappears when the external magnetic flux intercepted by the material ceases to be time-dependent. This would occur after a permanent magnet has been set up in position relative to such a sample. In other words, the induction effect only occurs while the magnet is being moved into place. Once it is stable, the effect is no longer observed.

When the induction process is in effect, within the bulk of the diamagnetic sample, there is a net magnetization in direct proportion to the strength of the external magnetic field that produces it, but it will point in an opposite, or negative, direction to that external field. The magnetization of the diamagnetic material thus opposes the external field. Since magnetic susceptiblity is defined as the ratio of the magnetization to the external field strength, then in a diamagnetic material, the magnetic susceptibility has a negative value.

To summarize, diamagnetism involves inducing magnetic moments in materials that normally have none. Induction opposes the cause that produces it, a necessary condition to guarantee conservation of energy. Diamagnetic materials thus have negative magnetic susceptibilities--the intrinsic distinction between this category of magnetic behavior and the paramagnetic and ferromagnetic states, for which magnetic susceptibilities are always positive.

Paramagnetism involves permanent magnetic moments in materials even in the absence of an external field. Yet there is always some thermal energy present that tends to randomize the molecular dipole moment orientation within a bulk sample of a given paramagnetic material. Thus, in the absence of an external magnetic field, the vector sum of the dipole moments of all the molecules vanishes. When a magnetic field is placed in the vicinity of a paramagnetic material, torques are exerted on each dipole moment, which attempt to align the magnetic moments along the field's direction. This is a consequence of minimizing potential energy in the field of force provided by the external magnetism. Still, thermal energy keeps this alignment from being total. However, there is a net magnetic moment along the direction of the external magnetic field. The degree of alignment diminishes with increasing temperature, as thermal agitation increases.

Thus a bulk sample of a given paramagnetic material has a net magnetization along the direction of an external magnetic field. As in the case of diamagnetism, magnetization could be defined as the net magnetic moment of the bulk sample per unit volume of the sample. This magnetization is directly proportional to the strength of the external magnetic field. Likewise, the dimensionless constant of proportionality between magnetization and external magnetic field intensity can be defined as magnetic susceptibility. In the case of paramagnetism, it can be shown that magnetic susceptibility depends directly upon the square of an individual atom's magnetic moment, depends directly upon the number of atoms per unit volume in the material, depends inversely upon temperature, and involves a pair of fundamental constants, the permeability of free space and the Boltzmann constant. The latter constant is a measure of how much thermal energy a body can attain per unit of temperature. This description of the magnetic susceptibility's dependence upon various physical parameters, specifically the temperature, is referred to as the Curie law. It should be noted that this discussion best describes how a paramagnetic material responds in the presence of a low-strength magnetic field at a reasonable temperature. If the magnetic field strength is increased, the magnetization that results eventually achieves a limiting saturation value, whereupon no further increase in magnetic field strength provides any further increase in magnetization of the sample.

Applications

To illustrate a situation of paramagnetic behavior in everyday life, consider what happens when one tries to pick up a paper clip with a permanent magnet. Many paper clips are composed of materials that themselves are not permanent magnets, which is to say that one paper clip does not magnetically attract another paper clip. The materials that are used to manufacture paper clips are paramagnetic and thus have permanent atomic magnetic moments, but these are arranged randomly throughout the bulk of the material, so that there is no net magnetization of the paper clip. However, when a permanent magnet is brought into close proximity to a paramagnetic paper clip, those permanent atomic magnetic moments attempt to align themselves with the external field of the permanent magnet. The degree of alignment depends upon temperature; at room temperature, the degree of alignment is quite high. Therefore the paper clip is attracted to the permanent magnet.

One could turn the paper clip, at least temporarily, into a net magnetic attractor by carefully, and repeatedly stroking the paper clip with a permanent magnet. This has the tendency to freeze the magnetic moments of the paper clip's atoms into a nearly aligned arrangement. Over time, this arrangement will degrade because of thermal energy; for a time, however, a paper clip so treated will behave as a permanent magnet and will attract other paramagnetic materials.

Similarly, one could take a paper clip, straighten it, stroke it carefully and repeatedly with a permanent magnet to align the clip's permanent magnetic moments, and use this to create a homemade compass. Fill a glass with water. Find a suitable lightweight material that will float on the water, such as a thin piece of plastic or small cork. Attach the magnetized paper clip to that floating material and carefully place it atop the water surface in the glass. The paper clip will now point toward the earth's north magnetic pole.

Another illustration of paramagnetic behavior is manifested in what happens to a permanent magnet when it is subjected to external work, such as high temperature or mechanical stress. If one takes a bar magnet and strikes it hard with a hammer or smacks it against some other object, the mechanical energy dissipated during the impact is often sufficient to disturb the magnetic alignment of the ferromagnetic atoms within the magnet, thereby randomizing the magnetic moments and reducing the magnet to a paramagnetic state. The same can be easily done by raising the temperature of the bar magnet above a certain limiting value called the Curie temperature. Here, once again, there is now sufficient thermal energy to overcome the quantum mechanical spin-spin interaction of neighboring atoms that provides a ferromagnetic material with its perfect alignment of magnetic moments. Whereas the mechanical destruction of the ferromagnetic alignment is not reversible, if a heated magnet is cooled down again, it will revert from the paramagnetic to the ferromagnetic state.

Whereas applications of paramagnetic and ferromagnetic materials are commonplace in everyday life, applications of diamagnetic materials are relatively uncommon. However, diamagnetic effects are quite evident in the behavior of superconducting materials. Until 1987, superconductivity, the total loss of electrical resistance in some materials at certain temperatures, was essentially a laboratory curiosity. Transition temperatures were all extremely low, from about 10 Kelvins to only milli-Kelvins above absolute zero. In 1987, the first high-temperature superconducting material, a compound composed of oxides of yttrium, barium, and copper, displayed superconductivity at a temperature above that of liquid nitrogen (77 Kelvins). If superconducting materials could be engineered to operate at even higher temperatures, relatively near room temperature, then transmission of electrical energy could be performed with minimal energy losses.

What does diamagnetism have to do with superconductors? One rather dramatic property of a superconducting material is that a low-mass permanent magnet physically placed atop a superconductor sample will levitate effortlessly above the sample when the superconductor is cooled below its transition temperature. This behavior, referred to as the Meissner effect, results because superconducting materials are also diamagnetic. When an external magnetic field is applied to a superconductor, magnetic dipoles are induced within the superconductor, repelling the external field. This magnetic repulsion, if greater than the weight of the external magnet, is responsible for the suspension of the magnet above the superconductor. If the superconductor's temperature rises above the transition temperature, the superconducting state is lost, the diamagnetic repulsion of external magnetic field is no longer in operation, and the Meissner effect ceases.

Context

It must be understood that the basic property involved in magnetism is the behavior of charge, and further, that charge is a property associated with matter that displays its character in terms of electromagnetic interactions. Charges in motion constitute a current.

In electrostatics, an isolated point charge is the simplest charged structure that can exist. If two such charges of opposite sign are placed near each other, they form an electric dipole characterized by a dipole moment of strength equal to the product of the magnitude of charge on each point charge and the distance separating these two. It is a vector that points from the negative point charge toward the positive point charge.

Lines of electric field diverge away from positive point charges and converge into negative point charges. Thus, it could be said that positive charge acts as a source for electric field, while negative charge acts as a sink for electric field. What are the analogous quantities for the magnetic field? Corresponding to the concept of an electric point charge is the concept of a magnetic pole. Rather than being referred to as "positive" or "negative," these are usually distinguished as "north" or "south" poles. North poles are sources of magnetic field lines, and south poles are sinks of magnetic field lines. However, in magnetism, unlike in electrostatics, isolated sources and sinks do not exist. There is no reputable experimental data to support the existence of isolated magnetic monopoles. Therefore, the simplest magnetic structure is the magnetic dipole, wherein lines of magnetic field circulate back from source to sink in continuous loops, characterized by a magnetic dipole moment. Examples of macroscopic magnetic dipoles are current loops, solenoids, and bar magnets. Electrons orbiting about the nucelus constitute microscopic current loops, the value of this equivalent current being the quotient of the electron's charge to the time it takes for the electron to complete a revolution about the nucleus. This microscopic current loop model can be used to describe the magnetic moment of individual atoms based upon the electronic structure of a given atom, each electron being attracted to the nucleus by a Coulomb force directing its acceleration centripetally.

The magnetic moments of individual atoms within a material determine whether or not that material is magnetic. In atoms with more than one electron, the atom's total magnetic moment is the vector sum of the individual electrons' orbital and also spin magnetic moments. In some atoms, this vector sum vanishes. Such atoms have no permanent magnetic moments. In other atoms, this vector sum is nonzero. Such atoms have a permanent magnetic moment.

Like electric dipoles placed in an external electric field, magnetic dipoles placed in an external magnetic field attempt to align themselves with the direction of the external field in order to minimize their potential energy. The response of a given magnetic material to an external field can be used to distinguish behaviors into the categories of diamagnetism, paramagnetism, and ferromagnetism. A detailed explanation of these subjects incorporates the principles of classical mechanics, electromagnetism, thermodynamics, and quantum mechanics.

Principal terms

ANGULAR MOMENTUM: A key measure of rotational motion; depends upon mass, velocity, and rotational orientation

DIAMAGNETISM: A property of magnetic materials that have induced atomic magnetic moments and are thus repelled by external magnetic fields

ELECTROMAGNETIC INDUCTION: Process in which a time-dependent magnetic flux induces the production of an electromotive force or voltage

ELECTRON: The elementary particle that carries quantized negative charge within atoms

FERROMAGNETISM: A property of magnetic materials that have permanent perfectly aligned atomic magnetic moments even without external magnetic fields

FLUX: A measure of the degree to which magnetic field lines pass through a given surface in space

KINETIC ENERGY: Energy of motion resulting from work being done by application of external force

MAGNETIC MOMENT: The multiplicative product of current and the area of a loop around which that current flows; perpendicular to the loop's plane

PARAMAGNETISM: A property of magnetic materials that have permanent magnetic moments, randomly oriented except in external magnetic fields

POTENTIAL ENERGY: Energy of position within a field of force; can be converted to useful work

THERMAL AGITATION: Atoms have kinetic energy directly proportional to the temperature (measured on the Kelvin scale); this represents a random agitation of the atoms

Bibliography

Beiser, Arthur. Physics. Menlo Park, Calif.: Benjamin/Cummins, 1982. A noncalculus- based survey of basic physics suitable for advanced high-school students or college-level nonscience majors. Provides a strong presentation of atomic physics, magnetism, and thermal motions.

Halliday, David, Robert Resnick, and Jearl Walker. Fundamentals of Physics. New York: John Wiley & Sons, 1997. Classic textbook for a thorough investigation of basic physics. Chapter 32 has full sections concerning diamagnetism, paramagnetism, and ferromagnetism and relates these behaviors to the basic physics of electromagnetism.

Instruction Manual for Superconductor Demonstration. Fort Collins, Colo.: Colorado Superconductor, 1987. This booklet is provided by a small scientific supply company that makes high-temperature superconductor demonstration kits suitable for the classroom. Provides a well-written, easily understood explanation of superconductor behavior, including the Meissner effect.

Krauskopf, Konrad B., and Arthur Beiser. Fundamentals of Physical Science. New York: McGraw-Hill, 1971. Provides descriptive diagrams of the origin of microscopic magnetism within a bulk sample. Shows how magnetic domains are oriented within the sample to produce a net magnetization.

McCliment, Edward R. Physics. San Diego, Calif.: Harcourt, Brace, Jovanovich, 1984. A noncalculus-based survey of basic physics suitable for advanced high-school students or college-level nonscience majors. Chapter 17 contains a thorough qualitative and quantitative chapter on diamagnetism, paramagnetism, and ferromagnetism.