Magnetic devices shape our world: they power our homes, tools, toys, and they even store our data. Quantum physics provides insights needed to understand magnetism and its relationship to the intrinsic nature of the electron.

Beginner

The History

When Hans Christian Oersted's observed that a compass needle moved whenever nearby wires were energized, the study of the interaction of electrical and magnetic fields began. These two areas of scientific knowledge, which had been considered two separate phenomenon before 1820 have been linked ever since. The first magnetometer, used to measure a magnetic material, was invented by Carl Friedrich Gauss in 1833. Many scientists added to the understanding of the new field of study, and the basics of electromagnetism were summarized by James Clerk Maxwell in the 1860s.  Now known as Maxwell's equations, they provide the foundations for the interaction of electrical and magnetic fields.  By 1890, electromagnets were being used in various applications.  In The Journal of the Society of Arts that year, Silvanus P. Thompson gave an overview of the electromagnet and listed four methods to measure permeability.  Electromagnets were being used to provide temporary lifting power and produce rapid vibrations for electric bells and tuning forks. Included in the article was a discussion on magnetic fields.  AllAboutCircuits.com has some excellent technical articles describing magnetic fields if you are interested in more information!

The Devices

Maxwell's equations led to the development of generators, motors, transformers, electromagnetic switches and circuit breakers. Magnetic storage devices retain data by interpreting magnetized/nonmagnetized areas as 0s and 1s. Powerful electromagnets are used to move bulk metals easily. Metal detectors are used to discover lost ships and civilizations, as well as keep us safe in public areas. Nondestructive testing is possible using electromagnetic techniques to check circuitboards. Magnetic imaging is used in the medical industry. Still, as this is an active research area, expect new information, applications, and devices to emerge.

The Science

Our understanding of electricity and electrical fields required looking at the atomic structure of atoms and learning that materials could be classified as electrical conductors or insulators based on the free electrons available in their outer shell. Understanding magnets and magnetic fields will also have us looking at the atom, this time with the insights provided by quantum physics. Materials can be classified as ferromagnetic, paramagnetic, or diamagnetic depending on unpaired electron spins in their outer most energy shell indicating how the material will react to the presence of a magnetic field.

Today, electron spin is one of the four quantum numbers used to describe the energy state of an electron:
1.  the principal quantum number (n), the energy level
2.  the orbital angular momentum quantum number (l), the number of subshells
3.  the magnetic quantum number (ml), the energy in a subshell
4.  the electron spin quantum number (ms), electon angular momentum

The electron spin quantum number has two states, referred to as either an upward spin, $$m(s) = +1/2$$ or a downward spin, $$m(s) = - 1/2$$ and you usually see up or down arrows indicating the spin direction, as shown in Figure 1.  An electron's magnetic field is due to its spin.

The first direct experimental evidence of the electron spin (though it was not referred to that at the time) was the Stern–Gerlach experiment of the early 1920s, which showed that electrons have a magnetic moment. The magnetic moment is a torque experienced in an external magnetic field. Otto Stern and Walther Gerlach were attempting to measure magnetic fields produced by orbiting electrons. The results of their experiments showed that electrons acted as if they were spinning around their axis, producing very small magnetic fields independent of the orbital motions around the nuclei. In 1924, Wolfgang Pauli introduced what he called a "two-valued quantum degree of freedom" associated with the electron in the outermost shell.  The idea of electron spin was introduced in 1925 when Samuel Goudsmit and George Uhlenbeck jointly proposed the concept. At that time, the electron was considered to have a charge, mass, and spin. The spin was considered to be the intrinsic angular momentum of the electron, producing an intrinsic magnetic field; the electron acted like a very small dipole magnet.  This agreed with Faraday's Law of Induction, later incorporated into Maxwell's Equations, which states that moving a moving charge induces a magnetic field. Whether the moving charge is in the form of an electrical current or a charged electron spinning as it orbits the atom, both bring about a magnetic field.  An electron pair is two electrons that occupy the same orbital but have opposite spins. The direction of spin and orbit of the electron will determine the direction of the resulting magnetic field.

Classical physics considered the ability of a material to become magnetized as the property of magnetic permeability, mu (μ). Measured in Henry per meter (H/m), it indicates how the material reacts to a magnetic field.  Table 1 gives the Relative Permeability of some materials. The relative permeability, μ(r) is the ratio of the permeability of a specific material,  μ(m)  to the permeability of free space,  μ0:

$$μ(r) = \frac{ μ(m) ( H/m) }{ μ0 (H/m)}$$, where μ0 = 4π × 10−7 H/m.

Diamagnetic materials have a  μ(r) < 1; paramagnetic materials have a  μ(r) > 1; ferromagnetic materials have a  μ(r) much greater than 1.

Today the response of a material to a magnetic field is also inferred from its atomic and molecular structure. Materials composed of atoms with filled electron shells and paired electrons have total dipole moments of zero. For these atoms where the electrons occur in pairs, the electron spin is in opposite directions in the orbital and any associated magnetic fields cancel each other; there is no net magnetic field. Only atoms with partially filled shells having unpaired spins have a net magnetic moment. The magnetic moment induced by the applied field is aligned with the field and rather weak. A SQUID (superconducting quantum interference device) magnetometer is used to detect it.   Magnetic properties only occur in materials with partially filled shells. The shells are filled according to Hund's Rule, which states orbits are filled with spin-up electrons (+1/2) first, then with -1/2 spin electrons.  If there is an odd number of electrons and the spins are not cancelled out, an unpaired spin will exist and the atom will have magnetic properties.

Diamagnetic materials like copper, silver and gold, have no permanent magnetic property. All their electrons are paired so there is no net magnetic moment per atom. These materials are slightly repelled by a magnetic field and will not retain magnetic properties when the external field is removed. Diamagnetic materials will be repelled by both ends of a bar magnet.

Paramagnetic materials like aluminum and platinum become weakly magnetized in the presence of a magnetic field. They are slightly attracted by a magnetic field and don't retain the magnetic properties when the external field is removed. Their magnetization is due to the presence of some unpaired electrons, and from the realignment of the electron paths caused by the external magnetic field.

Ferromagnetic materials exhibit different properties.  As shown in Table 1, their relative permeability is much greater than other materials. They have large groups of atoms ( on the order of 10**12 - 10**17) where the spins of their electrons align with one another. These alignments form magnetic domains. The magnetic domains are separate areas, with boundaries, and are unaffected by surrounding domains if they exist. When placed in a strong magnetic field, these individual magnetic domains can be aligned, making the magnetic effects even stronger, as shown in Figure 2. Natural magnets like Lodestone have atomic dipole moments which are aligned into domains that produce a strong enough effect that an external magnetic field results.

If a piece of iron is not magnetized, the random orientation of the domains yield no net magnetic field.  If placed in a strong external magnetic field, the domain walls will move, reorienting the domains so more of the dipoles are aligned with the external field. As the domains grow under the applied magnetic field, the movement of the domain walls occurs by discontinuous and abrupt jumps, referred to as the Barkhausen Effect. The jumps can induce a voltage in a winding coil of wire that in turn can produce Barkhausen noise if a speaker is included in the circuit.   The domains stay in this new configuration when the magnetic field is removed because the defects in the crystal lattice tend to limit the movement of the domain walls once magnetized.  However, a magnetized material can lose its magnetic properties.

Heating will increase thermal motion to the point the dipoles will lose their alignment. When the temperature rises beyond a certain point, called the Curie Temperature, the ability to be magnetized or attracted to a magnet disappears, although it will still respond to an external field. Materials can also be demagnetized by subjecting them to vibration, hitting them, or applying a rapidly oscillating magnetic field from a degaussing coil. These actions tend to release the domain walls from their changed state and the domain boundaries tend to reverse, demagnetizing the material.

Now the next time you use a magnet to hold a picture on your refrigerator, or want to chose a material to protect sensitive circuitry from unwanted effects of magnetic fields, you'll know the intrinsic property of the electron makes it possible.