Magnetic hysteresis

Last updated April 28, 2024

Theoretical model of magnetization m against magnetic field h. Starting at the origin, the upward curve is the initial magnetization curve. The downward curve after saturation, along with the lower return curve, form the main loop. The intercepts hc and mrs are the coercivity and saturation remanence. StonerWohlfarthMainLoop.svg — Theoretical model of magnetization $m$ against magnetic field $h$ . Starting at the origin, the upward curve is the *initial magnetization curve*. The downward curve after saturation, along with the lower return curve, form the *main loop*. The intercepts $h c$ and $m rs$ are the *coercivity* and *saturation remanence* .

Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized. Once magnetized, the magnet will stay magnetized indefinitely. To demagnetize it requires heat or a magnetic field in the opposite direction. This is the effect that provides the element of memory in a hard disk drive.

The relationship between field strength $H$ and magnetization $M$ is not linear in such materials. If a magnet is demagnetized ( $H = M = 0$ ) and the relationship between $H$ and $M$ is plotted for increasing levels of field strength, $M$ follows the initial magnetization curve. This curve increases rapidly at first and then approaches an asymptote called magnetic saturation. If the magnetic field is now reduced monotonically, $M$ follows a different curve. At zero field strength, the magnetization is offset from the origin by an amount called the remanence. If the $H - M$ relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop called the main loop. The width of the middle section along the H axis is twice the coercivity of the material.^[1]^{: Chapter 1}

A closer look at a magnetization curve generally reveals a series of small, random jumps in magnetization called Barkhausen jumps. This effect is due to crystallographic defects such as dislocations.^[1]^{: Chapter 15}

Magnetic hysteresis loops are not exclusive to materials with ferromagnetic ordering. Other magnetic orderings, such as spin glass ordering, also exhibit this phenomenon.^[2]

Physical origin

The phenomenon of hysteresis in ferromagnetic materials is the result of two effects: rotation of magnetization and changes in size or number of magnetic domains. In general, the magnetization varies (in direction but not magnitude) across a magnet, but in sufficiently small magnets, it doesn't. In these single-domain magnets, the magnetization responds to a magnetic field by rotating. Single-domain magnets are used wherever a strong, stable magnetization is needed (for example, magnetic recording).

Larger magnets are divided into regions called domains. Within each domain, the magnetization does not vary; but between domains are relatively thin domain walls in which the direction of magnetization rotates from the direction of one domain to another. If the magnetic field changes, the walls move, changing the relative sizes of the domains. Because the domains are not magnetized in the same direction, the magnetic moment per unit volume is smaller than it would be in a single-domain magnet; but domain walls involve rotation of only a small part of the magnetization, so it is much easier to change the magnetic moment. The magnetization can also change by addition or subtraction of domains (called nucleation and denucleation).

Measurement

Magnetic hysteresis can be characterized in various ways. In general, the magnetic material is placed in a varying applied $H$ field, as induced by an electromagnet, and the resulting magnetic flux density ( $B$ field) is measured, generally by the inductive electromotive force introduced on a pickup coil nearby the sample. This produces the characteristic $B - H$ curve; because the hysteresis indicates a memory effect of the magnetic material, the shape of the $B - H$ curve depends on the history of changes in $H$ .

Alternatively, the hysteresis can be plotted as magnetization $M$ in place of $B$ , giving an $M - H$ curve. These two curves are directly related since $B=\mu _{0}(H+M)$ .

The measurement may be closed-circuit or open-circuit, according to how the magnetic material is placed in a magnetic circuit.

In open-circuit measurement techniques (such as a vibrating-sample magnetometer), the sample is suspended in free space between two poles of an electromagnet. Because of this, a demagnetizing field develops and the $H$ field internal to the magnetic material is different than the applied $H$ . The normal B-H curve can be obtained after the demagnetizing effect is corrected.
In closed-circuit measurements (such as the hysteresisgraph), the flat faces of the sample are pressed directly against the poles of the electromagnet. Since the pole faces are highly permeable, this removes the demagnetizing field, and so the internal $H$ field is equal to the applied $H$ field.

With hard magnetic materials (such as sintered neodymium magnets), the detailed microscopic process of magnetization reversal depends on whether the magnet is in an open-circuit or closed-circuit configuration, since the magnetic medium around the magnet influences the interactions between domains in a way that cannot be fully captured by a simple demagnetization factor.^[3]

Models

The most known empirical models in hysteresis are Preisach and Jiles-Atherton models. These models allow an accurate modeling of the hysteresis loop and are widely used in the industry.

However, these models lose the connection with thermodynamics and the energy consistency is not ensured. A more recent model, with a more consistent thermodynamic foundation, is the vectorial incremental nonconservative consistent hysteresis (VINCH) model of Lavet et al. (2011). is inspired by the kinematic hardening laws and by the thermodynamics of irreversible processes.^[4] In particular, in addition to provide an accurate modeling, the stored magnetic energy and the dissipated energy are known at all times. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. That allows easily obtaining a vectorial model while Preisach and Jiles-Atherton are fundamentally scalar models.

The Stoner–Wohlfarth model is a physical model explaining hysteresis in terms of anisotropic response ("easy" / "hard" axes of each crystalline grain).

Micromagnetics simulations attempt to capture and explain in detail the space and time aspects of interacting magnetic domains, often based on the Landau-Lifshitz-Gilbert equation.

Toy models such as the Ising model can help explain qualitative and thermodynamic aspects of hysteresis (such as the Curie point phase transition to paramagnetic behaviour), though they are not used to describe real magnets.

Applications

There are a great variety in applications of the theory of hysteresis in magnetic materials. Many of these make use of their ability to retain a memory, for example magnetic tape, hard disks, and credit cards. In these applications, hard magnets (high coercivity) like iron are desirable so the memory is not easily erased.

Soft magnets (low coercivity) are used as cores in transformers and electromagnets. The response of the magnetic moment to a magnetic field boosts the response of the coil wrapped around it. Low coercivity reduces that energy loss associated with hysteresis.

Magnetic hysteresis material (soft nickel-iron rods) has been used in damping the angular motion of satellites in low Earth orbit since the dawn of the space age.^[5]

Related Research Articles

<span class="mw-page-title-main">Ferromagnetism</span> Mechanism by which materials form into and are attracted to magnets

Ferromagnetism is a property of certain materials that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are noticeably attracted to a magnet, which is a consequence of their substantial magnetic permeability.

Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism.

A magnetic field is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field.

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets.

An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole in the center of the coil. The magnetic field disappears when the current is turned off. The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet.

<span class="mw-page-title-main">Hysteresis</span> Dependence of the state of a system on its history

Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems, it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect.

Magnetostriction is a property of magnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of materials' magnetization due to the applied magnetic field changes the magnetostrictive strain until reaching its saturation value, λ. The effect was first identified in 1842 by James Joule when observing a sample of iron.

Remanence or remanent magnetization or residual magnetism is the magnetization left behind in a ferromagnetic material after an external magnetic field is removed. Colloquially, when a magnet is "magnetized", it has remanence. The remanence of magnetic materials provides the magnetic memory in magnetic storage devices, and is used as a source of information on the past Earth's magnetic field in paleomagnetism. The word remanence is from remanent + -ence, meaning "that which remains".

Coercivity, also called the magnetic coercivity, coercive field or coercive force, is a measure of the ability of a ferromagnetic material to withstand an external magnetic field without becoming demagnetized. Coercivity is usually measured in oersted or ampere/meter units and is denoted $H C$ .

In electromagnetism, permeability is the measure of magnetization produced in a material in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter μ. It is the ratio of the magnetic induction $to the magnetizing field as a function of the field in a material. The term was coined by William Thomson, 1st Baron Kelvin in 1872, and used alongside permittivity by Oliver Heaviside in 1885. The reciprocal of permeability is magnetic reluctivity.$

Seen in some magnetic materials, saturation is the state reached when an increase in applied external magnetic field H cannot increase the magnetization of the material further, so the total magnetic flux density B more or less levels off. Saturation is a characteristic of ferromagnetic and ferrimagnetic materials, such as iron, nickel, cobalt and their alloys. Different ferromagnetic materials have different saturation levels.

The Barkhausen effect is a name given to the noise in the magnetic output of a ferromagnet when the magnetizing force applied to it is changed. Discovered by German physicist Heinrich Barkhausen in 1919, it is caused by rapid changes of size of magnetic domains.

In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume. It is represented by a pseudovector M. Magnetization can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics.

In electromagnetism, the Preisach model of hysteresis is a model of magnetic hysteresis. Originally, it generalized hysteresis as the relationship between the magnetic field and magnetization of a magnetic material as the parallel connection of independent relay hysterons. It was first suggested in 1935 by Ferenc (Franz) Preisach in the German academic journal Zeitschrift für Physik. In the field of ferromagnetism, the Preisach model is sometimes thought to describe a ferromagnetic material as a network of small independently acting domains, each magnetized to a value of either $or . A sample of iron, for example, may have evenly distributed magnetic domains, resulting in a net magnetic moment of zero.$

The article Ferromagnetic material properties is intended to contain a glossary of terms used to describe ferromagnetic materials, and magnetic cores.

In magnetism, single domain refers to the state of a ferromagnet in which the magnetization does not vary across the magnet. A magnetic particle that stays in a single domain state for all magnetic fields is called a single domain particle. Such particles are very small. They are also very important in a lot of applications because they have a high coercivity. They are the main source of hardness in hard magnets, the carriers of magnetic storage in tape drives, and the best recorders of the ancient Earth's magnetic field.

In electromagnetism, the Stoner–Wohlfarth model is a widely used model for the magnetization of ferromagnets with a single-domain. It is a simple example of magnetic hysteresis and is useful for modeling small magnetic particles in magnetic storage, biomagnetism, rock magnetism and paleomagnetism.

The demagnetizing field, also called the stray field, is the magnetic field (H-field) generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement currents. The term demagnetizing field reflects its tendency to act on the magnetization so as to reduce the total magnetic moment. It gives rise to shape anisotropy in ferromagnets with a single magnetic domain and to magnetic domains in larger ferromagnets.

<span class="mw-page-title-main">Exchange spring magnet</span>

An exchange spring magnet is a magnetic material with high coercivity and high saturation properties derived from the exchange interaction between a hard magnetic material and a soft magnetic material, respectively.

In electromagnetism and materials science, the Jiles–Atherton model of magnetic hysteresis was introduced in 1984 by David Jiles and D. L. Atherton. This is one of the most popular models of magnetic hysteresis. Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material. Jiles–Atherton model enables calculation of minor and major hysteresis loops. The original Jiles–Atherton model is suitable only for isotropic materials. However, an extension of this model presented by Ramesh et al. and corrected by Szewczyk enables the modeling of anisotropic magnetic materials.

References

1 2 Chikazumi, Sōshin (1997). Physics of ferromagnetism (2nd ed.). Oxford: Oxford University Press. ISBN 9780191569852.
↑ Monod, P.; Prejean, J. J.; Tissier, B. (1979). "Magnetic hysteresis of CuMn in the spin glass state". J. Appl. Phys. 50 (B11): 7324. Bibcode:1979JAP....50.7324M. doi:10.1063/1.326943.
↑ Fliegans, J.; Tosoni, O.; Dempsey, N. M.; Delette, G. (2020). "Modeling of demagnetization processes in permanent magnets measured in closed-circuit geometry" (PDF). Applied Physics Letters. 116 (6): 062405. Bibcode:2020ApPhL.116f2405F. doi:10.1063/1.5134561. ISSN 0003-6951. S2CID 214353446.
↑ François-Lavet, V.; Henrotte, F.; Stainier, L.; Noels, L.; Geuzaine, C. (2011). "Vectorial incremental nonconservative consistent hysteresis model" (PDF). Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011). pp. 10–. hdl:2268/99208. ISBN 978-2-9601143-1-7.
↑ General Electric Spacecraft Department (16 November 1964). Magnetic Hysteresis Damping of Satellite Attitude Motion (PDF) (Technical report). U.S. Naval Weapons Laboratory, Dahlgren, Virginia. 64SD4252. Archived from the original (PDF) on October 2, 2016. Retrieved 1 October 2016.

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[Chikazumi-1] 1 2 Chikazumi, Sōshin (1997). Physics of ferromagnetism (2nd ed.). Oxford: Oxford University Press. ISBN 9780191569852.

[2] Monod, P.; Prejean, J. J.; Tissier, B. (1979). "Magnetic hysteresis of CuMn in the spin glass state". J. Appl. Phys. 50 (B11): 7324. Bibcode:1979JAP....50.7324M. doi:10.1063/1.326943.

[FliegansTosoni2020-3] Fliegans, J.; Tosoni, O.; Dempsey, N. M.; Delette, G. (2020). "Modeling of demagnetization processes in permanent magnets measured in closed-circuit geometry" (PDF). Applied Physics Letters. 116 (6): 062405. Bibcode:2020ApPhL.116f2405F. doi:10.1063/1.5134561. ISSN 0003-6951. S2CID 214353446.

[4] François-Lavet, V.; Henrotte, F.; Stainier, L.; Noels, L.; Geuzaine, C. (2011). "Vectorial incremental nonconservative consistent hysteresis model" (PDF). Proceedings of the 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011). pp. 10–. hdl:2268/99208. ISBN 978-2-9601143-1-7.

[5] General Electric Spacecraft Department (16 November 1964). Magnetic Hysteresis Damping of Satellite Attitude Motion (PDF) (Technical report). U.S. Naval Weapons Laboratory, Dahlgren, Virginia. 64SD4252. Archived from the original (PDF) on October 2, 2016. Retrieved 1 October 2016.

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