The magnetic hysteresis loop shows the characteristic “memory” of a magnetic material. Some materials hold on the field they’ve been in, not giving up the magnetism they’ve gained. Other materials could care less one way or another.
Even if you’ve never heard of the magnetic hysteresis loop, you’ll probably learn something interesting here. When rocks hold onto their old fields, it’s almost like a journal entry or a memory of what it encountered. In fact, this property is exactly what’s exploited in memory storage devices like hard drives and VCR tapes. The magnetic hysteresis loop explained just gives a visualization of how a material’s memory reacts.
The Foundational Property for Magnetic Hysteresis is Magnetic Remanence
Magnetic remanence measures as the leftover magnetism after applying and removing a field magnetic field. Some materials have a resistance to let go of older states.
Testing the remanence dissipates the strength over time. You can’t measure it over and over, or all the “juice” will “forget” the states. Or, if the material is heated past a certain temperature, the heat entropy also wipes the slate clean. (The “Curie temperature,” characteristic of a material.)
Remember that there are different types of magnetic material. What we normally think of as magnets are specifically ferromagnetic.
Everyday Magnetism is Ferromagnetism
In ferromagnetic material, there are a lot of unpaired electrons. They group into little districts (called domains) and are vulnerable to the influence of external magnetic fields. Each district in itself acts like a tiny magnet, and when more districts agree on a direction, a magnetic moment is set up, which is just a stronger magnetic capability.
When a material is put in a magnetic field, it may or may not pick up on the vibes (political campaigns) or the external magnetic field. I’m going to use these loose analogies of sentiments to describe the domains. Since studying this in depth, I don’t think it is inaccurate. When you think about a material in a magnetic field, it’s like a person in a certain social climate, like a protest or concert. They might be resistant to going along with the emotions of the crowd (para/dia magnet), or they might amplify it and then stay in that “mood” indefinitely (ferromagnets). The leftover mood is like the magnetic remanence.
History of Hysteresis – Beginning to Find Remanence
In 1881 Scottish physicist Sir James Alfred Ewing first termed termed hysteresis as the “history of the system.” Ewing mainly studied engines, earthquakes, and magnetic defects in amorphous materials. These ideas interested the funding entities for war reasons.
Hysteresis first described stress and strain, like a rubber band that does not snap back fully once stretched past a certain point. This same idea cropped up again for magnetism. Scientists could see the effects, measuring different values for different materials and cataloguing each’s resistance or willingness to hold onto prior magnetic states. But development of the theory behind it needed both classical and quantum mechanics together, quantum being when nonlinear effects dominate, considering effects on scales smaller than a single atom. The exact mechanics of how and why materials display magnetic hysteresis just began to tighten up in the 1970s. Russian researchers such as Krasnosel’skii used the datasets to set forth possible regimes for explaining magnetic hysteresis.
Hysteresis theories started off explaining remanence just like the framework for stresses and strains physically in material. [1] This is the 2011 paper by Lavet et al. that has the most current model that researchers in the field would use. Prior models used scalars, step functions ([2] 1935 Germany), and ODEs ([3] 1984 USA). The Lavet model is called VINCH (vectorial incremental nonconservative consistent hysteresis) and works by means of minimization of thermodynamic potential. [5]
Magnetic Hysteresis Loop Explained
You’ll learn the most about the magnetic hysteresis loop by following along the journey with the plot itself. To understand the points along the graph using the same nomenclature the researchers use, we’ll want to define some terms first.
Defining Hysteresis Loop Terms
Variables are just letters we use to represent the quantities as a shorthand and for use in formulas. H was the only variable used for magnetic field until people started used using a related value (magnetic flux density) more in calculations and had to define it separately as B. The units give you an idea of what the quantity physically represents.
In theoretical considerations, B is useful on the microscopic level, such as in the vaccuum between the atoms. H is more for macroscopic situations over the course of a whole piece of material. In practical applications like engineering, everything is measured at the macro level. Field strength H is the main thing that matters. Flux density B is the response of the medium magnetized by H, for them.
B, H, J, and M:
- B in [T]. 1 Tesla is also equal to 1 kg/s2 A or N/m⋅A
- H in [A/m]
- M, Magnetization in [A/m]
- J, Magnetic polarization in [T]
The unit A is amps, a SI unit for electrical current. 1 amp represents a speed of electric flow of 1 Coulomb of charge passing every second.
Magnetization is the sum of all the individual “directions” of the domains (called the magnetic moment, and measured in A⋅m2, and scaled per m2 of volume). J and M are really telling you the same thing, J is just scaled by the permeability constant so that J = μ⋅M. In vacuum there is no material, no magnetization, J = M = 0, and B = H⋅μ. In material this is B = μ⋅(H+M).
Permeability & Susceptibility are Parameters in Many Magnetism Equations
μ – permeability constant. μ0 in units of [N/A2] or [kg⋅m / s2A2] is a measure of the magnetization in response to an applied electric field. In vacuum the value is always 1.256⋅10-6 and people used to always approximate this is 4𝜋⋅10-7 until a more formal way to measure it was reach just in 2019. Relative permeability of a material is μ/μ0 = μr. The naughts are free space. (We also have M = μ0-1 – μ-1, because algebra.
In vacuum & material the equations thus differ by the constants used to scale how B, H, and M behave in the presence of either ~nothingness~ or specific materials. If you want to study those, the best round up of them I found was on this Magnetism Encyclopedia, boxes with equations 1a-d and 2a-d.
χ – Magnetic susceptibility – a measure of how much a material will become magnetized in an applied magnetic field. χ = μr – 1.
| susceptibility* examples | ||
| Diamagnet | Bin small & negative (if Bext is nonzero), and proportional to susceptibility | Copper, -10-5 Water, -9*10-6 Nitrogen gas, -5*10-9 Silicon Dioxide -6*10-9 Calcium Carbonate -4*10-9 |
| Paramagnet | Bin small & positive, susceptibility proportional to 1/Temperature. | Aluminum, 2*10-5 Oxygen gas, 2*10-6 Oxygen Liquid, 3.5*10-3 Clays 13-65*10-8 Biotite 79*108 Siderite 100*10-8 Pyrite 30*10-8 |
| Ferromagnet | Bin larger | Iron ores 102-105 |
Interpreting other Sources
There are a few more definitions that will become clearer as we go on the loop journey. Some places will use J differently, some will introduce other letters like Q to corral variables together depending on applications, and some will differ from this common regime. But please don’t worry, I looked at all the confusing sources and this is the most commonly accepted way things are done. If you love pain and confusion you can read more about the common mixups at this wonderful Wiki-style site deidicated to magnetism. But we are staying right on track here and here is finally the main story.
The Story and Journey of Magnetic Hysteresis
The Hc is magnetic coercivity, a measure of the ability of a ferromagnetic material to withstand an external magnetic field without becoming demagnetized. This is an amount of A/m like H. Coercivity tells you about the hardness of a magnet too. (In case you were wondering, M = M0 + Xm(H-Hc).)
Retentivity is the capacity to retain a magnetic field after removing the external source. The mr value is the remnant magnetism, the amount of mood that lingers (retained) after he leaves the party.
Saturation, the leveling off between points 2 and 3, is when a stronger magnetic field won’t magnetize the material further. Essentially, all its domains are already pointing together, and that’s as strong as its magnetism can get. For some materials, like wood, or plastic, there aren’t many unpaired electrons anyway, so there’s no one at the party to have a vibe in the first place. That’s why those materials are diamagnetic, aka, not magnetic.
More Hysteresis Loop plots
Hard and soft magnets
| Hard Magnets | Soft Magnets |
| “permanent” magnets | electromagnet core material |
| retain saturation, high retentivity, high coercivity, (remembers) | easy to demagnetize, low retentivity, low coercitvity (forgets) |
| good for recording tape applications | good for transformers/motors |
| thicker hysteresis loop area with a high BR | thinner loop area, with a low BR |
| has significant energy losses since the applied field doesn’t change the vibe as well | minimizes dissipation |
| Examples: iron oxides, titanomaghetite, ilmenohematite, limonite, maghemite, pyrrhotite, neodynium | Pure iron, nickel, steel |
Magnetic Hysteresis Examples and Applications
One of the most interesting applications of magnetic hysteresis to me is in the field of paleomagnetism. Researchers find natural rocks and use their hysteresis measurements to deduce information about the history of the Earth’s magnetic field locally where the rock formed. But we humans have engineered some very useful technology basically emulating that same effect.. and you are probably exploiting it right now on a computer!
Hysteresis in Hard Drives Memory Storage
Imagine a hard drive that a computer can both “read” and “write” to. When you see these circuit boards, the “snake”-like patterns are like wires, or routes, carrying current. The dot-like components are usually the part that is engineered to hold the state that is to be read or written, like a notepad. They also generally contain a single domain so that that there is one single direction of magnetization for the whole particle. Currents induce magnetic fields, so those snakes are in effect bringing magnetic fields into and out of the components.
Remember that computers do everything they do by reading long series of zeroes and ones, binary code. So all we need to communicate and execute with a computer is a bunch of “slots” where each can have a zero or one state. All those dot components are the slots, and the 0’s and 1’s are going to be a zero/null magnetic state, or a non-zero magnetic state.. That’s the simplest picture of what we need!
Those components are ferromagnetic, becoming magnetized in the direction of the field passed through them. After field removal, their states relax, but not back to zero. Since all these components are triggered repeatedly, every magnetic signal will not give it an exact magnetization anymore. An exact bias signal will make a number of components average to zero though!
How to Talk to a Computer
- ZERO (0): bias + nothing = null magnetic field
- ONE (1): bias + signal = signal offset
Permanent magnet materials like iron and chromium oxides retain their magnetic state indefinitely. (More in the “soft magnets” chart above.) That’s why those materials make great components in computer disks or coatings for tape recorders.
Measuring Magnetic Hysteresis Loops
Notice the elliptical shape on the oscilloscope.
Know the Significance of Magnetic Hysteresis Loops
Even the strips in credit cards have magnetic tape similar to VCRs in them. Now those credit card strips are mainly a chip that’s even harder to demagnetize. This principle is known by inventors and engineers and is actually all around us in daily life. So now you have a little more intuition about how technology works. And you can also consider this when you find a cool rock, maybe even a rock with ferromagnetic inclusion, or a rock that conducts electricity!
Sources
[1] Becker, R. “Internal strains and magnetism.” Proceedings of the Physical Society 52.1 (1940): 138.
[2] Mayergoyz, Isaak D., and G. Friedman. “Generalized Preisach model of hysteresis.” IEEE transactions on Magnetics 24.1 (1988): 212-217.
[3] Jiles, David C., and David L. Atherton. “Theory of ferromagnetic hysteresis.” Journal of magnetism and magnetic materials 61.1-2 (1986): 48-60.
[5] VINCH model: François-Lavet, Vincent, et al. “Vectorial incremental nonconservative consistent hysteresis model.” 5th International Conference on Advanded COmputational Methods in Engineering (ACOMEN2011). 2011.
General magnetism info: https://cse.umn.edu/irm/2-classes-magnetic-materials
Some “bad” nomenclature: https://www.britannica.com/science/rock-geology/Hysteresis-and-magnetic-susceptibility
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