Yep, “hysteresis.” Not to be confused with “hysteria,” which is how you might be feeling the first time your professor drops this word on you (you probably heard it for the first time when you learned about magnets). Hysteresis is a fancy word from math/physics, with a surprisingly simple meaning.
Hysteresis means that some behavior is history-dependent. When two variables with hysteresis are graphed, they generally form a “hysteresis loop.”
The most common example of hysteresis is ferromagnetic hysteresis, which shows “magnetic memory” in the relationship between an applied magnetic field and the material’s internal magnetism.
If you don’t know much about magnetism, don’t worry–this article will tell you everything you need to know to understand magnetic hysteresis! And if you want to know everything about magnetic materials, I wrote a huge post on the subject which you can find here.
From a thermodynamic perspective, hysteresis indicates an irreversible thermodynamic change. This can be due to many things, but in the case of magnetism, the hysteresis curve shows that work is being done
Since we use magnetic work for tons of things (such as hard drive memory or transformers), magnetic hysteresis is very important. Additionally, engineers categorize magnets for different applications based on their hysteresis curve.
What is Hysteresis?
This post is mostly about magnetic hysteresis, but I know that for many of my readers, this is the first time you’ve encountered the word “hysteresis.” Expand the box below to get a general idea of what hysteresis means, and I won’t mention magnetism at all.
Click here to learn about hysteresis.
Hysteresis means that a behavior is history-dependent. Current behavior is partially dependent on previous behavior.
When you graph hysteresis, it forms a loop–we call this a hysteresis loop.
So let’s graph something that I hope everyone is familiar with: restaurant lines (or queues).
Imagine that you have restaurant with a certain level of food quality–we’ll graph that on the x-axis. On the y-axis, we’ll graph the line (queue) size.
You might think that as food quality increases, the line size increases proportionally. However, this thinking wouldn’t consider social proof.
It turns out that people trust restaurants more when they have a long line! So at any given moment, the length of the line outside the restaurant is related to the food quality and the previous length of the line.
So imagine we ran an experiment to change the food quality and measure the length of the line outside the restaurant.
At first, food quality is poor. Almost no one comes. The food quality increases, but only a few more people come. In general, people don’t trust a restaurant without a line. There is not enough social proof.
As the food quality increases, at some point the restaurant does have a sizable line! Now the line increases quickly, even though the food quality continues to increase at the same rate.
Eventually, the restaurant runs out of people. Everyone has joined the line, so no matter how much the quality increases, the line has reached its maximum size.
But now, what happens if we decrease the quality of the food? Line length will NOT retrace the same path it took as quality increased!
The restaurant starts out at excellent food quality and a maximum line. As the food quality decreases, the line only decreases a little bit. Most people still see the long line and stick around because of social proof.
As the restaurant quality decreases, the line will continually shrink. The smaller the line becomes, the faster it shrinks.
However, even when the restaurant has decreased its quality to the original value, the line length is still longer than it was at the start!
At the exact same food quality, it’s possible to have two different line lengths, based on the line length at some time in the past.
What is Magnetic Hysteresis?
Okay, first things first. It’s not really “magnetic” hysteresis. It’s ferromagnetic hysteresis.
Click here for a minor technicality.Okay, fine, it could also be a ferrimagnet. I’ll discuss this and other details on my comprehensive article about magnetism in materials. Also, you can check out this article to find a list of ferromagnetic and ferrimagnetic materials!
Ferromagnetism is what most people think of as regular magnetism, and it’s the type of magnet that has this hysteresis curve.
Actually, all materials are magnetic, but since they aren’t ferromagnetic they don’t have a hysteresis curve and therefore aren’t interesting to most people.
This article is just about the hysteresis curve, so don’t worry about diamagnetism or paramagnetism. But just to illustrate, here is the magnetic curve for “regular” paramagnetic materials. You can see it’s just linear, there is no hysteresis.
You can see, there is no “history-dependence.” For every value of H, there is a unique value of B. It doesn’t matter whether you are increasing H or decreasing H, B will always be the same.
This is a B-H curve, or magnetization curve. Imagine I apply a magnetic field. What magnetic field will my material have? That’s what this graph tells us.
I’m not sure why these variables were chosen but H, on the x-axis, is the applied magnetic field. It can be positive or negative (just like an electric field).
H is just the field we create ourselves. We can increase positive H by bringing a magnet near the sample, and we can increase negative H by bringing the opposite pole of a magnet near the sample. We could also use an electromagnet–it doesn’t really matter. H is just the magnetic field that we control and use to explore B or M.
On the y-axis, the graph has B or M. For now, I’m just going to use B, because it’s more common in physics/materials science. If you want to know more about what M and B actually mean (and their small difference), you can check out this short article I wrote.
If you just want to know about hysteresis, don’t worry about it. B is called the magnetic induction or magnetic flux density. It’s the magnetic field produced within the material. It’s basically how much of the magnetic field the material “feels.”.
So you see, for a regular material, you apply a magnetic field (H) and the material also experiences that magnetic field (B). But then if you remove the external magnetic field, the material also loses its field.
For a ferromagnetic material, the material can “hold” or “remember” that magnetic field. Check out the graph below which shows what happens as you increase the external magnetizing force, then decrease it.
If you notice, this graph looks exactly the same as my graph of restaurant line size. Magnetic B is like the number of people in line, and magnetic H is like the quality of the restaurant.
Look, the ferromagnet can have different values of B while H equals zero. At first, B is also zero, but later it has a positive, non-zero value. This is history-dependence, and it’s the defining feature of ferromagnets.
Why Hysteresis Occurs (Ferromagnetism)
In ferromagnets, when an external magnetic field is applied, the ferromagnetic domains align to match the field.
This is typical behavior for most materials. However the ferromagnetic domains are so strong that–once they are aligned–they reinforce each other and stay aligned even after the applied magnetic field is turned off. (This is similar to my example with the restaurants–when domains line up, they reinforce each other the same way humans reinforce each other through social proof).
That’s why ferromagnets have hysteresis or history dependence. Depending on the previous state of the applied magnetic field, the material’s magnetic induction will be different.
In fact, the ferromagnetic domains will retain their memory even in the presence of an opposite applied magnetic field–up to a point.
Once the negative applied magnetic field is strong enough to realign the domains, B will have the opposite value.
In the case of magnetism, negative is just an arbitrary definition–it could be the north or south pole of a magnet, as long as it’s the opposite from the direction you started. For convention, we usually set the positive end as North, and the negative end as South.
If you apply a positive field again, the magnet will again switch. Cycling between positive and negative applied magnetic fields creates a hysteresis loop.
As you can see, depending on the previous state of H which changes domain alignment (controlling B), B can be many different values.
B could be zero at its initial position. If you applied and released a small H, you could have a small B. Applying and releasing a larger H would result in a larger B (up to a limit). The same applies to negative values of H and B.
Now you know why ferromagnets are history-dependent (i.e.: have hysteresis)!
Important Values on the B-H Hysteresis Loop
As you can imagine, different points on the B-H curve have special names so scientists and engineers can talk about stats and use math.
For now I’ll just use English names because the specifics change a little depending on whether you are graphing B or M, so if you want to know more specific variable names you can check out that article.
So we start at B=0 and H=0, then we cycle between some positive and negative values of H to get the regular hysteresis curve.
The left and right ends of the loop (a and d) are called the saturation points. At the point, all the domains are aligned, so there is no more hysteresis effect. As long as H remains higher than the saturation point, there is only one value of B for one value of H–the previous value of H no longer matters.
The point where B intersects the y-axis (b and e) is called remanence, retentivity, or residual magnetism. This tells us how much magnetism is generated by the material itself, once the external field is removed. Specifically, remanence is the value of residual magnetism which occurs if H is taken to the saturation point.
If H were taken halfway to the saturation point and reduced back to zero, the residual magnetism in this moment would be lower than the theoretical retentivity.
The point where B intersects the x-axis (c and f) is called coercivity. The coercive force is the force required to remove the residual magnetism, and return the inductivity to zero.
The slope of the B-H curve is called permeability. This tells you how easy it is for the material to magnetize (how easily the domains align). If you measure permeability over a range, it is “apparent permeability.” Otherwise, “incremental permeability” is the derivative.
The opposite of permeability is reluctance. Like conductivity and resistivity, permeability and reluctance are two ways to describe the same phenomenon.
The area within the hysteresis curve is the energy spent, or work done, by each cycle. The work depends on the remanence, saturation point, and coercivity of the material.
Based on the width of the hysteresis loop (coercivity), we can quantify a material as “hard” or “soft.” Hard and soft magnets have very different uses in technology.
Soft vs Hard Magnets: Applications
Magnetic “softness” or “hardness” is a continuum. However, magnets are usually classified as one or the other depending on their intended application.
Hard magnets are used as permanent magnets. They are designed to maintain their magnetic remanence, even in the presence of opposing magnetic fields.
Soft magnets are used as temporary magnets. They are designed to constantly switch polarity.
For a good hard magnet, engineers want a material with high coercivity (and high remanence, because that makes the magnet stronger). This makes the area inside the hysteresis curve large, meaning that it will take a lot of work to remove the magnetism from the material.
Since this kind of magnet is difficult to demagnetize, they make good permanent magnets. This is the kind of magnet that you stick to a refrigerator. Hard magnets are also used for computer storage in hard drive memory.
Hard magnets are used in:
- Hard drives
- Refrigerator magnets
- Electric motors
- NMR / MRI body scanner
- Anti-lock braking system (ABS)
Some examples of hard magnets are:
- Alnico (typical composition 35% Fe, 35% Co, 15% Ni, 7% Al, 4% Cu, 4% Ti)
- NdFeB Magnets (that contain magnetic phase Nd2Fe14B)
- Samarium Cobalt (SmCo5, Sm2Co17)
- Hard Ferrites (BaO.6Fe2O3 and SrO.6Fe2O3)
- Garnets (A3Fe5O12, where A = Sm, Eu, Gd, Dy, Ho, Er, Tm, etc. any rare-earth element)
For a soft magnet, engineers want a material with a small energy loss from cycling. This means they should have a low coercivity, and small remanence. However, since remanence is basically the strength of the magnet, the material still needs to have a high enough remanence to perform its intended application. Unfortunately, coercivity and remanence tend to go together. A material with low coercivity will likely also have low remanence.
For example, hard drive memory relies on little magnets to “remember” their state (this is why you shouldn’t bring a powerful magnet too close to your computer). These magnets are constantly switching as the hard drive writes, so the smaller the area in the hysteresis curve, the less energy is required to write data.
However, the data still needs to be read, so the remanence can’t be too low. In the case of hard drives, not losing memory is more important than wasting energy, so the magnets tend to be hard.
One really common use for soft magnets is in electrical transformers. These switch the magnetic field very rapidly, so minimizing energy loss is a priority.
Soft magnets are used in:
- Transformer cores
- Electric motors (to enhance the magnetic field)
- Magnetic shielding
Some examples of soft magnets are:
- Ni-Fe alloys (permalloy: 80% Ni, 20% Fe, Mu-metal: 77% Ni, 16% Fe, 5% Cu, 2% Cr or Mo, supermalloy: 75% Ni, 20% Fe, 5% Mo)
- Silicon Steel–typically consisting of 1-4% Si, 96-99% Fe
- Soft Ferrites (MO.Fe2O3, where M = Ni, Mn, Zn)
- Nanocrystalline alloys like FINEMET
Yes, if you noticed, iron can be either a hard magnet or a soft magnet. Like most properties, magnetism can be dependent on microstructure. In the case of iron, if you make the grains very small (smaller than a regular magnetic domain), it will be a hard magnet. “Regular” grained iron or steel will be softer.
Does Hysteresis Occur Outside of Magnetism?
Yes, hysteresis is a fundamental concept in science, and it occurs in many places outside of magnetism. In addition to ferromagnetic or ferrimagnetic induction curves, hysteresis can be found in:
Ferroelectric polarization curvesFerroelectrics actually have nothing to do with iron. Whichever scientists named this thought the hysteresis curves looked exactly like ferromagnetic hysteresis curves, so he decided to call them “ferroelectrics.”
Rubber band stress-strain curvesYou were probably taught that rubber bands were elastic, but from a scientific perspective, that’s not quite true. When you pull a rubber band, it actually doesn’t quite return to its original shape.
Shape memory alloysShape memory alloys (SMAs) have hysteresis curves because of stress-induced phase transformation.
I hope that now you know everything about magnetic hysteresis! You learned about why the hysteresis loop appears, and what the magnetization curve says about a magnet. You also learned how to classify a magnet as “hard” or “soft,” and why magnetic softness is useful.
If you want to get into graphical details about the magnetization curve, I recommend you check out my article on magnetic induction vs magnetization.
If you want to learn all about magnetic materials, including paramagnetism, diamagnetism, and other types that I skipped in this article, be sure to check out my comprehensive guide to magnetic materials.
References and Further Reading
If you want to know more about the differences between B-H and M-H loops, don’t forget to read this post.
Check out this article to learn about magnetism and that one to see which metals are magnetic.
If you at to learn more detailed information about hard magnets and soft magnets, these two pages from the University of Birmingham are an excellent resource.