|Magnetism is not just about those
magnets you use to fix the refrigerator art of you kids to the door of your
refrigerator. Magnetism belongs to what we call the "electromagnetic"
phenomena, and thus is always a part of whatever one associates with words like
"electricity", "light" (more generally: "electromagnetic
waves"), or "elementary particles".
In turn, words like "electricity" or "electromagnetic phenomena" are just expressions for: "things that electric charges can do" - just as expressions like "gravity", "weight" or "trajectories of cars, planets or satellites" refer to "things that gravitational charges can do". However, since most of us are lazy and traditionally minded, we never use the term "gravitational charge" but the simpler word "mass".
all things consist of
some elementary particles
(essentially electrons, protons, neutrons, the atoms they form, and photons).
What "things" do depends on some basic properties of those particles.
As far as the topic here is concerned, all we need to know about the properties
of the everyday particles listed above is:
|On the left
we have a particle with a mass. That could be any particle that can sit still,
i.e. a neutron, an atom, an electron, and so on. The field is schematically
represented by field lines that simply
indicate the directions of the force that another particle with the proper
"charge" - here simply mass - will experience. The force is always
attractive in this case.
On the right we have particles with either a positive charge (e.g. a proton) or a negative charge (e.g. an electron). The field produced looks exactly the same as the gravitational field, but the forces can be attractive (between opposite charges) or repulsive (same charge) as shown. The magnitude of electrical forces between particle, however, is far larger (about a factor of 1040) than the gravitational forces they experience.
|We have the monopoles covered. Now
let's look at dipoles.
A dipole can be formed if a charge and an exact opposite charge is kept at a fixed distance. Since gravitational charges called "mass" only come with one sign, there can't be mass dipoles. We can easily make electrical dipoles, however:
|We now need to learn two basic truths
|In fact, some elementary particles, while
producing an electrical and gravitational monopole field due to their electrical and
gravitational monopole charge, produce a
magnetic dipole field despite the fact that
there are no little magnetic monopoles inside.
Magnetically, an electron or proton looks like this:
|A magnetic dipole field as shown is often
"abbreviated" by a simple arrow or an elongated little magnet with a
"north" and "south" pole. The electron in the figure above
has also its usual electrical monopole field (not shown) around it, and its
gravitational monopole field. The latter, however, is utterly unimportant and
will never be mentioned again.
So let's commit to memory as a basic truth: Some elementary particles are intrinsic magnetic dipoles; it is an unalienable part of their existence.
|Now we need to learn another basic truth about magnetic dipole fields:|
| An electron moves if it goes from here to there.
It may do so because it feels a force from some electrical field that happens
to be around, but it may also move for different reasons. We have a special
word for moving charges, we call that an
If a hell of a lot of electrons move in a large circle, something we call: "a large current flowing through a coil", a big magnetic dipole field is generated that looks exactly like the field of a huge big magnetic dipole. We have made an electromagnet!
Inside an atom electrons also kind of move in a circle, and the very weak magnetic dipole fields produced in this way must be added to the magnetic dipole fields that the electrons carry around directly. Since quantum mechanics kicks in, the many little dipole arrows inside an atom cannot point in any directions but only "up" or "down". We add all these little "arrows" and the effects may exactly cancel: "up" + "down" = zero. The way the electrons arrange themselves inside atoms actually promotes cancellations, and many atoms have no net magnetic dipole field.
|The long and short of this is that there are plenty of magnetic dipole moments inside atoms, and that after adding up, single atoms can have a permanent (small) magnetic dipole moment as we are going to call this dipole field from now on. That requires that all the little dipole moments of the electrons add up to something that is not zero. That must happen in all elements with an odd number of electrons because an "up" dipole can be perfectly canceled by a "down" one. For an even number of electrons cancellation is possible and happens for most (but not all) of those atoms and you get nothing.|
|Atoms thus either have some magnetic dipole field, or they don't. The question is: how can we tell? The answer is: Same as with electrical or gravitational fields. Wherever there is a magnetic field of whatever shape, there is a force on particles with a magnetic dipole moment. The dipole feels a force that tries to move it along the field lines and in addition - and that is new - a momentum that tries to rotate the dipole in such a way that its little magnetic arrow points in the direction of the field line arrow.|
|By now you are probably about to exclaim: "Much ado about nothing! I know that some piece of material is magnetic if it sticks to a magnet. I use magnets all the time when I put up refrigerator art from the kids".|
|I don't mind you quoting Shakespeare at me, but
now tell me what, exactly, constitutes a magnet? Can you, personally, make one
"from scratch" meaning from a bunch of suitable atoms? Very few
people - and that includes scientists - could answer this question or pick the
right kinds of atoms after just thinking hard for a while.
Let's see why "making" a magnet is a difficult conceptual enterprise:
|Easy and self-explaining. Diamagnetic
materials are simply not magnetic at all, meaning they cannot produce any
magnetic fields. Paramagnetic materials produce tiny little dipole fields on
atomic dimensions but since they are distributed randomly, adding them up gives
zero on somewhat larger dimensions. Only in ferromagnetic materials as drawn
above will the tiny little dipole fields of the individual atoms add up to a
big strong dipole field of the crystal - we would get a magnet with a magnetic
north and south pole.
The obvious question now is: Which elements are what? Looking not too closely and at room temperature, there is an easy answer:
|Looking a bit more closely, things get way more
complicated. I'll give you a few points:
|Now that we have fancy Latin names
for the three basic magnetic types, and some idea of what's going on
magnetically in the periodic table, we feel much better,
and are now ready to tackle the tough question:
|Looking into this in some detail would require an advanced lecture course in physics or Materials Science. In what follows I will therefore cover only a few essentials.|
|1. How Come?|
|Why do iron atoms in a bcc crystals
align their magnetic moments in the same directions (ÝÝÝÝ), producing
ferromagnetic order, while quite similar other elements don't care? And why do
they refuse to do that when you force them to make a fcc crystal? Why does
chromium pick the anti-ferromagnetic order (ÝßÝß), and so on?
There is a simple and an supremely difficult part to those questions.
part goes first. Obviously, if the magnetic moments of neighboring atoms align
(or anti-align) themselves, they must "feel" each other. There must
be an interaction, a force, an energy between those moments that is strong
enough to compete with whatever mechanisms try to destroy order.
This force obviously depends sensitively on parameters because it - obviously - is rather strong for iron atoms in a bcc lattice and rather weak for iron atoms in a fcc lattice, rather strong for cobalt atoms but rather weak for copper atoms, and so on.
Sometimes this interaction wins, but mostly it looses.
|The difficult part is to write down proper equations for this interaction force, and then to solve these equations. We must delve rather deeply into more involved quantum theory to do this. Scientists have been doing this for many years by now, and quite a number of high-powered guys are doing this right now. A lot was achieved - but nobody at present can really make a ferromagnetic material from scratch, meaning calculating all its properties knowing only that it is iron or cobalt.|
|When we extend this to compounds, alloys, amorphous materials, nanostuff, and so on, we are talking about one of the larger and flourishing research fields we have right now in physics or Materials Science. And that is all I'm going to say to question No 1.|
|2. What Makes a Magnet?|
|Some pieces of iron or of any
ferromagnetic materials are strong magnets, some are not. How come?
Let's look at what we mean by the word "magnet" first.
|A material-based magnet, or a bit more precisely, a permanent magnet, is a piece of material that always attracts ferromagnetic materials that are not magnets themselves, and attracts or repulses other magnets.|
|A magnet, in other words, is simply some ferromagnetic material that has a sizeable magnetic dipole field around itself. We can make that field "visible" by having small ferromagnetic particles around (simply iron filings, for example) that we disperse on a glass plate above a magnet. The filings orient themselves in the field of the magnet, and if we do it right, friction will prevent them from moving close to the poles of the magnet. What we get looks like this:|
|And here you have the reason why all ferromagnetic materials do their best not to be a magnet.|
|If you are a magnet, you fill the space around you with a magnetic dipole field and that field, like all fields, contains energy. Quite a lot, actually. That goes straight against the second law that states in no uncertain terms that you must minimize your free energy. Since magnetic fields are also orderly things, it doesn't help to invoke entropy, The simple truth is|
|On the other hand, the very fact that we discuss ferromagnets here means that in the quest for nirvana, alignments of magnetic moments at the atomic level is good. It lowers the energy of the interaction between the atoms and low energy is a pre-requisite for nirvana. But alignment of the dipoles for many atoms creates that big external field with lots of energy that is bad for nirvana... Help!|
|Can you help those ferromagnetic crystals that
want to be orderly but have to pay a high prize for it? I doubt it. But they
don't need you help, they know what to do: Compromise!
Be orderly - but not in the same way everywhere. Don't do like shown in the left-had side of the figure below, but in a smarter way:
domains are formed. In well-defined regions of the crystals the
magnetic momentums of the atoms are all aligned in the same direction (usually
a prominent crystal direction, called an
"easy" direction); in other regions they point in some other
directions as shown above. If done smartly (right side of the figure above),
the rather big magnetic fields of those magnetic
domains overlap in such a way that they essentially cancel each
other outside the crystal. In other words,
summing up the the red arrows above that we will call magnetization vectors of the domains, gives a net
magnetization of the crystal close to zero.
Of course, the first law of economics must not be denied either, so there is a price to pay. Between the domains are what's called domain walls, thin regions where the alignment is out of whack, and that costs some energy.
|The crystal must do a tricky optimization job. It
wants alignments of the magnetic moments, as much as possible, but needs to
avoid external fields. That calls for lots of domain (far right in the figure
above) - but this costs dearly in terms of domain walls. Moreover, in different
crystal grains the "easy" directions are different, and that needs to
be accounted for.
There is much more to consider but that is beyond your ken, dear reader. Actually, considering everything and then coming up with the best possible domain structure, is even beyond our ken. Even Materials Scientists cannot calculate the optimum domain structure at present.
|Funny enough, our ferromagnetic crystals don't have that problems. They just make the best possible domain structures. Here are some examples of what you observe in reality:|
|The arrows were drawn in and show the direction
of the field.. Otherwise: different shades / colors = different orientations.
Those magnetic materials produce amazing to outright beautiful structures! By the way, if you think that the inability to calculate those structures in details reflects badly on our mathematical prowess, think again. All I'm going to say is that you will encounter functions that mathematicians, for good reasons, call diabolical functions, with various degrees of diabolicity.
|Whatever the domain structure looks like in detail, the effect is always that the material has no magnetic field on the outside and thus is not a "permanent magnet"!|
|So why is it attracted by a magnet?|
|Ferromagnetic Materials in a Magnetic Field|
|Let's put a ferromagnetic material that is not a permanent magnet because of its domain structure into a magnetic field. We do that, for example, by putting the material inside a coil. A current running through the coil produces a magnetic field inside the coil, and if we crank up the current, the strength of the magnetic field increases. The crystal responds and what we measure is the magnetization M of the crystal, the total effect of the alignment of the magnetic moments. It is close to zero in the beginning because of its the domain structure.|
|What we will get as a result looks like that:|
|A rather rich picture. What does it show? Let's
look at it like 1, 2, 3, ..
|Here is what it really looks like:|
|Saturation, by the way, occurs very roughly at a
field strength around 1 Tesla for the best magnetic materials we have.
"Tesla" is a weird and stupid unit for the
strength of magnets; it replaced the sensible and dignified "Gauss". If you know anything about the guys with
these names, you get my point.
Anyway, now you know why it is extremely difficult to go beyond 1 Tesla in technology. Materials can't help anymore. Only brute force, meaning enormous electrical currents, will do the job. If you want to go into high magnetic field research, you better buy yourself a sizeable power plant first.
|The fun starts when we run our experiment backwards. After we reached saturation of the material we start to decrease the field by cranking the current down. What we will get looks like this:|
|We do not simply run down the same curve we produced running "up" (the virginal curve, shown in thin lines above) but run "in circles" or in a hystereses loop as it is called. The reason for this is simple:|
|Running up the magnetic field moved domain walls,
but ever so reluctantly. Only because increasing the field increased the force on those walls, did they
condescend to move on a bit. Now you decrease the field. The domain walls move
back to some extent but then gets stuck. You decrease the field even more - and they will stay
That describes roughly the behavior of the blue curve that is typical for what we call "hard magnetic materials". When the field is reduced to zero, there is still a lot of magnetization in the material, described as the "remanence" of the material. You need to apply a sizeable magnetic field in the opposite direction to get those domain walls to move back to the original position with a zero magnetization of the material. The strength of this magnetic field we call the coercity of the material.
You realize, of course, that I just gave you the recipe for making a permanent magnet: get a hard magnetic material. Stick it into a coil and run up the current until you get saturation. Switch of the current, take your material out: it's a permanent magnet now - with a strength given by the remanence of the material you picked.
material have little remanence and coercity an thus are not good for
Of course, the obvious question now is: what makes magnetic materials "soft" or "hard"? The obvious answer is: in soft magnetic material , domain wall can be moved rather easily, in contrast to hard magnetic materials. The real question thus is: What, exactly, determines how easy or difficult it is to move a domain wall? Or, to put the question another way: how can I magnetically harden or soften my material?
|You guessed it. By optimizing the kind of material you use (don't just take some iron, alloy it with this and that!) and then doing some defect engineering (small / large grains, precipitates dislocations, ...)|
|The basic principles are rather similar to what we do for hardening iron / steel mechanically. We are simply talking basic Materials Science and Engineering principles here.|
|Back to magnetic materials. Let's just look ever so cursorily at what one does with magnetic stuff. I'll give you two lists - one for soft, and one for hard magnets|
|Basic uses of hard magnets:
|Basic uses of soft magnets:
|How About Temperature?|
|Imagine all the magnetic moments of
the atoms in a ferromagnetic material to be nicely aligned at room temperature.
The atoms do that because that lowers the energy, or more precisely, the
enthalpy of the system by some DHorder. It's good for nirvana.
Now heat up the material to a temperature T.
|Perfect alignments means perfect order and
entropy S. That's fine
at low temperature, including possibly room temperature, because the entropic
part TS of the free enthalpy G would be small
even if there would be disorder.
At higher temperatures, however, it simply doesn't pay anymore to save some energy DHorder, if TSdisorder would be larger, i.e. G = H TS would be smaller for disorder.
|So for exactly the same reason why an ordered arrangement of atoms (called solid crystal) gives way to a disordered arrangement (called liquid) at some special temperature called "melting point", ferromagnetic ordering of magnetic moments gives way to paramagnetic disorder at a special temperature called Curie temperature.|
|Loosing magnetic order is a gradual process. The perfection of the alignments and thus the magnitude of the resulting magnetization decreases with increasing temperature. At the Curie temperature the distribution of the atomic magnetic moments is completely random and the magnetization zero. This is shown below|
|The circles show experimental data. The red
curves and the green squares were calculated with the presently best theories:
QMC" for "quantum Monte Carlo" and IMFT for "dynamical
mean-field theory". cMC stands for the older "classical Monte
|I like to make two points to these diagrams|
|1. The saturation magnetization Msat and the Curie point temperatures TCurie for the three metals shown above are quite different. But if you plot with "reduced" quantities (M/Msat and T/TCurie), they are very similar. This simply shows that the underlying mechanism is the same.|
|2. All three theories are rather sophisticated and need big computers to produce results. While the "classical" Monte Carlo approach produces a curve that is not too close to the measured ones, the more sophisticated theories are getting there. The difference is simply raw computer power. One thing, however, is obvious:|
Periodic Table of the Elements
Overview of Major Steels: Scientific Steels
Diffusion in Iron
5.2.1 The Gang of Four
Bravais Lattices and Crystals
Alloying Elements in Detail
Diffusion in Iron
Gibbs Phase Rule
Additional Pictures - Chapter 1
4.4.2 Moving Atoms Around
Experimental Techniques for Measuring Diffusion Parameters
Overview of Major Steels
The Second Law
Large Format Pictures - Chapter 6.2
Melt Spinning of Metals
Additional Pictures - Chapter 7.1
Going to Hell in Style
© H. Föll (Iron, Steel and Swords script)