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I recently bought some buckyballs, considered to be the world's best selling desk toy. Essentially, they are little, spherical magnets that can form interesting shapes when a bunch of them are used together.

After playing around with these buckyballs for a while, I wondered: "Can these guys ever lose their magnetism?" Then I went a step further and thought, "How are magnets affected by the 2nd law of thermodynamics?"

So, how are magnets affected by the 2nd law of thermodynamics? Do they break down and lose their magnetism over time (like iron rusts over time)?

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What kind of "law of entropy" do You have in mind? What kind of "affection" do You have in mind? –  Georg Apr 4 '11 at 16:17
    
To where it breaks down and loses its magnetism. –  Stephen Watkins Apr 4 '11 at 16:20
    
Buckyballs aren't particularly magnetic, according to the Wikipedia article I just skimmed. en.wikipedia.org/wiki/Fullerene –  Mark Eichenlaub Apr 4 '11 at 16:23
    
I'd say, they are not "magnetic" in the popular sense at all. Presumably diamagnetic? –  Georg Apr 4 '11 at 16:33
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@Steve: well, that's just one consequence of the law of entropy (or as it's more properly called, the 2nd law of thermodynamics). As you may have figured out by now, it refers to the fact that physical systems tend to become more "disordered" over time. –  David Z Apr 4 '11 at 21:11
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3 Answers

up vote 4 down vote accepted

The second law of thermodynamics - about the increasing entropy - which is apparently what you're talking about - holds for any system. Permanent magnets are no exception.

A ferromagnet may look "more ordered" than a non-magnetic material because the spins are oriented in the same direction, rather than random directions. But physical systems may only try to maximize their entropy among configurations that conserve energy (much like the momentum, charge, and other conserved quantities). For ferromagnets, the configuration with spins oriented in random directions would have a much higher energy - because one reduces the energy by orienting the spins, elementary magnets, in the same direction.

So the spontaneous disappearance of the uniform electrons' spin would violate the energy conservation.

Among the configurations with the same energy, the magnet still tries to maximize its entropy. In particular, the heat is flowing from warmer pieces of the material to colder ones, and so on. More generally, the entropy never goes down, and that's the only general statement that follows from the second law of thermodynamics.

Ferromagnets are not special among physical objects that could have a higher entropy if you allowed the energy to increase. For example, any object would raise its entropy - the amount of disorder - if its temperature increased. But a higher temperature requires a higher energy, too. One can't violate the first law of thermodynamics (energy conservation) just because it would make it more straightforward to satisfy the second law. Both of them hold in Nature.

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Ferromagnets below Curie-Temperature without macroscopic magnetisation exist, they just have crystalline compartments (Weiss domains) magnetised in random directions. This is a state which ferromagnets achieve after long times (or unwise handling) –  Georg Apr 4 '11 at 17:55
    
Ok. I'm downvoting this. I thought about the decision for a while then I realized the only reason I was giving it so much thought is because the wrath of @Lubos can be truly brutal. But that should not be any reason to let an answer pass which does not answer the question. Yes, the laws of thermodynamics are valid. That's why the OP is asking the question. It might seem naive but it gets to the heart of the 2nd law. If I build a house it falls apart. The human body decays. So do neutrons and nuclei. Why should a ferromagnet or a buckyball be any different? –  user346 Apr 5 '11 at 3:59
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Since this question has linked, I would like to note that Lubos's answer is essentially correct, except it does not include the formation of magnetic domains, which Georg enigmatically referred to above. –  BebopButUnsteady Sep 14 '11 at 20:29
    
-1 because (a) a magnet is not a closed system, it's energy does not have to be constant (b) the magnetic after-effect is driven by energy minimization, not by entropy maximization. –  Edgar Bonet Sep 21 '11 at 19:45
    
-1 (sorry) because of the magnetic domain issue. Magnetic domains will spontaneously form, and they lower the energy because they lower the bulk field. It is strange that a local wall will lead to a bulk loss of energy, but this is a phenomenon almost unique to magnets. –  Ron Maimon Dec 12 '11 at 10:47
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In a material with a net magnetization, the domains are aligned and are in a higher energy state than they would be if not aligned. The second law of thermodynamics says that because there are overwhelmingly more states in which the domains are not aligned (or 'ordered'); it is overwhelmingly more probable that the material transitions into a state with unaligned domains (or 'less order'). However, life is not that simple. There is a finite, often extremely long delay in the transition to the less ordered state, due to 'snagging' of the crystal lattice.

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The main reason a magnet may lose it's total magnetization is not entropy but energy. The demagnetized state does have slightly more entropy, but the above all it has a lot less energy, specifically less demagnetizing field energy. –  Edgar Bonet Sep 21 '11 at 17:19
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Entropy has little to do with magnets loosing their magnetization. The problems is that magnets store large amounts of energy in their magnetic fields. This is usually described as the energy of the demagnetizing field, and it's just another way to refer to the magnetic coupling of individual magnetic dipoles (not the exchange coupling, just the classical dipole-dipole interaction).

A magnetic material can lower this energy by adopting a magnetic configuration that minimizes magnetic charges (i.e. magnetic poles). It does so by moving it's domain walls in a way that lowers the total magnetic moment. A good magnet has many crystallographic defects that pin the walls. However, if the temperature is high enough, and if you wait long enough, the walls will eventually “creep”. This is called “magnetic after-effect” and gives a characteristic variation of the magnetization which is linear in $\log(t)$. This behavior can be explained by the fact that domain walls face a very wide distribution of energy barriers.

Good permanent magnets are supposed to show very little magnetic after-effect. As a special case, single domain magnets are a type of nanomagnets that do not show this after-effect at all, simply because they have no creepy domain walls as they would cost too much exchange energy. An assembly of such particles can however loose its magnetization because of individual particles switching from one magnetic orientation to another. This is called superparamagnetism and is an obstacle to increasing bit density in magnetic storage (i.e. hard drives).

Edit:

There is some evidence that the demagnetization of a magnet is driven by its dipolar energy rather than by entropy. First, there is the van den Berg construction (see for example the book Principles of Nanomagnetism, by Alberto Passos Guimarães). This is a geometrical way of predicting the magnetic configuration that minimizes dipolar energy in a flat magnet. The predicted configurations have actually been seen on real micron-sized samples, when imaged by MFM, Kerr or XMCD. If the walls were driven by the urge to maximize their entropy, then one would see them wandering randomly all around the sample. Instead, on soft samples, they can be seen to adopt the exact configuration that was predicted to minimize the magnetic dipolar energy.

Another evidence is numerical micromagnetics. This is the art of numerically predicting the magnetic configuration of microstructures. The predictions are done by minimizing the total magnetic energy (sum of dipolar, Zeeman, anisotropy and exchange), with little consideration to entropy. The fact that numerical micromagnetics can be quite successful is an evidence that energy is more important than entropy in the behavior of magnets.

On the other hand, if one considers a diluted assembly of magnetic nanoparticles close to their blocking temperature, then the demagnetization of the assembly is actually entropy-driven. Only when the nanoparticles get quite close to one another their interaction energy starts to play a significant role.

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@downvoter: could you please explain your problem with my answer? –  Edgar Bonet Oct 23 '11 at 14:09
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I personally added my own downvote, your second one, because you impliticly say that the reason why the magnetization stays is the energy of the magnetic field itself, like $\int B^2/2$. However, the latter is positive, so Nature would surely love to spontaneously reduce it if it could. This was really the (valid) point of the OP. The actual reason why it doesn't happen is that there is a negative interaction energy from the elementary magnets' being oriented in the same direction. –  Luboš Motl Jan 11 '12 at 8:21
    
@Luboš Motl: Please, show me where I am implicitly saying that. I did not say a word about exchange interaction, or microscopic magnetization. I am only talking about magnetic configuration, i.e. the arrangement of domains and domain walls. –  Edgar Bonet Jan 11 '12 at 9:04
    
Frankly the phrasing of this answer is sketchy in my mind because while energy concerns must be dealt with that simple does not dismiss entropy concerns: it simple adds a term to the free energy that should be considered. Adding a quantitative indication of the dominance in at least one of your sections would help. –  dmckee Oct 20 '12 at 17:18
    
@dmckee: Adding a single domain wall in the middle of the magnet decreases its energy by a macroscopic amount (proportional to the size of the magnet). But since the wall is microscopically thin, and has very little degrees of freedom, its presence only increases the entropy by a microscopic amount. –  Edgar Bonet Nov 16 '12 at 11:08
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