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Misreporting on spin ices and 3rd law of thermodynamics

Laura Bovo and 7 equally British co-authors published an article on spin ices in Nature Communications:

Restoration of the third law in spin ice thin films (full paper in HTML)

First thin films of spin ice reveal cold secrets (London Nano press release)
They created thin films out of a spin ice, a cute form of matter, and observed that their large entropy goes away at 0.5 °C above the absolute zero. They argue that a necessary condition for this loss of entropy in their setup is that the atoms of the spin ice are strained by the underlying substrate. This general research direction could improve hard drives and other technologies that depend on a "high concentration of magnets" in materials even though the relevance could be more indirect than some writers suggest.

At any rate, this loss of entropy means that the third law of thermodynamics is restored. After all, the word "restoration" is the first word in the title of the paper in Nature. So even a linguist should be able to understand that the physicists claim – and claim for the first time – that they may show that the third law of thermodynamics actually does hold again when something is done to the spin ice.

Crazily enough, some journalists writing about this paper got up upside down. Once again. Ladies and Gentlemen, which part of the word "restoration" do you misunderstand?

There are numerous reports in the mainstream media (more links) but Rebekah Marcarelli chose the following title:
Spin Ice Defies Third Law Of Thermodynamics; Finding Could Lead To Devices That Use 'Magnetricity'
Ambarish Ganesh chose a nearly identical title; the two articles are probably not independent from one another.

Cool. Except that the point of the new breakthrough is exactly the opposite – namely that not even spin ice may eternally defy the third law of thermodynamics.

Recall that the first law of thermodynamics is essentially the energy conservation law; the second law of thermodynamics is the law that prohibits entropy from decreasing and that makes macroscopic phenomena irreversible as a consequence.

The third law of thermodynamics says that the entropy of a physical object goes to zero, \(S\to 0\), if the absolute temperature \(T\) converges to zero (i.e. if the temperature converges to the absolute zero, if you want a reformulation of the statement for a general temperature scale), \(T\to 0\,{\rm K}\).

In classical (non-quantum) physics, the entropy was only determined up to an unknown additive constant \(\Delta S\). One could only consider "entropy changes" to be well-defined but not the absolute magnitude of the entropy itself. From the perspective of statistical physics, this ambiguity isn't hard to understand. The entropy \(S\) is \(k\) times the logarithm of the volume of the phase space.

But the arguments of logarithms should better be dimensionless in order to avoid nonsensical results such as "the logarithm of a joule second" so the volume of the phase space has to be divided by a natural "unit of the volume in phase spaces". But there is no "natural" or "canonical" unit cell in classical physics \(\Omega_0\), so we must write the entropy as\[

S = k \ln\zav{ \frac{\Omega}{\Omega_0} } = k\ln \Omega - k \ln \Omega_0.

\] The second term is additive and equal to a universal unknown constant (independent of the state of the physical system we consider). However, in quantum mechanics, this ambiguity goes away because the volume \((2\pi\hbar)^N\) of the phase space defines the natural "quantum cell" where a single "quantum state" may live. The uncertainty principle prevents us from dividing the phase space more finely.

So in quantum statistical physics, the entropy is well-defined and the additive ambiguity from classical physics is eliminated. We may therefore ask what is the value of entropy \(S\) of a physical object for \(T\to 0\,{\rm K}\). And yes, the answer of the "quantum-refined" third law of thermodynamics is \(S\to 0\).

This statement means that the quantum state of the physical object becomes essentially unique for \(S\to 0\). Which state is it? It is the ground state i.e. the energy eigenstate corresponding to the lowest possible energy eigenvalue. All excited states are prohibited at \(T=0\,{\rm K}\).

This claim, \(S\to 0\), is sort of self-evident for the crystals. Crystals pick predictable "right" locations for all the nuclei which minimize the energy. Their oscillations about these optimum positions look like quantum harmonic (or just slightly anharmonic) oscillators and those have a strictly separated ground state, too. So everything is found in a unique ground state.

If you use a basic-school simplified version of condensed matter physics, you may say that gases become liquids at lower temperatures and those freeze into solids, namely crystals, at even lower temperatures. So at \(T=0\,{\rm K}\), all materials become solid crystals and those crystals' ground state is unique, as the previous paragraph wanted to explain.

However, since the quantum revolution in the 1920s, condensed matter physics for "adults" began to flourish and expand. Solids, liquids, and gases (and plasma) are not the only forms of matters. Condensed matter physics distinguishes metals, Fermi gases, Fermi liquids, superconductors, superfluids, and many other things. These categories are not disjoint. Lots of adjectives may be added in front of these forms of matter to describe subsets of the materials, and so on.

Just like the schoolkids may say that "everything is solid" at \(T=0\,{\rm K}\), more adult physicists may conjecture that all materials tend to become Fermi liquids at the absolute zero. There's some simplicity and the uniqueness of the ground state – the vanishing of the entropy – is sort of manifest.

The most famous form of matter that has the "potential" to violate the third law of thermodynamics are the spin ices, first hypothesized by Linus Pauling in 1935. Pauling was thinking about the ordinary water ice. He would decide that the crystals were effectively composed of tetrahedrons and oxygen atoms at the vertices were surrounded by two hydrogen atoms. Depending on the precise shape of the "bended" \(H_2O\) molecule and the orientation of the electronic spins, we may say that each vertex of the tetrahedron contains either an outgoing arrow or an incoming arrow.

Pauling's key realization was that the nearest-neighbor interactions yield the same contribution to the energy if two of the vertices are outgoing and two of the vertices are incoming. And for this "balanced" situation, we really tend to minimize the energy.

But there are (six) different ways how to divide the four vertices 1,2,3,4 into two incoming and two outgoing ones: 12-34, 13-24, 14-23, 34-12, 24-13, 23-14. So the state of the atom isn't unique. Each tetrahedron carries something like \(\ln(6)\) nats of information (or \(\log_2 6\) bits of information, if you wish) and the amount of this information scales with the number of oxygen atoms i.e. with the volume of the material. (It's really less than \(\ln 6\) because the adjacent tetrahedrons are not independent but I don't want to go into details; there are some free choices.) In other words, the spin ice carries a volume-extensive entropy. It seems to violate the third law of thermodynamics because the ground state isn't unique.

Some more practical and realistic models of the spin ice were found – they usually contain several "exotic" elements at the same moment.

I think it's necessary to emphasize that these insights about the non-unique ground state were not realized now in 2014. They have been known since the first moment in 1935 when Linus Pauling coined the idea of the spin ices! For many decades, it's been also known that the spin ices allow (emergent) magnetic monopoles to exist.

However, I have mentioned the "nearest-neighbor interactions" above. They are not the only interactions that operate in the material. In particular, there are non-nearest-neighbor interactions that I neglected. When the (tiny) energies caused by these (much weaker) interaction terms are taken into account, the aforementioned proof that all the configurations of the tetrahedrons carry the same energy breaks down. There are new terms in the Hamiltonian that make some configurations energetically favored over others, after all. The energy differences are small which means that you need to go to really low temperatures for the "slightly lower-energy states" to become significantly more likely and "chosen".

The experimenters' decision to construct "thin films" out of spin ices is just a particular strategy to increase the relative importance of the non-nearest and other neglected interactions that kill the precise degeneracy between the would-be ground states. The physical system ultimately chooses some arrangements of the "arrows in the tetrahedrons" and the entropy goes away. Even though you could have been afraid of the third law of thermodynamics when you were thinking in terms of the spin ice, the law is restored (i.e. it holds once again) if the temperatures become really low (and the law instructs you to consider the true \(T\to 0,{\rm K}\) limit).

I realize that one may easily commit basic "binary" errors if she hasn't gone through a course on the basics of condensed matter physics (or any other scientific discipline, for that matter). Journalists still want to produce stories. They like to pretend that stories may be produced from "scratch". The readers are supposed to appreciate a revolution in condensed matter physics even though they know nothing about condensed matter physics to start with.

But it's not really possible. Pretty much all the research in 2014 builds upon some (well, lots of) insights that were found 10, 20, 40, 80, 160, 320, or 640 years ago. Yes, we were talking about the "intermediate" case of 80 years here. ;-) It may sound sad to someone but one first needs some knowledge and appreciation of the older achievements of physics (and science) in order to appreciate what's going on today, too.

And yes, what I see in between the lines written by those "defiant" journalists is the obsession with violations of the famous laws. I would bet that they are left-wingers opposing the "evils" and "oppression" by capitalism and empires, too. But physics can't work like that, along the paradigms held by Marxist revolutionaries. Physics is really the search for the laws that govern phenomena in Nature. The more oppressive, universal, and tightly constraining these laws are, the better. Sometimes, older laws are shown inadequate but the whole advance actually includes the replacement of the old laws by even more accurate, "oppressive" newer ones. Moreover, the older laws are still relevant for some limiting situations, the same situations where they were previously successful. A person who likes physics (or science) must like such things. Even if he or she is biased towards the newly found laws which may be more exciting, he or she must finally have some more or less unchanging tastes and these tastes make him or her appreciate the old laws, too. It can't be otherwise.

The laws of thermodynamics, including the third one, are among those that hold in Nature. Their violation is always just an illusion or an artifact of approximations. The exact degeneracy of ground states that would be needed for the entropy to be nonzero at zero absolute temperature is infinitely unlikely, virtually impossible. Such an exact degeneracy would have to be protected by an explanation, probably by a symmetry, and no symmetry that would imply exponentially huge degeneracies of the ground state of a material exists in the laws of physics as we know them.

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snail feedback (8) :

reader Scott said...

To understand the title of the paper all one has to know is English, not physics. A "restoration" is not a "violation." You would think that journalists would know that.

reader zbynek said...

Hi - obvious mistake of acute/obtuse angle - the pilot arriving at bitod had to change course by about 5 degrees but input 175 into the auto pilot, said good night and sat back not noticing the plane turned around - the thai airforce found an unidentified aircraft entering their airspace and shot it down and realising it was civilian have removed all evidence

reader Uncle Al said...

400 tonnes of something is somewhere. It might have invisibly augered into one of the most heavily traveled ship channels on Earth, etc. We lack rigorous characterization of the topology and function of cluelessness. (Substitute institutional incompetence or criminality as pleases you. NASA's Space Scuttles are the business model for all three.)

reader papertiger0 said...

David Copperfield - It's an outside chance but if a guy can make the Statue of Liberty disappear. Maybe someone should check his private airport.

reader Dilaton said...

LOL, just today my nice office mate showed me a crazy homepage of a really dumb crackpot who claimed that almost all well-known laws of physics are wrong, in particular the ones relevant in cosmology.
Maybe it would be fun to evaluate some popular reports of journists who have no clue what they are writing about by means of the John Beaz crackpot index?

reader John Archer said...

"U.S. investigators suspect that Malaysia Airlines Flight 370 stayed in the air for about four hours past the time it reached its last confirmed location, according to two people familiar with the details, raising the possibility that the plane could have flown on for hundreds of additional miles under conditions that remain murky.

Aviation investigators and national security officials believe the plane flew for a total of five hours, based on data automatically downloaded and sent to the ground from the Boeing Co. 777's engines as part of a routine maintenance and monitoring program.
" - WSJ

Via an iPhone app that popped up. I don't know how old this news is.

reader FlanObrien said...

Quite an expert but horrific hypothesis here that gels with John Archer's comment:

A decompression disables all humans aboard but autopilot continues.

reader Bob C said...

"Additionally, the airline confirmed it had expanded its active search area to include a several-hundred-square-mile zone in the Indian Ocean as well as each of the seven or 22 additional spatial dimensions posited by string theory.",35524/

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