## Friday, September 04, 2009

### Magnetic monopoles seen in CM physics

Science Magazine has published a paper by 14 British and German authors,
Dirac strings and magnetic monopoles in spin ice Dy2Ti2O7 (click),
who claim to have seen, via diffuse neutron scattering, emergent magnetic monopoles in a spin ice on the highly frustrated pyrochlore lattice.

These magnetic monopoles appear at the ends of "observable Dirac strings". This is way too bizarre a terminology, to say the least, because a basic defining property of the Dirac strings, as realized by Paul Dirac, is that they must be unobservable! ;-) OK, fine, they mean some magnetic flux tubes that actually don't respect the Dirac flux quantization rule.

Nature (popular),
Physics World, PhysOrg, Science Daily (click).
Let me say a few words about the Dirac strings.

If you imagine a magnetic monopole of charge Q, i.e. an isolated North (or South) pole of a magnet (that is normally coming in the dipole form - with both poles - only), the magnetic field around is radial and it goes like "Q / R^2". Remember the letter "Q". The vector function "(X,Y,Z)/R^3" in three dimensions has the feature that its divergence equals zero. Well, not quite: it is a multiple of a delta-function.

Consequently, the magnetic field "B" may be written as "curl A" using a vector potential "A" almost everywhere. But you must remove not only the point where the monopole is located but also a semi-infinite string from this point to infinity.

The monopole may therefore be visualized as a very long dipole magnet - or solenoid - with one end moved to infinity (where its existence becomes unobservable). Because the infinitely thin solenoid must also be invisible for us to be able to say that we only have the monopole, there must also be no Aharonov-Bohm effect around this solenoid. This implies the Dirac quantization rule, namely the condition that "Q.e" must be a multiple of "2.pi" for all electric charges "e" of isolated particles (that orbit around the solenoid).

Because the fine-structure constant of the electric force is small, "1/137.036" or so, the corresponding elementary magnetic charge must be large, with its dual fine-structure constant equal to 137.036 up to powers of "2.pi" and "4.pi". Also, the theories that can actually predict the existence of fundamental magnetic monopoles and their properties, usually estimate their masses to be near the (very high) GUT scale, so they can't be produced by colliders (or in labs).

Don't get carried away: this German-U.K. work is not gonna transform particle physics even though we might like it. ;-) The total magnetic charge of the whole material is exactly zero and moreover, the magnetic flux tube in between the two poles is still observable even though it got pretty thin. The observed flux tubes would only deserve the name "Dirac string" and their endpoints would only deserve to be called "magnetic monopoles" if the flux tubes became unobservable - which is only partially realized here.

Of course, the magnetic monopoles seen by these experimenters are just quasiparticles, not true elementary particles. In condensed matter, many kinds of bizarre quasiparticle phenomena are possible. The most catchy ones include the fractional charges (in fractional quantum Hall effect), the separation of the spin and the charge, and now - if the paper is correct - the magnetic monopoles.

Via Pavel Vachtl and Can Kilic at Facebook.

1. Thanks for clearing that up! I only saw the popular press blurbs which, of course, water down the gruel.

2. No, this won't transform particle physics as we know it. It's the other way around.

Morris et al. managed to express the properties of the magnet known as spin ice in terms of magnetic monopoles and strings connecting them. When spin ice is placed in an external magnetic field along certain directions, Dirac strings carrying the flux between pairs of magnetic charges are stretched mostly along the direction of the field but also wander aimlessly in the two perpendicular directions. In this way the properties of atomic magnetic dipoles can be calculated in terms of strings doing a random walk in 2+1 dimensions.

The authors of that paper performed the calculations and confirmed the results experimentally by measuring spin correlations through neutron scattering. In a sense they borrowed ideas from particle physics to gain understanding of a condensed-matter system.

3. Fascinating, thanks. But here's my problem with even this attempt to make monopoles reasonable, save monopoles from A-field problems etc: if E and B are truly equivalent, then there isn't even a reason for only B to have a correlated A field! There would have to be an "A for E" type field as well (per definition, "equivalent") Then charges have to be corralled within this weird scheme of being ends of dipoles, worrying about A-B effect etc. and what charge would be specified? Well, to be consistent, the same charge (in absolute, "Gaussian" terms)! Well, it isn't ... Did I miss anything?

(I think your fast-comment section is having problems.)

4. Dear Neil,

indeed, one can always formulate electromagnetism in terms of the "A for E" field which is known the "dual gauge potential" and labeled "A tilde" or by similar symbols.

You also correctly determine why this is not a convenient choice for ordinary electromagnetism: there are too many normal electric charges and Dirac strings for "A tilde" would have to run from each of them - which would be a lot of unphysical choices etc.

But the logic would otherwise be identical. You could do it and these dual Dirac strings would have to be invisible, i.e. the A-B effect would have to lead to a trivial phase for (now:) magnetic monopoles that orbit such dual Dirac strings.

The role of the electric and magnetic charge would be exactly reverted, relatively to the formalism with the normal "A for B" potential. At any rate, the phase in the Aharonov-Bohm effect for one charge orbiting the Dirac string coming from the other type of charge is always of the kind

exp(i.Q_{electric}.Q_{magnetic})

which is already symmetric with respect to the electric and magnetic "worlds", "indices", or 'adjectives", so nothing would change about it. You would still conclude that Q_{e}.Q_{m} must be a multiple of 2.pi in the quantum relativistic (electromagnetically rationalized) units.

So it's about convenience, not about the truth: we know quite a lot of el. charges but have seen no magnetic ones, so we use the "A for B" vector potential and not "A for E" - "E" is determined from the (minus) gradient of the scalar potential "phi" (minus the time derivative of A).

There is no problem here and there is also no problem with the fast comments now.

Best wishes
Lubos