In spin ice systems magnetic monopole-like excitations are sources or sinks of $H$, not the $B$ field, why is that? Is it because the strings carries magnetic moment $M$ and not solenoidal $B$ filed like the Dirac string.
How is it different from Dirac construction of magnetic monopole?
In the Dirac case we still have incoming flux from the solenoid and out going from the monopole that will result in 0 for any sphere around the end. How he goes around this (why is it justified to not count the singularity) and why is not possible for the spin ice case?
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$\begingroup$ Just a nice image to explain the formations of monopoles from spin flip , with comments "The emergence of magnetic monopoles: If two of the spins point into the tetrahedron and two out of it (top left), their magnetic charges cancel (bottom left). When a spin flips, two monopoles form (top and bottom right)." Extracted from this paper $\endgroup$– TrimokCommented Oct 5, 2013 at 18:56
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$\begingroup$ @dj_mummy : Yes, I agree. This is what the image strongly suggest. Each spin (top images)could be looked as a couple of pseudo-monopoles (bottom images). In standard situations (2 spin pointing in the tetrahedron, 2 spin pointing out) (left images) there is no net result pseudo-monopole at the center of the tetrahedrons. But, if one spin flip (right images), then appears a pseudo monopole $+$ at one tetrahedron center, and another pseudo monopole $-$ at the center of the next tetrahedron. $\endgroup$– TrimokCommented Oct 8, 2013 at 9:07
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2 Answers
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A magnetic monopole for B (not H) is the situation discussed by Dirac, 't Hooft, and many other particle physicists, and that's the situation which would be interesting for various fundamental physics reasons.
For 75+ years, physicists were using the term "magnetic monopole" to refer to a very specific thing: Magnetic monopoles for B. People had analyzed them theoretically and searched for them experimentally. Whole books were written about them.
Then in the 2000s, certain scientists discovered phenomena in spin ice and other systems that had nothing whatsoever to do with that, but nevertheless they made the decision to call these things "magnetic monopoles". Pause to think about this. For 75+ years, "magnetic monopoles" was a term with a specific technical meaning in physics that everyone agreed on ... but then these scientists used the same term to describe a completely unrelated phenomenon. Why would they do this?? Um, well, presumably, they intended to mislead gullable science journalists and the general public into thinking that they made the long-awaited discovery of "true" magnetic monopoles (for B). The spin-ice and other experiments were legitimately interesting and exciting works of condensed-matter physics, but it sounds much more exciting when it is described in this extremely misleading way! [I don't know their actual thought process, I'm speculating.]
Well, if they were trying to mislead people, they were successful! In many many popular-science articles in the weeks and months following this work, journalists confused the spin-ice (so-called) monopoles with the (true) magnetic monopoles. In the wikipedia article, which I was monitoring at the time, well-intentioned readers changed the article again and again to say that the Dirac monopole has now been discovered.
To be clear: Electrons are not (true) magnetic monopoles, i.e. they are not sources or sinks for B. The same is true for protons and neutrons, and all known particles. Therefore if you put together electrons and protons and neutrons into any possible configuration, no matter how many there are or what the configuration looks like, it is mathematically impossible to create a source or sink of B. Therefore a "true" magnetic monopole will never ever be created using condensed-matter physics wizardry.
It seems to me that the right starting point is to say that the Dirac monopole and the spin-ice "monopole" are two completely unrelated phenomena in different branches of physics. They were only mixed up due to false advertising. If you have a question about Dirac's discussion of magnetic monopoles, you should pose it as a separate stackexchange question, and likewise if you have a question about spin-ice monopoles, you should pose it as a separate question. I will try to summarize quickly:
The "Dirac string" isn't a real thing, it's merely a mathematical construction. We expect and demand that the string is unobservable, because in reality there is no string. On the other hand, a spin-ice "monopole" has an actual "string" - a chain of flipped spins - that is an observable physical object.
To prove charge quantization from a Dirac monopole, you start with the assumption that the Dirac string is unobservable (in one mathematical approach). If the string is a real physical string that can be observed, the argument doesn't work -- so charge does not have to be quantized.
answered Oct 6, 2013 at 2:53
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2$\begingroup$ Well, I wouldn't call it "genius", because it's somewhat natural and justifiable. If the term "magnetic monopole" wasn't already taken, it would have been an obvious and appropriate phrase to use. But the term was already taken! It's analogous to if you found an unusually heat-conductive material and called it "super-conductivity". Or if you found some weird new phenomenon related to electron spins in iron heterostructures, and you called it "ferro-magnetism". Or if you start a company writing microwave software and call it "microsoft". $\endgroup$ Commented Oct 8, 2013 at 12:12
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$\begingroup$ I couldn't agree more. I have been working in the field of frustrated spin systems for years and I think the use of "monopole" and especially "Dirac string" is completely bonkers. Nowadays these scientists even use "anti-monopole"...nuts. These are magnetic north and south poles connected by the according flux closure. Unfortunately, once this nonsense has been established, you need to use this pseudo science to get your projects financed. Nobody gives you money for frustrated spin systems, but a Higgs mechanism in spin ice with magnetic monopoles and Dirac strings...that's a different animal. $\endgroup$ Commented Apr 21, 2015 at 8:43
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I have to disagree to the previous answers. This paper (https://arxiv.org/pdf/0710.5515.pdf) explains how the DipolarSpinIce (DSI) model (eq 1) which is a lattice of classical spins/moments, can be mapped to a fluid of magnetic charges that interact via a coulomb-like potential (2). That is a pretty big leap/insight, please tell me another physical example (of quasi-particles or real particles) that interact as the magnetical equivalent of electrons.
It is true that these dont violate $\nabla \cdot B = 0$, we rather have $\nabla \cdot (H + M) = 0$, so $\nabla H = - \nabla M$, the sink in M is a source of H.
By decomposing configurations $M=M^d+M^m$ in divergenceless and divergenceful components, we can recover the magnetic field lines of these quasi-monopoles. Furthermore the "dirac-string" can be obtained by simple subtraction of states.
Before I reveal too much, I can tell you that condensed matter is a field where we can easily conduct experiments and simulations, now that we know we have a comparable phenomena to Dirac's monopoles. Therefore we now have a new playground to test things without too much hypothesizing.
