To be or not to be: the magnetic monopole

You might have read it in Nature News, Starts with a Bang, or Science: physicists have discovered magnetic monopoles. Sort of.

Positive and negative charges are happily independent, but north and south poles always come in twos. As the textbook example goes, cut a bar magnet in half, and you’ll get two smaller bar magnets—you can never isolate one from another. Monopoles—a lone north or south pole—simply don’t exist.

Or so I was told when I first heard about monopoles, in my first college course on electromagnetism. I heard about them for the second time from Shou-Cheng Zhang, a condensed-matter physicist who studies exotic phases of matter. He seemed to have a rather different opinion.

As my hand struggled to keep up with the interview, it occurred to me that Stanford clearly thought very highly of Zhang; sunlight flooded through a large window into the generously proportioned office, which was located just next door to one of the department’s Nobel laureates.

Profiling Zhang was my first real assignment as an intern at SLAC National Accelerator Laboratory, and I couldn’t have wished for a better subject. Well-spoken and patient, Zhang made his research both fascinating and accessible. He works on the quantum spin Hall effect, a strange state of matter where the spin of an electron is determined by its direction of motion. Zhang likened it to a graceful dance from the days of Jane Austen; couples moving counterclockwise around a room also spin counterclockwise, and vice-versa with couples moving clockwise. If this happened in a real material, he said, the current could flow without causing the material to heat up.

Shock enough for anyone who’s heard how Moore’s Law, which says that processing speed doubles every 18 months, may be reaching its limit as the ever-tinier transistors get hotter. But then Zhang said something even more astonishing. This kind of material, he said, would give rise to a magnetic monopole.

I remember being dumbfounded. Surely I didn’t hear the word monopole come out of his mouth. Quadrupole, maybe? The look on my face must have given me away, because Zhang just grinned.

Stanford had a history, he told me, of monopole searches. “People were literally waiting for it to fall out of the sky,” he said. Not only was a Nobel laureate around the corner from Zhang’s office, but Blas Cabrera, lifetime monopole hunter, wasn’t too far away either. Here’s how Ethan Siegel, an assistant professor in physics at Lewis and Clark College, recapped the search in Friday’s “Starts with a Bang” post:

Magnetic monopoles have always been a curiosity for physicists, and many of us think that they ought to exist. In the 1970s, there were searches going on for them, and the most famous one was led by a physicist named Blas Cabrera. He took a long wire and made eight loops out of it, designed to measure magnetic flux through it. If a monopole passed through it, he would get a signal of exactly eight magnetons. But if a standard dipole magnet passed through it, he’d get a signal of +8 followed immediately by one of -8, so he could tell these apart.

So he built this device and waited. Occasionally he’d get one or two magnetons, but the fact that it wasn’t eight was hardcore evidence that something funny was going on with just one or two loops. (Three or more was never seen.) In February of 1982, he didn’t come in on Valentine’s day. When he came back to the office, he surprisingly found that the computer and the device had recorded exactly eight magnetons on February 14th, 1982. Huge devices with larger surface areas and more loops were built, but despite extensive searching, another monopole was never seen. Stephen Weinberg even wrote Blas Cabrera a poem on February 14th, 1983:

Roses are red,
Violets are blue,
It’s time for monopole
Number TWO!

And, as of today, no one has seen good evidence for a second magnetic monopole, leading us to believe that the first one was spurious.

But Zhang wasn’t talking about monopoles falling from the sky; instead, he said you could see it in the mirror image of an electron. I’ll quote the article I ended up writing for symmetry:

To understand how a material can act like a magnetic monopole, it helps to examine first how an ordinary metal acts when a charge—an electron, say—is brought close to the surface. Because like charges repel, the electrons at the surface retreat to the interior, leaving the previously neutral surface positively charged. The resulting electric field looks exactly like that of a particle with positive charge the same distance below the surface—it’s the positive mirror image of the electron. In fact, from an observer’s point of view, it’s impossible to tell the difference.

The concept of an image charge is something undergraduate physics students encounter in their very first electricity and magnetism class, along with the idea that the magnetic monopole doesn’t exist. But Zhang’s “mirror” alloy is no ordinary material. It’s what’s called a topological insulator, a strange breed of solid Zhang specializes in, in which “the laws of electrodynamics are dramatically altered,” he says. In fact, if an electron was brought close to the surface of a topological insulator, Zhang’s paper demonstrates, something truly eerie would happen. Instead of an ordinary positive charge, Zhang says, “You would get what looks like a magnetic monopole in the ‘mirror.'”

The image charge analogy is important—there’s no physical half a bar magnet lodged somewhere inside this material. Instead, the monopole’s point-source magnetic field, its signature, its defining characteristic, emerges from the behavior of the electrons inside. [For further reading, see Zhang’s paper in Science.]


The research that’s making the news today comes out of the same world as Zhang’s strange material—condensed matter physics. It’s called “spin ice” because its constituents, magnetic ions, are arranged in the same tetrahedral configuration as water molecules in solid ice. Adrian Cho at ScienceNOW explains:

The magnetic ions sit at the tips of four-sided pyramids or tetrahedra connected corner to corner (see diagram). At temperatures near absolute zero, they should organize themselves by a simple rule: In each tetrahedron, two ions point their north poles inward toward the center and two point outward.

Flaws in this pattern are the monopoles. If one ion flips–perhaps because it gets energized by the thermal energy in the crystal—it leaves one tetrahedron with three ions pointing inward and the neighboring tetrahedron with only one ion pointing inward (see figure). The two imbalanced tetrahedra act like north and south magnetic poles, respectively. If nearby spins also flip, the imbalances can shift independently from one tetrahedron to the next, so that the north and south poles end up connected only by a string of ions that point from one to the other. Thus the imbalanced tetrahedra become magnetic monopoles.

Now, are these magnetic monopoles in a sense that would satisfy the likes of Blas Cabrera? Probably not. While the researchers detected these strings of ions, seeing the monopoles themselves is going to be a lot trickier, as Geoff Brumfiel at Nature News explains:

Like any charged particle, opposites attract, and the north and south poles typically cluster together less than a nanometre from each other. That makes them extremely hard to detect individually.

Siegel of Starts with a Bang is even more critical, though he praises the research as important in its own right elsewhere in his post:

What they did was create magnetic “strings”, or very long, thin magnets on a lattice, where North and South poles are separated by great distances. If you only look at one side of this string, you only see one pole. But the other pole is still there, and so this isn’t a monopole. If you tried to snap the string, you still wouldn’t isolate one magnetic charge…

So the evidence isn’t clear as day whether this is really a magnetic monopole. But my question is whether spin ice could be at least used to study the creatures by analogy, because they’re of great interest.

Why? “Many of us think that they ought to exist,” Siegel writes, which leaves a some explanation to to be desired. Adrian Cho fleshes it out:

Monopoles would be the magnetic equivalent of electrically charged particles, and there are several reasons physicists would like to see them. In 1931, famed British theorist Paul Dirac argued that the existence of monopoles would explain the quantization of electric charge: the fact that every electron has exactly the same charge and exactly the opposite charge of every proton. In the 1980s, theorists found that the existence of monopoles is a basic prediction of “grand unified theories,” which assume that three forces—the electromagnetic, the strong force that binds the nucleus, and the weak force that causes a type of radioactive decay—are all different aspects of a single force.

Monopoles are a part of the high-energy physics menagerie of exotic, never-before-seen particles. A few of their zoo-mates include anyons, 2-dimensional particles that straddle the properties of fermions and bosons, and axions, feebly interacting particles that “clear up” problems with charge-parity violation in quantum chromodynamics like Axion detergent cleans dishes (hence the name. Thanks Frank Wilczek). Then there’s the most famous hypothetical particle of them all, the Higgs boson.

These entities are lynchpins in our best descriptions of the universe. But so far there’s no sign of them—at least in cosmic ray showers or the short-lived spaghetti of particles in a collider’s detector. Meanwhile, it seems like you can’t swing an atomic-force microscope in a condensed-matter system without hitting one of these things.

Let’s go back to Shou-Cheng Zhang. A particle physicist by training, Zhang had a very philosophical view of the relationship between condensed matter physics and high-energy physics. Using the words of English poet William Blake, he said that studying condensed matter physics was like “seeing a world in a grain of sand.”

“It means that the structure of subatomic particles is reflected in the systems they make up—the solid, the grain of sand,” he told me. Or you could think of it as an Escher waterfall: just when you think you’ve gotten to the top of the waterfall with whole systems of particles, you find yourself at the bottom, with the fundamentals.

Spin-ice and topological insulators are hardly the only materials where high-energy physics might find their elusive particles. Take graphene, for instance. A single-atom-thick layer of graphite, the same stuff that’s in your pencil, the stuff’s been hailed for the last five years or so as the new wonder material for electronics because electrons zip effortlessly through it. But the same physics that makes it so promising for lucrative applications also make it a playground for high-energy pursuits. One reason is that electrons in graphene don’t act like regular old electrons. They act sort of like photons with charge and spin 1/2. There’s an excellent article by Robert Service in the May 15 issue Science on the subject that’s unfortunately only available to subscribers, but I’ll quote some of it here.

In the lattice of a typical metal, electrons feel the push and pull of surrounding charges as they move. As a result, moving electrons behave as if they have a different mass from their less mobile partners. When electrons move through graphene, however, they act as if their mass is zero—behavior that makes them look more like neutrinos streaking through space near the speed of light. At such “relativistic” speeds, particles don’t follow the usual rules of quantum mechanics. Instead, physicists must invoke the mathematical language of quantum electrodynamics, which combines quantum mechanics with Albert Einstein’s relativity theory. Even though electrons course through graphene at only 1/300 the speed of neutrinos, physicists realized several years ago that the novel material might provide a test bed for studying relativistic physics in the lab.

Service goes on to say that graphene could be used to study a number of predictions of high-energy physics in a sort of lab-on-a-chip setting, mentioning especially something called Klein tunneling, a 1929 thought experiment of Swedish physicist Oskar Klein:

Klein realized that when electrons travel at relativistic speeds, the likelihood that they will tunnel through a barrier can skyrocket. That’s because in the spooky world of quantum mechanics, within which particles can wink in and out of existence, a relativistic particle that hits a barrier can generate its own antiparticle, in this case a positron. The electron and positron can then pair up and travel through the barrier as if it weren’t even there.

In March of this year, Columbia physicist Philip Kim reported observations of the tunneling in a real-world material—good old graphene.

So whether or not spin-ice monopoles are just as good as the kind Blas Cabrera hoped would fall from the sky, they’re worth creating and studying. Condensed matter physics holds out an immediate and fairly inexpensive way to test out the predictions of Grand Unified Theories. While I’m not expecting anyone to find the Higgs boson in a sheet of graphene, maybe high-energy physicists will make worthwhile discoveries by looking in the grain of sand, instead of the galaxies, for signs of their universe.

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