Emergent monopoles

One of the truly remarkable things about condensed matter physics is the idea that, from a large number of interacting particles that obey comparatively simple rules, there can emerge new objects  (in the sense of having well-defined sets of parameters like mass, charge, etc.) with properties that are not at all obviously related to those of the original constituents.   (One analogy I like:  Think about fans in a sports stadium doing The Wave.  The propagating wave only exists because of the cooperative response of thousands of people, and its spatial extent and propagation speed are not obviously related to the size of individual fans.)

A fairly spectacular example of this occurs in materials called spin ices, insulating materials that have unusual magnetic properties. A prime example is Dy₂Ti₂O₇.  The figure here shows a little snipped of the structure.  The dysprosium atoms (which end up having angular momentum \(J = 15/2\), very large as compared to a spin-1/2 electron) sit at the corners of corner-sharing tetrahedra.  It's a bit hard to visualize, but the centers of those tetrahedra form the same spatial pattern as the locations of carbon atoms in a diamond crystal.  Anyway, because of some rather deep physics ("crystal field effects"), the magnetic moments of each Dy are biased to point either radially inward toward or radially outward from the center of the tetrahedron.  Moreover, because of interactions between the magnetic moments, it is energetically favored so that for each tetrahedron, two moments (shown as a little arrows) point inward and two moments point outward.  This is the origin of the "ice" part of the name, since this two-in/two-out rule is the same thing seen in ordinary water ice, where each oxygen atom is coordinated by four hydrogen atoms, two strongly (closer, covalently bound) and two more weakly (farther away, hydrogen bonding).  The spin ice ordering in this material really kicks in at low temperatures, below 1 K.  

So, what happens at rather warmer temperatures, say between 2 K and 15 K?  The lowest energy excitations of this system act like magnetic monopoles (!).  Now, except for the fact that electrical charge is quantized, there is no direct evidence for magnetic monopoles (isolated north and south poles that would interact with a Coulomb-like force law) in free space.  In spin ice, though, you can create an effective monopole/antimonopole pair by flipping some moments so that one tetrahedron is 3-out/1-in, and another is 1-out/3-in, as shown at right.  You can "connect" the monopole to the antimonopole by following a line of directed magnetic moments - this is a topological constraint, in the sense that you can see how having multiple m/anti-m pairs could interfere with each other.  This connection is the analog of a Dirac string (where you can think of the m/anti-m pair as opposite ends of an infinitesimally skinny solenoid).  

This is all fun to talk about, but is there really evidence for these emergent monopoles?  Yes.  A nice very recent review of the subject is here.  There are a variety of experiments (starting with magnetization and neutron scattering and ending up with more sophisticated measurements like THz optical properties and magnetic flux noise experiments looking at m/anti-m generation and recombination) that show evidence for monopoles and their interactions.  (full disclosure:  I have some thoughts on fun experiments to do in these and related systems.)  It's also possible to make two-dimensional arrays of nanoscale ferromagnets that can mimic these kinds of properties, so-called artificial spin ice.  This kind of emergence, when you can end up with excitations that act like exotic, interacting, topologically constrained (quasi)particles that seemingly don't exist elsewhere, is something that gets missed if one takes a reductionist view of physics.