Determining the magnetic charge of monopoles in a crystalline host seemed a mountain too high for physicists to climb. An experiment based on Wien's theory of electrolytes has now measured its value.
The exotic class of crystalline solids known as 'spin ices' has proved, perhaps surprisingly, to be a repository of some elegant physical phenomena. Spin ices are rare, three-dimensional systems in which the magnetic moments (spins) of the ions remain disordered even at the lowest temperatures available. In these crystalline solids, it has been recognized that a material's collective excitations above the ground state behave as point-like objects that are the condensed-matter versions of magnetic monopoles1 — particles that, unlike iron magnets, have a single magnetic pole and hence carry an overall magnetic charge.
Initially, it was not evident that their charge could be measured in a straightforward way. After all, magnetic monopoles live in a lattice at a moderate density under normal laboratory conditions — not the sort of setting in which you could carry out a magnetic version of Millikan and Fletcher's oil-drop experiment to determine the electric charge of the electron. Happily, such obstacles have triggered ingenuity, and on page 956 of this issue Bramwell and colleagues2 report a measurement of the magnetic charge of the monopoles in spin ice that is in surprisingly good agreement with the robust theoretical prediction1 of the same.
The route that Bramwell et al. take begins with the Wien effect. In its normal incarnation, this is the increase in the conductance of an electrolyte at strong electric fields. The theory underlying this phenomenon was first worked out by Lars Onsager3, and central to it is the association and dissociation of the molecules of the electrolyte under the influence of an applied electric field. Essentially, the electric field rips molecules apart into oppositely charged ions at an enhanced rate while they recombine at a rate that is unchanged — the latter phenomenon was first discovered by Paul Langevin4 in 1903. The net result is a greater density of ions and hence an enhanced conductance. Specifically, the increase is linear, with a coefficient that readily allows determination of the charge of the ions — a memory of the attraction between the ions, which the electric field overcomes.
In their study, Bramwell and colleagues2 map the fractionalization of magnetic dipoles in a spin-ice material (Dy2Ti2O7) on to the ionization of molecules in Onsager's theory. The dipoles can be viewed as 'molecules' consisting of monopole–anti-monopole pairs. The monopoles and anti-monopoles play the part of ions that can separate and take on a reality through spin-flipping processes. The dissociation of dipoles is stimulated by an externally applied magnetic field, and the energetics of this process involve the magnetic 'Coulomb' interaction — in exactly the same manner as the energetics of molecule dissociation under the action of an electric field involves the true Coulomb interaction.
So far, so good — as far as the application of Onsager's theory to magnetic dipoles goes. All that is left to be done is to measure the magnetic conductance of the spin-ice material. Unfortunately, this is not so easy — our magnetic monopoles live only in spin ice, and the analogue of the external electric circuit in an experiment with an electrolyte is not obvious (although it could conceivably be done with various pieces of spin ice).
To get around this obstacle, Bramwell et al. turned to another insight from Onsager's theory — that the enhanced density of ions (or of the magnetic monopoles in the authors' mapping) should bring with it an enhanced relaxation rate for departures of the ionic density (monopole density) from its equilibrium value. As fluctuations of the monopole density produce fluctuations of the magnetic fields inside the material, their task was reduced to measuring the relaxation rate for such fluctuations in an applied magnetic field. For spin ice, they chose to probe the relaxation rate with a technique known as muon spin rotation, which consists of implanting spin-polarized muons in the material and detecting the positrons emitted when they decay. The distribution of the positrons 'remembers' the orientation of the muons, and its time evolution yields information about the time evolution of the magnetic fields in the material. Happily, the authors found a linear enhancement of the relaxation rate with increasing magnetic field, and extracted a magnetic-monopole charge that agrees surprisingly well with the theoretical prediction1.
I think it is clear that Bramwell and colleagues' result2 is a triumph of a bold experimental foray down a chain of inference that others may have prudently refrained from following. For that very reason, though, it raises several fascinating questions that will occupy theorists until the 'Wien effect' in spin ice can be declared a closed subject. For one thing, Onsager's theory is for a system out of thermal equilibrium, and the set-up in spin ice is, in theory, an equilibrium set-up. That said, the experiment itself and the determination of the charge of magnetic monopoles are striking, and strongly suggest that we are on our way to developing a consistent picture of the low-temperature behaviour of spin ice — one in which magnetic monopoles become entirely familiar objects. The results of the latest low-temperature neutron-scattering experiments5,6 also line up very well with the physics of monopoles in these spin-ice materials. No doubt there is still room for more insightful experimental work in this area.
Beyond establishing the basic physics of magnetic monopoles, it would be interesting to see whether monopoles could be manipulated in a controlled manner. For example, one could aim to build the magnetic counterparts of alternating-current electrical circuits. On the way to turning the study of monopoles into a proper applied science, it will be necessary to ask if the basic ideas of dipole fractionalization that give a spin-ice material its special properties can be realized in other magnetic settings. Spin ice may be the first fractionalized magnet in three dimensions, but surely should not be the only one.
Castelnovo, C., Moessner, R. & Sondhi, S. L. Nature 451, 42–45 (2008).
Bramwell, S. T. et al. Nature 461, 956–959 (2009).
Onsager, L. J. Chem. Phys. 2, 599–615 (1934).
Langevin, P. Ann. Chim. Phys. VII 28, 433 (1903).
Fennell, T. et al. Science doi:10.1126/science.1177582 (2009).
Morris, D. J. P. et al. Science doi:10.1126/science.1178868 (2009).
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Scientific Reports (2018)
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