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Freedom for the poles

Magnetic poles always come in twos, a north and a south. That received wisdom has not stopped physicists from searching for 'monopoles' in accelerators and cosmic rays. Theory now indicates a better place to look.

Despite some tantalizing clues for their existence from the realms of quantum physics, magnetic monopoles — single magnetic poles without a partner — remain elusive after decades of searching. Do they exist at all in the real world? On page 42 of this issue1, Castelnovo, Moessner and Sondhi argue yes: monopoles are alive and well in an exotic class of magnetic material known as spin ice2.

An iron magnet has two poles, north and south: Earth's iron core makes it an extremely large example of the genre. These poles are positive and negative magnetic charges, acting as sources and sinks of the magnetic field. In general, magnetic interactions are very similar to electrical interactions: like poles repel and unlike attract, with a force inversely proportional to the square of their separation. But whereas positive and negative electric charges can exist independently, magnetic poles always seem to occur in pairs. Rather as the sorcerer's apprentice hacks his enchanted broom into pieces only for each to spring to life as a new whole broom, breaking a bar magnet in two yields smaller magnets, each with a north and a south pole, and an overall magnetic charge of zero.

This asymmetry extends to the subatomic level. Elementary particles can carry a positive or negative electric charge, but the magnetic charge is zero without exception. Yet theory offers some hints that single magnetic poles might exist in nature. In the 1930s, Paul Dirac showed that magnetic monopoles could explain the observed quantization of electric charge. Extensions of the standard model of particle physics include particles with magnetic charge.

One environment in which monopoles might pop up is crystalline solids. In a crystal at a low temperature, excitations above the ground state often behave like elementary particles: they carry a quantized amount of energy, momentum, electric charge and spin. In their theoretical study, Castelnovo et al. find the first instance of such an excitation with a non-zero magnetic charge. Under certain conditions, these magnets behave as a gas of independent magnetic poles. There is even a phase transition at which a thin vapour of these monopoles condenses into a dense liquid.

How a monopole can be created in a world of magnetic dipoles can be understood by considering a one-dimensional string made by laying tiny dipoles end to end. In this case, a single misaligned dipole gives rise to two independent magnetic charges that can be moved far apart, for the price of putting some energy into the system (Fig. 1a–c). The monopoles that arise are boundaries separating regions with perfectly aligned dipoles. These topological defects, known as domain walls, or 'kinks', have recently been studied in magnetic nanowires3.

Figure 1: Making monopoles.

a, In the lowest-energy state, all the elements in a chain of magnetic dipoles point in the same direction: the north pole (magnetic charge +qm) of one magnet touches the south pole (magnetic charge −qm) of the next. The charges cancel out all the way along the string, except at the ends. b, Flipping one of the dipoles in the middle excites the chain out of its ground state, creating two magnetic charges +2qm and −2qm. c, Each of these charges can be moved independently of the other by flipping a dipole next to it — they are free monopoles. d, Castelnovo et al.1 study spin orientations in spin ice. Shown here is square spin ice, a two-dimensional variant that has been produced in an artificial form, as an array of nanoscale magnets10. Four magnetic poles meet at each point on the square lattice, and the energy is lowest when two are north poles and two are south poles. Spin ice in the ground state can be construed as a series of strings of magnetic dipoles embedded in a higher-dimensional lattice. e, Flipping dipoles on a single string (the black one) creates a pair of well-separated magnetic poles just as in one dimension.

The emergence of free magnetic monopoles is an example of the phenomenon known as 'fractionalization': that the collective behaviour of many particles in a condensed-matter system is most effectively described in terms of fractions of the original particles. Fractionalization is often tied to topological defects4 and is common in one-dimensional systems, such as the string already mentioned. The only confirmed case in two dimensions is the fractional quantum Hall effect, which occurs in a cold gas of electrons placed in a strong magnetic field5. Measurements of conductance6 and electrical noise7 in this system indicate the involvement of 'quasiparticles' with one-third of an electron's charge.

Castelnovo and colleagues provide the first example of fractionalization in a three-dimensional system. But how does the physics of free monopoles on a string survive in a higher-dimensional setting? The answer lies in the special nature of the ground states of the authors' chosen system, spin ice, which allows one-dimensional ideas to be transferred to two and three dimensions (Fig. 1d,e).

The monopoles in spin ice are magnetic analogues of electrically charged defects H3O+ and OH in water ice. The movement of these defects through water ice causes it to conduct electricity when an electric field (potential difference) is applied across it. Might it be possible to create a steady magnetic current in spin ice by placing it in a magnetic field? Unfortunately not. The motion of a kink alters the state of a string, making it impassable to the next magnetic charge. In water ice, a kink of a different flavour, known as a Bjerrum defect8, repairs the damage done by the original defect. Because there is no analogue of Bjerrum defects in spin ice, magnetic monopoles are somewhat limited in their motion, and cannot sustain a direct magnetic current.

That still leaves the possibility of generating an alternating magnetic current, which would be interesting in its own right. In any case, learning how to move magnetic monopoles around would be a step towards technologies such as magnetic analogues of electric circuits and magnetic memories9 operating on the atomic scale.


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Tchernyshyov, O. Freedom for the poles. Nature 451, 22–23 (2008).

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