Contents - Max-Planck-Institut für Physik komplexer Systeme

2.10 Experimental Manifestations of Magnetic Monopoles
In 2008, it was predicted that the magnetic material
spin ice [1] should exhibit unusual quasiparticles which
have properties of magnetic monopoles [2]: they experience
mutual magnetic Coulomb forces; couple to
an external magnetic field in the same way as electric
charges couple to electric fields; are sources and
sinks of the magnetic field H; and would show up
in a SQUID-based monopole search experiment in the
same way as (elementary) cosmic monopoles would.
Figure 1: Left: The Ising spins in spin ice are constrained to point
along the direction connecting the centres of the tetrahedra they
belong to. The lowest energy for a tetrahedron is obtained for a
two-in-two-out configuration, as illustrated. Applying a field, B ||
[001], results in a preference for aligning the tetrahedral magnetisation
with the applied field direction. In the three dimensional pyrochlore,
Dirac strings of flipped spins terminate on tetrahedra where
magnetic monopoles reside. Right: The measured heat capacity per
mole of Dy2Ti2O7 at zero field (open squares) is compared with a
Debye-Huckel theory for the monopoles (blue line) and the best fit
to a single-tetrahedron (Bethe lattice) approximation (red line). The
ice blue (yellow) backgrounds indicate the spin ice (paramagnetic)
regimes, respectively.
The next logical step was to determine whether magnetic
monopoles in fact do occur experimentally. To
reach this goal, a number of potential signatures
were considered, which probe different aspects of the
physics of monopoles and the underlying magnetic
Coulomb phase which acts as their vacuum [3–10].
Our work focused on several aspects. Firstly, the fact
that these emergent monopoles are connected by flux
strings which – unlike the Dirac strings of elementary
monopoles – are observable; these “Dirac strings”
have characteristic features due to their extended, onedimensional,
nature. Secondly, we considered the collective
behaviour of the dilute liquid of monopoles
at low temperature, which is quite analogous to that
found in electrolytes, and should therefore share its
universal properties. Finally, we have considered nonequilibrium
phenomena probing the energy landscape
which arises from interactions between the monopoles.
This presents the possibility of probing the behaviour
L. D. C. JAUBERT, R. MOESSNER
of pointlike topological defects in a three-dimensional
magnet.
Crucially, the emergent monopoles in spin ice are deconfined:
they can separate and move essentially independently.
Thus, the equilibrium defect density is
determined not by the cost of a spin flip but by the
properties of the gas of interacting monopoles. In Fig.
1(right), the measured heat capacity is compared to
Debye-Huckel theory [11], which describes a gas of
monopoles with Coulomb interactions. This theory is
appropriate to low temperatures, where the monopoles
are sparse, and it captures the heat capacity quantitatively.
At higher temperatures, spin ice turns into a
more conventional paramagnet and the monopole description
breaks down. Previous to our work, no analytical
treatment of the low-temperature thermodynamics
of spin ice had been available.
Monopole deconfinement is also reflected in the spin
configurations: as two monopoles of opposite sign separate,
they leave a tensionless string of reversed spins
connecting them, a classical analogue of a Dirac string:
in the theory of Dirac [12], these are infinitely narrow,
unobservable solenoidal tubes carrying magnetic flux
density (B-field) emanating from the monopoles. In
our case, the strings are real and observable thanks to
the preformed dipoles of the spins; strings can change
length and shape, at no cost in energy other than
the magnetic Coulomb interaction between their endpoints.
As the strings consist of magnetic dipoles, the method
of choice for imaging them is magnetic neutron scattering.
The application of a large magnetic field along
one of the principal axes orients all spins. The resulting
ground state is unique and free of monopoles. Upon
lowering the field through a critical field hS [13] sparse
strings of flipped spins appear against the background
of this fully magnetised ground state. In the absence
of monopoles, such strings must span the length of the
sample and terminate on the surface; otherwise, they
can terminate on magnetic monopoles in the bulk. Each
link in the string involves a spin being reversed against
the field.
The panels in Fig. 2 show reciprocal space slices of the
neutron scattering results at a field near saturation of
h = 5/7hS: cone-like scattering emanates from what
was the position of the pinch points [4, 7] in zero field.
These can be modeled by noting that the strings execute
a random walk; when their density is small, interactions
between them can be neglected to a first approximation,
so that the spin correlations are those of
60 Selection of Research Results