Contents - Max-Planck-Institut für Physik komplexer Systeme

a diffusion process with the z coordinate assuming the
role usually played by time:
C(x,y,z) ≈ 1
z exp
−γ x2 + y2
. (1)
z
Figure 2: Magnetisation and diffuse neutron scattering with field applied
along the [001] axis. Left: 3D representation of the single crystal
neutron diffraction data from E2, HZB, at 5/7hS and 0.7 K showing a
cone of scattering coming from (020) Bragg peak. Right: Calculation
of diffuse scattering characteristic of the weakly biased random walk
correlations with bias of 0.53 : 0.47 and Bint|| [001].
The scattering from a large ensemble of such walks has
been calculated including all the geometrical factors for
the neutron scattering cross section. As can be seen
from the side-by-side comparison of the data and modelling,
the string configurations account very well for
the data and reproduce the cone of scattering observed
(Fig. 2).
It turns out that the interactions between the strings
– considered to be of a hard-core exclusion nature in
the theory above – can elegantly be tuned by modulating
the exchange constants in different directions
of the pyrochlore lattice. By choosing exchange constants
as displayed in Fig. 3, we obtain a very unusual
“infinite order” phase transition out of the Coulomb
into a fully ordered phase, at a critical temperature
Tc = 4δ/(3ln 2).
Mathematically, the system can be described using a
transfer matrix to ‘propagate’ the strings along the
[001] direction. This transfer matrix is block-diagonal
in the number of strings, and one finds that (i) below
Tc the magnetisation is saturated; and (ii) at Tc all sectors
are equiprobable and all configurations within a
sector are equiprobable, reflecting the absence of interactions
between strings [14]. Indeed, at Tc, the transfer
matrix exhibits a symmetry enhancement from U(1)
to SU(2)! A consequence of the absence of interactions
between strings is that the surface tension between oppositely
magnetised domains vanishes and the domain
wall width diverges as Tc is approached from below.
At T − c the magnetisation profile away from the domain
wall centre M(y) is a function only of y/L⊥. Below Tc
the domain wall width ℓ −1
w ∝ (1 − T/Tc) 1/2 (Fig. 3). It
is striking to find broad domain walls in an Ising magnet;
they may be detectable using small angle neutron
scattering.
Figure 3: In-plane magnetisation profile vs y/L⊥ at T = 0.999Tc for
plane size L⊥ = {6, 8, 10, 12, 16, 20}. Inset: A tetrahedron of the pyrochlore
lattice with exchange J and J − δ as indicated: the dashed
bonds lie in (001) planes. One of the two ground states for δ > 0 is
shown.
The natural way to generate the required degeneracy
lifting in a magnetic compound is to apply uniaxial
pressure along the [001] axis of a single crystal. To
see this exotic “infinite-order” phase transition, pressures
about a factor three larger then the ones studied
so far [15] are necessary. We hope our work will stimulate
further experimental efforts to realise this unusual
transition.
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2.10. Experimental Manifestations of Magnetic Monopoles 61