Page 19 - ILL Annual Report 2019

b)
a) The ice rule (2-in/2-out) obeying spins of a spin ice on the pyrochlore lattice (tetrahedron) and fluxes of a lattice vector field on the bonds of the diamond lattice (tetrahedron centres) are in direct correspondence and connect simply with an ice rule for an Ising antiferromagnet on the pyrochlore lattice (2-up/2-down).
b) The cations of a charge ice map onto the spins of the Ising antiferromagnet.
c) In a pyrochlore Heisenberg antiferromagnet, any configuration in which the spins on a tetrahedron sum to zero is a ground state; all such states can be characterised by three families of Ising pseudo-spins, one for each component of the vector spins, simultaneously satisfying their ice rule. All these systems are Coulomb phases and all have the same underlying correlation functions encoded by the ice rules.
0 0.2 0.4 0.6 0.8 1 1.2
ħω 0.5 meV 2
1
0
-1
-2
-3
012
Figure 2
Magnetic Coulomb phase dynamics in CsNiCrF6 measured at ThALES (with FlatCone analyser) at 1.5 K.
a)
Figure 1
Coulomb phases on the pyrochlore lattice.
(h,h,0) (r.l.u.)
SCIENTIFIC HIGHLIGHTS
16 -17
spin degrees of freedom have power-law correlations, as shown by the presence of pinch points in the diffuse scattering. Our numerical model of the structural diffuse scattering suggests that both a cation charge ice and anion displacement ice are present.
The presence of a magnetic Coulomb phase in the presence of such structural disorder is not completely unexpected—the simplest model of a magnetic charge ice has such a phase [2]. However, antiferromagnetic Coulomb phases on the pyrochlore lattice are few and far between. Thus, it is interesting to compare the magnetic dynamics with those of the pyrochlore Heisenberg antiferromagnet, which has been studied theoretically
in considerable detail [3]. Inelastic neutron scattering measurements on the ILL spectrometer ThALES show that there is a connection. The pinch point structure factor
of the diffuse scattering appears again at finite energy transfer, as expected, albeit with broadened pinch
points (figure 2). Measurement of the wavevector dependence of the width and the energy of the inelastic response shows further elements of the theory of an ideal antiferromagnetic Coulomb phase: quasi-elastic scattering with identical width and linear temperature dependence appears at generic points on the structure factor, as expected for the relaxational dynamics of magnetic charge fluctuations (though due to the continuous spins, the monopoles of this system are not discrete quasiparticles
as they are in spin ice); a weakly dispersive broad feature (a type of spin wave or fast dynamics of the correlated disordered structure) appears along nodal lines joining the pinch points, also as predicted.
In conclusion, diffuse and inelastic neutron scattering experiments provide considerable information about
the structural and magnetic correlations and magnetic dynamics of CsNiCrF6. Despite the structural disorder, the magnetic dynamics show features of an ideal model frustrated antiferromagnetic Coulomb phase, suggesting a universality in the emergent dynamics of such systems. Further details can be found in [4].
c)
(0,0,l) (r.l.u.)
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