8.1 Future Directions
63
S B z (ω, T ) from Dy 2 Ti 2 O 7 showing the magnetic monopole GR attributes (Fig. 8.1)
add to the growing evidence for the existence of magnetic monopoles in spin ices
[10–12].
The additional refinement of the generation-recombination for magnetic monopoles
in spin ices observed in the modified power law for ω is understood by studying
different magnetic charge dynamic models. The comparisons of power law ’b’
observed in experiment and the different models indicate the existence of correlations in magnetic monopole dynamics. The presentation of autocorrelation functions
C B z (t)/C B z (0) show us good correspondence between experimental measurements
and the DSIM which includes both dipolar interactions and Dirac string constraints.
These observations further the understanding of the affect of correlations in spin ice
magnetic monopole plasma. Overall, we find detailed and comprehensive agreement
between current theories for thermal generation and recombination of a correlated
±m ∗ magnetic monopole plasma and the phenomenology of magnetic-flux noise
spectral density in Dy 2 Ti 2 O 7 that is revealed by spin-noise spectroscopy.
8.1 Future Directions
8.1.1 Telegraph Noise
Although the monopole noise spectral density has not yet been measured in the
sub-kelvin temperature range, it is our immediate objective, but one that will
require construction of a next-generation spin noise spectrometer based on a dilution
refrigerator. We have chosen this temperature range carefully since the density
of monopoles is optimal for measurement of this kind of noise. Furthermore, we
actually anticipate that the simple magnetic-flux noise spectrum of a monopole
plasma studied here, will disappear quickly and transform into a telegraph noise
spectrum at slightly lower temperatures as predicted by generalizations of the GR
model [8]. These are challenges that can only be addressed in future research.
8.1.2 Understanding Correlations Analytically
Noting that the power law for ωτ in the expression for spin noise does not equal
two as expected suggests a deeper look into the derivation of monopole number
fluctuations causing generation recombination noise. The last term in the Langevin
equation describes an uncorrelated stimulus to the monopole number changing as a
function of time. However it is known that the monopoles are allowed to move only
on the centers of tetrahedra the Dy spins sit on. This constrains the motion of these
monopoles in a way that is quite different from that of a free monopole plasma.
Correlations arising from such constraints are expected to be added to the last term
in equation.
63
S B z (ω, T ) from Dy 2 Ti 2 O 7 showing the magnetic monopole GR attributes (Fig. 8.1)
add to the growing evidence for the existence of magnetic monopoles in spin ices
[10–12].
The additional refinement of the generation-recombination for magnetic monopoles
in spin ices observed in the modified power law for ω is understood by studying
different magnetic charge dynamic models. The comparisons of power law ’b’
observed in experiment and the different models indicate the existence of correlations in magnetic monopole dynamics. The presentation of autocorrelation functions
C B z (t)/C B z (0) show us good correspondence between experimental measurements
and the DSIM which includes both dipolar interactions and Dirac string constraints.
These observations further the understanding of the affect of correlations in spin ice
magnetic monopole plasma. Overall, we find detailed and comprehensive agreement
between current theories for thermal generation and recombination of a correlated
±m ∗ magnetic monopole plasma and the phenomenology of magnetic-flux noise
spectral density in Dy 2 Ti 2 O 7 that is revealed by spin-noise spectroscopy.
8.1 Future Directions
8.1.1 Telegraph Noise
Although the monopole noise spectral density has not yet been measured in the
sub-kelvin temperature range, it is our immediate objective, but one that will
require construction of a next-generation spin noise spectrometer based on a dilution
refrigerator. We have chosen this temperature range carefully since the density
of monopoles is optimal for measurement of this kind of noise. Furthermore, we
actually anticipate that the simple magnetic-flux noise spectrum of a monopole
plasma studied here, will disappear quickly and transform into a telegraph noise
spectrum at slightly lower temperatures as predicted by generalizations of the GR
model [8]. These are challenges that can only be addressed in future research.
8.1.2 Understanding Correlations Analytically
Noting that the power law for ωτ in the expression for spin noise does not equal
two as expected suggests a deeper look into the derivation of monopole number
fluctuations causing generation recombination noise. The last term in the Langevin
equation describes an uncorrelated stimulus to the monopole number changing as a
function of time. However it is known that the monopoles are allowed to move only
on the centers of tetrahedra the Dy spins sit on. This constrains the motion of these
monopoles in a way that is quite different from that of a free monopole plasma.
Correlations arising from such constraints are expected to be added to the last term
in equation.