48
5 Analysis
Fig. 5.5 Plot of measured
variance of flux σ 2
shows
that it is approximately
constant as a function of
temperature, in the entire
temperature range of our
experiment
1
2
3
4
Temperature (K)
0
0.02
0.04
0.06
0.08
0.1
0.12
2
(
0
2
)
From Fig. 5.5, it is noted that σ 2
is weakly dependent on temperature. This validates
monopole GR theory prediction for σ 2
N (T ). Figure 1.8 suggests that different
activation processes describe the dynamics of spin ices, and that τ (T ) across a wide
temperature range has different behaviors. A deeper understanding of why σ 2
is
approximately constant in the range of 1.2K–4K would be revealed by extending
the temperature range of the experiment and knowledge of the exact mechanism of
spin flips [6] determining the generation and recombination rate of monopoles.
5.4 Comparison with MC Calculations
Finally we examine our experimental measurements in the context of MC calculations of magnetic field noise coming from Dy 2 Ti 2 O 7 . The MC study of magnetic
field fluctuations arising in a sample of Dy 2 Ti 2 O 7 by simulating the spin flips
according to DSIM (Eq. 1.1) is an important and profound prediction for magnetic
field noise we should expect to see in our experiment.
To compare the MC calculations and experiment on the same footing, it would
be useful to have x-axis of Fig. 3.8 in actual time units. This is done by converting
from MC-step to seconds (described in Appendix C.2), so that angular frequency
for MC ω(rad/sec)=2π /t(sec) and S B z (ω, T ) [T 2 s].
From Fig. 5.6 we see that both experiment S (ω, T ), and MC S B z (ω, T ) from a
Dy 2 Ti 2 O 7 sample retain the overall characteristic predictions of GR noise (Fig. 4.2)
as is apparent from respective fits to the functional form S B (ω, T ) ∝ τ/(1+(ωτ ) b ).
It is now possible to test the prediction of S(ω = 0, T ) ∝ τ (T ) for MC magnetic
field noise from magnetic monopole GR theory. When S B z (0, T ) is plotted versus
τ (T ) (Fig. 5.7 bottom), they are approximately proportional, once an offset to all
values of S B z (0, T ) due to numerical Nyquist (sampling) noise is considered.
5 Analysis
Fig. 5.5 Plot of measured
variance of flux σ 2
shows
that it is approximately
constant as a function of
temperature, in the entire
temperature range of our
experiment
1
2
3
4
Temperature (K)
0
0.02
0.04
0.06
0.08
0.1
0.12
2
(
0
2
)
From Fig. 5.5, it is noted that σ 2
is weakly dependent on temperature. This validates
monopole GR theory prediction for σ 2
N (T ). Figure 1.8 suggests that different
activation processes describe the dynamics of spin ices, and that τ (T ) across a wide
temperature range has different behaviors. A deeper understanding of why σ 2
is
approximately constant in the range of 1.2K–4K would be revealed by extending
the temperature range of the experiment and knowledge of the exact mechanism of
spin flips [6] determining the generation and recombination rate of monopoles.
5.4 Comparison with MC Calculations
Finally we examine our experimental measurements in the context of MC calculations of magnetic field noise coming from Dy 2 Ti 2 O 7 . The MC study of magnetic
field fluctuations arising in a sample of Dy 2 Ti 2 O 7 by simulating the spin flips
according to DSIM (Eq. 1.1) is an important and profound prediction for magnetic
field noise we should expect to see in our experiment.
To compare the MC calculations and experiment on the same footing, it would
be useful to have x-axis of Fig. 3.8 in actual time units. This is done by converting
from MC-step to seconds (described in Appendix C.2), so that angular frequency
for MC ω(rad/sec)=2π /t(sec) and S B z (ω, T ) [T 2 s].
From Fig. 5.6 we see that both experiment S (ω, T ), and MC S B z (ω, T ) from a
Dy 2 Ti 2 O 7 sample retain the overall characteristic predictions of GR noise (Fig. 4.2)
as is apparent from respective fits to the functional form S B (ω, T ) ∝ τ/(1+(ωτ ) b ).
It is now possible to test the prediction of S(ω = 0, T ) ∝ τ (T ) for MC magnetic
field noise from magnetic monopole GR theory. When S B z (0, T ) is plotted versus
τ (T ) (Fig. 5.7 bottom), they are approximately proportional, once an offset to all
values of S B z (0, T ) due to numerical Nyquist (sampling) noise is considered.