Chapter 6
Correlations in Magnetic Monopole
Motion
To understand the correlations in ±m ∗ GR noise, we compare our experimental
knowledge to S B z (ω) MC predictions made by three different spin interaction
hamiltonians for spin ices as explained in Sect. 5.4. By varying certain parameters
like dipolar coupling D or constraints on ±m ∗ motion, we learn about how the
magnetic monopole noise is more complex than that of a free plasma of ±m ∗
charges.
6.1 Power-Law Exponent b
The MC predictions of exponent b for the power-law falloff of magnetic-flux noise
from the three theories DSI (blue), NNSI (green) and free monopoles (red) can
be determined by fitting each simulated S B z (ω, T ) to τ (T )/(1 + (ωτ (T )) b(T ) ).
The results are shown in Fig. 6.1. Experimentally measured b(T ) from fitting to
S B z (ω, T ) in Fig. 5.1 are shown as black dots.
We find that amongst the three ±m ∗ dynamics models studied, DSIM predictions
for the exponent b, are most consistent with the experimental measurements of
b. This indicates that both topological constraints (lacking in the free plasma
model) and strong dipolar interactions between spins (suppressed in NNSI) play
important roles in magnetic monopole dynamics in Dy 2 Ti 2 O 7 . The slight difference
between DSIM b(T ) and experimental b(T ) suggests that the correlated monopole
dynamics is more complex than can be anticipated by available MC simulations.
A fully accurate Hamiltonian for the spin dynamics of Dy 2 Ti 2 O 7 or Ho 2 Ti 2 O 7 is
known to more complex than the spin-ice Hamiltonian of Eq. 1.1, with significant
effects from correlations [1]. However, simulation of the dynamics in such complex
Hamiltonians, that may require more near neighbor exchange parameters, exceeds
the numerical capacity of MC simulations today.
© Springer Nature Switzerland AG 2021
R. Dusad, Magnetic Monopole Noise, Springer Theses,
https://doi.org/10.1007/978-3-030-58193-0_6
53
Correlations in Magnetic Monopole
Motion
To understand the correlations in ±m ∗ GR noise, we compare our experimental
knowledge to S B z (ω) MC predictions made by three different spin interaction
hamiltonians for spin ices as explained in Sect. 5.4. By varying certain parameters
like dipolar coupling D or constraints on ±m ∗ motion, we learn about how the
magnetic monopole noise is more complex than that of a free plasma of ±m ∗
charges.
6.1 Power-Law Exponent b
The MC predictions of exponent b for the power-law falloff of magnetic-flux noise
from the three theories DSI (blue), NNSI (green) and free monopoles (red) can
be determined by fitting each simulated S B z (ω, T ) to τ (T )/(1 + (ωτ (T )) b(T ) ).
The results are shown in Fig. 6.1. Experimentally measured b(T ) from fitting to
S B z (ω, T ) in Fig. 5.1 are shown as black dots.
We find that amongst the three ±m ∗ dynamics models studied, DSIM predictions
for the exponent b, are most consistent with the experimental measurements of
b. This indicates that both topological constraints (lacking in the free plasma
model) and strong dipolar interactions between spins (suppressed in NNSI) play
important roles in magnetic monopole dynamics in Dy 2 Ti 2 O 7 . The slight difference
between DSIM b(T ) and experimental b(T ) suggests that the correlated monopole
dynamics is more complex than can be anticipated by available MC simulations.
A fully accurate Hamiltonian for the spin dynamics of Dy 2 Ti 2 O 7 or Ho 2 Ti 2 O 7 is
known to more complex than the spin-ice Hamiltonian of Eq. 1.1, with significant
effects from correlations [1]. However, simulation of the dynamics in such complex
Hamiltonians, that may require more near neighbor exchange parameters, exceeds
the numerical capacity of MC simulations today.
© Springer Nature Switzerland AG 2021
R. Dusad, Magnetic Monopole Noise, Springer Theses,
https://doi.org/10.1007/978-3-030-58193-0_6
53