Chapter 7
Fluctuation Dissipation Theorem
In our experiment, we have measured spin noise spectrum of a Dysprosium Titanate
sample at equilibrium, from 1.2K to 4K using a DC-SQUID. From the Fluctuation
Dissipation (FD) theorem, we know that statistical fluctuations in a physical variable
of a system are related to the linear response to a small force applied to the system.
In this chapter our experimental results of flux noise coming from a sample of
Dy 2 Ti 2 O 7 are discussed in the context of previous boundary-free AC susceptibility
measurements of Dysprosium Titanate.
If we take the system as magnetic monopole fluid in Dy 2 Ti 2 O 7 , the power
spectrum of the fluctuations of magnetic field in this fluid is related to χ (ω, T ),
the imaginary part of susceptibility of the magnetic fluid to small external forces
S B z ∝
χ (ω, T ) · k B T
ω
(7.1)
With the SNS, we have measured the flux noise spectral density S (ω, T ) ≈
2 (ω, T ) generated due to equilibrium thermal fluctuations in Dysprosium
Titanate. This flux noise S (ω, T ) is proportional to magnetic field noise S B z (ω, T )
picked up by our spectrometer.
S (ω, T ) = =
2 (ω, T ) = σ
2 S B z
(7.2)
where σ is the area of the SQUID input coil. Using our measurements of S (ω, T )
and equivalent S B z (ω, T ) (Eq. 7.2) for a Dy 2 Ti 2 O 7 sample, χ (ω, T ) was determined (Fig. 7.1) in arbitrary units (Eq. 7.1).
This measured χ (ω, T ), extracted from flux noise measurements was then fit
to the Havriliak Negami form of χ (ω, T ) that Kassner et al. [1] ac susceptibility
experiment determined as
χ(ω, T ) = χ ∞ +
χ 0
(1 + (iωτ ) α ) γ
(7.3)
© Springer Nature Switzerland AG 2021
R. Dusad, Magnetic Monopole Noise, Springer Theses,
https://doi.org/10.1007/978-3-030-58193-0_7
57
Fluctuation Dissipation Theorem
In our experiment, we have measured spin noise spectrum of a Dysprosium Titanate
sample at equilibrium, from 1.2K to 4K using a DC-SQUID. From the Fluctuation
Dissipation (FD) theorem, we know that statistical fluctuations in a physical variable
of a system are related to the linear response to a small force applied to the system.
In this chapter our experimental results of flux noise coming from a sample of
Dy 2 Ti 2 O 7 are discussed in the context of previous boundary-free AC susceptibility
measurements of Dysprosium Titanate.
If we take the system as magnetic monopole fluid in Dy 2 Ti 2 O 7 , the power
spectrum of the fluctuations of magnetic field in this fluid is related to χ (ω, T ),
the imaginary part of susceptibility of the magnetic fluid to small external forces
S B z ∝
χ (ω, T ) · k B T
ω
(7.1)
With the SNS, we have measured the flux noise spectral density S (ω, T ) ≈
2 (ω, T ) generated due to equilibrium thermal fluctuations in Dysprosium
Titanate. This flux noise S (ω, T ) is proportional to magnetic field noise S B z (ω, T )
picked up by our spectrometer.
S (ω, T ) = =
2 (ω, T ) = σ
2 S B z
(7.2)
where σ is the area of the SQUID input coil. Using our measurements of S (ω, T )
and equivalent S B z (ω, T ) (Eq. 7.2) for a Dy 2 Ti 2 O 7 sample, χ (ω, T ) was determined (Fig. 7.1) in arbitrary units (Eq. 7.1).
This measured χ (ω, T ), extracted from flux noise measurements was then fit
to the Havriliak Negami form of χ (ω, T ) that Kassner et al. [1] ac susceptibility
experiment determined as
χ(ω, T ) = χ ∞ +
χ 0
(1 + (iωτ ) α ) γ
(7.3)
© Springer Nature Switzerland AG 2021
R. Dusad, Magnetic Monopole Noise, Springer Theses,
https://doi.org/10.1007/978-3-030-58193-0_7
57