58
7 Fluctuation Dissipation Theorem
10
1
10
2
10
3
10
4
Frequency (Hz)
0
0.1
0.2
0.3
0.4
0.5
0.6
Im
1.2
1.26
1.29
1.32
1.35
1.4
1.45
1.5
1.55
1.6
1.7
1.8
2
2.25
2.5
3
3.5
4
Temperature(K)
Fig. 7.1 Imaginary part of susceptibility of a fluid of monopoles in Dy 2 Ti 2 O 7 in arbitrary units,
extracted from our S (ω, T ) measurements, vs frequency is plotted here for temperature range of
1.2K to 4K
Free parameters for the fitting procedure were χ 0 , τ , α and γ . The fits are of
good quality, with R 2 > 0.99 for all temperatures studied (Fig. 7.2). We have
demonstrated some elements of the FD theorem for Dy 2 Ti 2 O 7 samples by using
our spin noise studies to predict imaginary part of susceptibility for this material.
The functional form of χ
(ω, T ) is equivalent to that of χ
M (ω, T ) determined by
Kassner et al. [1].
7.1 Sample Geometry Effects
There is a slight difference between τ and τ M and might be present due to
sample geometries in the two experiments being quite different. It will require
quantitative tests to establish a relationship between geometry of sample and the
microscopic time constant τ (extracted from fit shown in Fig. 7.1). As noted in
some previous transport measurements [2], edges of a rod-shaped magnetic sample
create demagnetizing stray fields that are picked up by a detector.
Shape effects could occur in such spin noise measurements. This is because even
though we are measuring a cuboidal sample with a coil around the middle, spins
at the ends of the sample still contribute partially. Our experiments measure flux
7 Fluctuation Dissipation Theorem
10
1
10
2
10
3
10
4
Frequency (Hz)
0
0.1
0.2
0.3
0.4
0.5
0.6
Im
1.2
1.26
1.29
1.32
1.35
1.4
1.45
1.5
1.55
1.6
1.7
1.8
2
2.25
2.5
3
3.5
4
Temperature(K)
Fig. 7.1 Imaginary part of susceptibility of a fluid of monopoles in Dy 2 Ti 2 O 7 in arbitrary units,
extracted from our S (ω, T ) measurements, vs frequency is plotted here for temperature range of
1.2K to 4K
Free parameters for the fitting procedure were χ 0 , τ , α and γ . The fits are of
good quality, with R 2 > 0.99 for all temperatures studied (Fig. 7.2). We have
demonstrated some elements of the FD theorem for Dy 2 Ti 2 O 7 samples by using
our spin noise studies to predict imaginary part of susceptibility for this material.
The functional form of χ
(ω, T ) is equivalent to that of χ
M (ω, T ) determined by
Kassner et al. [1].
7.1 Sample Geometry Effects
There is a slight difference between τ and τ M and might be present due to
sample geometries in the two experiments being quite different. It will require
quantitative tests to establish a relationship between geometry of sample and the
microscopic time constant τ (extracted from fit shown in Fig. 7.1). As noted in
some previous transport measurements [2], edges of a rod-shaped magnetic sample
create demagnetizing stray fields that are picked up by a detector.
Shape effects could occur in such spin noise measurements. This is because even
though we are measuring a cuboidal sample with a coil around the middle, spins
at the ends of the sample still contribute partially. Our experiments measure flux