26
3 Experiment
or the presence of multiple grains. Performance of Rietveld refinement on the
diffraction data yields a unit cell lattice constant of 10.129 Å; this implies a
maximum possible level of “spin stuffing” (substitution of Dy 3+ ions on Ti 4+ sites)
of ∼ 2.9% and a most likely spin-stuffing fraction< 1%.
Disk shaped Dy 2 Ti 2 O 7 crystals obtained from Prof. Luke’ group were then cut
into rod-shaped samples with the help of a dicing saw encrusted with diamond bits
on the blade. From previous transport experiments [1] on Dy 2 Ti 2 O 7 crystals it was
learned that orientation of these crystals does not affect magnetic response of the
material. Therefore, no particular crystal axis direction was chosen when the rodshaped samples were cut.
3.2.3 Recording Sample Spin Fluctuations
A typical operation cycle of the SNS aboard the 1K cryostat consists of cooling
down experiment to 1.2K and then using PID controls to vary temperature from
1.2K to 4K with temperature stability at each point of 2.5 mK. Once the temperature
is stable at a desired set-point, spin fluctuations inside DTO sample are detected by
the pickup coil connected to the SQUID input coil. The DC SQUID used in this
SNS operates in a flux-locked loop supported by the electronics on the SQUID chip
and preamplifier. The detected flux is output from the SQUID electronics box as
an analog voltage V SQU I D (t) calibrated to the flux detected by a transfer function
(Appendix C.2).
To perform spectral analysis of the signal, V SQU I D (t) is fed into a SR780
Dynamic Signal Analyzer with input noise of ∼ 300nV /
√
H z, much below that
of the SQUID noise floor. The SA then calculates the autocorrelation function C(τ )
of V SQU I D (t) and then takes the Fourier transform of C(τ ) to generate a power
spectrum (averaged) S v (ω, T ) that is sent to a PC to be to be recorded. A schematic
diagram of spin noise detection scheme is shown in Fig. 3.5. Unprocessed data
at each temperature consists of 5 datasets of bandwidth (BW) 2.5kHz, each of
which is an outcome of averaging of 1000 acquisitions where acquisition time =
(1/resolution BW), resulting in the measured SQUID output as voltage-flux noise
spectral density detected at the SQUID. This power spectrum S v (ω, T ) is then
converted to S (ω, T ) using calibration described in Appendix C.2.
3.3 Initial Observations
The first temperature controlled noise measurements of Dy 2 Ti 2 O 7 , showed that
flux noise from rod shaped samples of Dysprosium Titanate displayed a strong
dependence on temperature and frequency. The noise spectrum at 4K had a distinct
shape—a plateau followed by an eventual decay. The decay could be characterized
by a cutoff frequency, that shifted to a lower value as the sample was cooled.
3 Experiment
or the presence of multiple grains. Performance of Rietveld refinement on the
diffraction data yields a unit cell lattice constant of 10.129 Å; this implies a
maximum possible level of “spin stuffing” (substitution of Dy 3+ ions on Ti 4+ sites)
of ∼ 2.9% and a most likely spin-stuffing fraction< 1%.
Disk shaped Dy 2 Ti 2 O 7 crystals obtained from Prof. Luke’ group were then cut
into rod-shaped samples with the help of a dicing saw encrusted with diamond bits
on the blade. From previous transport experiments [1] on Dy 2 Ti 2 O 7 crystals it was
learned that orientation of these crystals does not affect magnetic response of the
material. Therefore, no particular crystal axis direction was chosen when the rodshaped samples were cut.
3.2.3 Recording Sample Spin Fluctuations
A typical operation cycle of the SNS aboard the 1K cryostat consists of cooling
down experiment to 1.2K and then using PID controls to vary temperature from
1.2K to 4K with temperature stability at each point of 2.5 mK. Once the temperature
is stable at a desired set-point, spin fluctuations inside DTO sample are detected by
the pickup coil connected to the SQUID input coil. The DC SQUID used in this
SNS operates in a flux-locked loop supported by the electronics on the SQUID chip
and preamplifier. The detected flux is output from the SQUID electronics box as
an analog voltage V SQU I D (t) calibrated to the flux detected by a transfer function
(Appendix C.2).
To perform spectral analysis of the signal, V SQU I D (t) is fed into a SR780
Dynamic Signal Analyzer with input noise of ∼ 300nV /
√
H z, much below that
of the SQUID noise floor. The SA then calculates the autocorrelation function C(τ )
of V SQU I D (t) and then takes the Fourier transform of C(τ ) to generate a power
spectrum (averaged) S v (ω, T ) that is sent to a PC to be to be recorded. A schematic
diagram of spin noise detection scheme is shown in Fig. 3.5. Unprocessed data
at each temperature consists of 5 datasets of bandwidth (BW) 2.5kHz, each of
which is an outcome of averaging of 1000 acquisitions where acquisition time =
(1/resolution BW), resulting in the measured SQUID output as voltage-flux noise
spectral density detected at the SQUID. This power spectrum S v (ω, T ) is then
converted to S (ω, T ) using calibration described in Appendix C.2.
3.3 Initial Observations
The first temperature controlled noise measurements of Dy 2 Ti 2 O 7 , showed that
flux noise from rod shaped samples of Dysprosium Titanate displayed a strong
dependence on temperature and frequency. The noise spectrum at 4K had a distinct
shape—a plateau followed by an eventual decay. The decay could be characterized
by a cutoff frequency, that shifted to a lower value as the sample was cooled.