2.1 Searches for Monopoles
15
such experiments are discussed here—each involving a study of the response of the
magnetic monopole fluid to an applied field.
The first experiment studied neutron scattering spectra from DTO and detected
signatures of Dirac strings connecting between monopoles. In zero field, the spectra
exhibited pinch points as expected from the coulomb nature of the spin-ice rules
(Fig. 2.4a). Next, a strong magnetic field was applied along the [001] direction to
magnetize the sample completely and generate a unique ground state. Above 0.6K,
when the applied field was reduced to Kasteleyn field h K = [k B T ln(2)]/(2/
√
3),
a small fraction of the spins were able to overcome the field and flip with the help
of thermal energy. This generated a sparse distribution of Dirac strings executing
a random walk. The resultant neutron scattering spectra exhibited cone-like dispersion pattern (Fig. 2.4b), consistent with expectation for diffusion like correlation
(C(x, y, z) ≈
1
z exp(γ
x 2 +y 2
z 2 )) among the low density Dirac strings. When the
applied field was tilted toward the [011] direction, the random walk of Dirac strings
was biased, and the cone of diffusion collapsed onto sheets of scattering (Fig. 2.4c).
These observations corroborated with simulations of random walks on a pyrochlore
lattice, for both biased and unbiased cases (Fig. 2.4). This experiment showed good
agreement between theoretical predictions and experimentally observed signatures
of Dirac strings executing random walks in Dy 2 Ti 2 O 7 .
Secondly, the prediction of magnetic monopole fluid inspired physicists to
measure the flow of this monopole fluid by applying magnetic fields. Two groups
approached this problem in distinct ways. The first group measured the AC response
of a rod-shaped single crystal of DTO upon the application of a magnetic field [9].
The second experiment performed at Cornell employed boundary free conditions
for detection of monopole flow via emf generated from change of magnetization
(Fig. 2.5a) in both DTO and HTO [10, 11]. In this experiment, the magnetic
‘fluid’ was driven by AC and DC fields each and the response of the fluid was
measured. While the simple Debye picture [1] of a magnetolyte of monopoles
[13] predicted to exist in this system was contradicted by the ac susceptibility
experiments (Fig. 2.5b,c), a more nuanced understanding of the dynamics in these
spin ice materials was deduced [10, 11].
2.1.1 New Proposal
Since magnetic monopoles in spin ice are deemed to be sources or sinks of magnetic
flux, an instrument that can directly detect this flux would be ideal for imaging these
charges. A Superconducting QUantum Interference Device (SQUID) is a highly
sensitive magnetic flux detector that can be used for this purpose. In fact, such an
experiment was carried out in search for the actual Dirac monopole by Cabrera
[14]. The principal scheme for such an experiment is described here. A moving
fundamental magnetic monopole charge m 0 passing through a superconducting (SC)
coil changes the flux through the coil by 0 = ±h/e, where 0 is the flux quantum.
15
such experiments are discussed here—each involving a study of the response of the
magnetic monopole fluid to an applied field.
The first experiment studied neutron scattering spectra from DTO and detected
signatures of Dirac strings connecting between monopoles. In zero field, the spectra
exhibited pinch points as expected from the coulomb nature of the spin-ice rules
(Fig. 2.4a). Next, a strong magnetic field was applied along the [001] direction to
magnetize the sample completely and generate a unique ground state. Above 0.6K,
when the applied field was reduced to Kasteleyn field h K = [k B T ln(2)]/(2/
√
3),
a small fraction of the spins were able to overcome the field and flip with the help
of thermal energy. This generated a sparse distribution of Dirac strings executing
a random walk. The resultant neutron scattering spectra exhibited cone-like dispersion pattern (Fig. 2.4b), consistent with expectation for diffusion like correlation
(C(x, y, z) ≈
1
z exp(γ
x 2 +y 2
z 2 )) among the low density Dirac strings. When the
applied field was tilted toward the [011] direction, the random walk of Dirac strings
was biased, and the cone of diffusion collapsed onto sheets of scattering (Fig. 2.4c).
These observations corroborated with simulations of random walks on a pyrochlore
lattice, for both biased and unbiased cases (Fig. 2.4). This experiment showed good
agreement between theoretical predictions and experimentally observed signatures
of Dirac strings executing random walks in Dy 2 Ti 2 O 7 .
Secondly, the prediction of magnetic monopole fluid inspired physicists to
measure the flow of this monopole fluid by applying magnetic fields. Two groups
approached this problem in distinct ways. The first group measured the AC response
of a rod-shaped single crystal of DTO upon the application of a magnetic field [9].
The second experiment performed at Cornell employed boundary free conditions
for detection of monopole flow via emf generated from change of magnetization
(Fig. 2.5a) in both DTO and HTO [10, 11]. In this experiment, the magnetic
‘fluid’ was driven by AC and DC fields each and the response of the fluid was
measured. While the simple Debye picture [1] of a magnetolyte of monopoles
[13] predicted to exist in this system was contradicted by the ac susceptibility
experiments (Fig. 2.5b,c), a more nuanced understanding of the dynamics in these
spin ice materials was deduced [10, 11].
2.1.1 New Proposal
Since magnetic monopoles in spin ice are deemed to be sources or sinks of magnetic
flux, an instrument that can directly detect this flux would be ideal for imaging these
charges. A Superconducting QUantum Interference Device (SQUID) is a highly
sensitive magnetic flux detector that can be used for this purpose. In fact, such an
experiment was carried out in search for the actual Dirac monopole by Cabrera
[14]. The principal scheme for such an experiment is described here. A moving
fundamental magnetic monopole charge m 0 passing through a superconducting (SC)
coil changes the flux through the coil by 0 = ±h/e, where 0 is the flux quantum.