2.1 Searches for Monopoles
13
Fig. 2.2 Schematic representation of the spin ice excited state in which two magnetic charges
±m ∗ are generated by a spin flip, and propagate through the material. A single flip of an Ising
Dy 3+ spin converts the 2-in/2-out m α = 0 configuration in adjacent tetrahedra, to a situation with
adjacent m α = ±m ∗ for 3-out/1-in in one and m α = −m ∗ for 3-in/1-out in the next
H =
μ 0
4π
α<β
m α m β
r αβ
+
ν
2
α
m
2
α
(2.3)
The first term in the Eq. 2.3 represents a Coulombic interaction between magnetic
charges ±m ∗ . The second, contains ν and enforces the m α = 0 or 2-in-2-out ground
state at T=0. In this picture, the cost of creating two neighboring monopoles ±m ∗
can be determined from Eq. 2.3 as ≈ 2(2ν(μ/d) 2 ) − (
μ 0
4πk b
m 2
α
r 2
nn
) = 5.5K. An
existing 3-out-1-in (3-in-1-out) tetrahedron can be converted to a doubly charged
monopoles ±2m ∗ (4-in-1-out and vice versa) with a spin flip of the fourth (out)
spin. At temperatures close to the thermal energy barrier for spin flips out of the 2in-2-out-state ∼ 4.35K, a plasma or fluid of these ±m ∗ , with a small population of
energetically unfavorable ±2m ∗ charges [4] would exist due to thermal fluctuations.
In general, the magnetic charges in spin ice can move apart via a sequence of
spin flips on the tetrahedral network of the pyrochlore lattice (Fig. 2.2). A trail
of flipped spins connects the two charges and is colloquially termed as a ‘Dirac
String’, highlighted in yellow in Fig. 2.2. Once a monopole takes a certain path
with a Dirac string trailing behind it, another magnetic charge of the same sign
cannot sequentially traverse the same path [5]. This is because spin flips required
to allow the second monopole of the same sign to traverse a path previously taken
are energetically unfavorable. This obstruction is clearly illustrated in Fig. 2.3. This
poses constraints on motion of magnetic monopoles in Dy 2 Ti 2 O 7 .
2.1 Searches for Monopoles
Since the prediction of the existence of a magnetic monopole fluid was proposed
a decade ago, various experiments have looked for these magnetic charges ±m ∗ in
Dy 2 Ti 2 O 7 [6–12]. A multitude of techniques were employed in these experiments
to detect the existence of monopoles—such as study of μSR decay rates, neutron
scattering and measurement of susceptibility of magnetic fluid in this material. Two
13
Fig. 2.2 Schematic representation of the spin ice excited state in which two magnetic charges
±m ∗ are generated by a spin flip, and propagate through the material. A single flip of an Ising
Dy 3+ spin converts the 2-in/2-out m α = 0 configuration in adjacent tetrahedra, to a situation with
adjacent m α = ±m ∗ for 3-out/1-in in one and m α = −m ∗ for 3-in/1-out in the next
H =
μ 0
4π
α<β
m α m β
r αβ
+
ν
2
α
m
2
α
(2.3)
The first term in the Eq. 2.3 represents a Coulombic interaction between magnetic
charges ±m ∗ . The second, contains ν and enforces the m α = 0 or 2-in-2-out ground
state at T=0. In this picture, the cost of creating two neighboring monopoles ±m ∗
can be determined from Eq. 2.3 as ≈ 2(2ν(μ/d) 2 ) − (
μ 0
4πk b
m 2
α
r 2
nn
) = 5.5K. An
existing 3-out-1-in (3-in-1-out) tetrahedron can be converted to a doubly charged
monopoles ±2m ∗ (4-in-1-out and vice versa) with a spin flip of the fourth (out)
spin. At temperatures close to the thermal energy barrier for spin flips out of the 2in-2-out-state ∼ 4.35K, a plasma or fluid of these ±m ∗ , with a small population of
energetically unfavorable ±2m ∗ charges [4] would exist due to thermal fluctuations.
In general, the magnetic charges in spin ice can move apart via a sequence of
spin flips on the tetrahedral network of the pyrochlore lattice (Fig. 2.2). A trail
of flipped spins connects the two charges and is colloquially termed as a ‘Dirac
String’, highlighted in yellow in Fig. 2.2. Once a monopole takes a certain path
with a Dirac string trailing behind it, another magnetic charge of the same sign
cannot sequentially traverse the same path [5]. This is because spin flips required
to allow the second monopole of the same sign to traverse a path previously taken
are energetically unfavorable. This obstruction is clearly illustrated in Fig. 2.3. This
poses constraints on motion of magnetic monopoles in Dy 2 Ti 2 O 7 .
2.1 Searches for Monopoles
Since the prediction of the existence of a magnetic monopole fluid was proposed
a decade ago, various experiments have looked for these magnetic charges ±m ∗ in
Dy 2 Ti 2 O 7 [6–12]. A multitude of techniques were employed in these experiments
to detect the existence of monopoles—such as study of μSR decay rates, neutron
scattering and measurement of susceptibility of magnetic fluid in this material. Two