Chapter 2
Magnetic Monopoles in Spin Ices
The simplest excitations out of the lowest energy 2-in-2-out configuration of the
Dy spins in Dy 2 Ti 2 O 7 are not the typically expected spin waves. In fact, individual
spin flips breaking the ice rules are the elementary excitations in this compound.
These individual flips may be generated by temperature fluctuations, or applied
magnetic fields of the order of a few Tesla. Since the pyrochlore lattice is comprised
of interconnected tetrahedra, a single spin flip would result in a 3-out-1-in and 3in-1-out spin configuration on two adjoining tetrahedra (Fig. 2.1 left). The center
of a tetrahedron for these positive (negative) defects [1] can be thought of as a
source(sink) of magnetic flux and was thus termed as magnetic monopole (antimonopole) [2, 3] for this solid state system. In this chapter, I discuss the energetics of
these monopoles, how they are predicted to interact with each other, as well as some
of the past searches for these elusive particles in Dysprosium Titanate. Towards
the end of the chapter, a new technique employing a Superconducting QUantum
Interference Device is proposed to look for magnetic monopoles.
To understand how these magnetic defects can act like magnetic monopoles, it
is important to understand the dumbbell model (Fig. 2.1 right) that inspired this
picture. In this model, a Dy spin acting like a magnetic dipole μ can be recast as a
dumbbell of opposite signed magnetic charges ±q m = μ/d with separation d. The
ratio between diamond lattice constant d and a is :d =
√
3/2a = 4.38Å. In the limit
of this separation tending to zero, the dipolar part of the DSIM is reproduced exactly.
The separation between the two charges d is chosen to be the distance between two
diamond lattice vortices, described by the centers of tetrahedra in the pyrochlore
lattice. Casting each dipole as a dumbbell, the center of each tetrahedron will then
contain four dumbbell ends each of charge either +q m or −q m .
The interaction energy V(r ij ) between charges q i and q j (residing on sites i,j,
separated by distance r ij ) can be represented by
© Springer Nature Switzerland AG 2021
R. Dusad, Magnetic Monopole Noise, Springer Theses,
https://doi.org/10.1007/978-3-030-58193-0_2
11
Magnetic Monopoles in Spin Ices
The simplest excitations out of the lowest energy 2-in-2-out configuration of the
Dy spins in Dy 2 Ti 2 O 7 are not the typically expected spin waves. In fact, individual
spin flips breaking the ice rules are the elementary excitations in this compound.
These individual flips may be generated by temperature fluctuations, or applied
magnetic fields of the order of a few Tesla. Since the pyrochlore lattice is comprised
of interconnected tetrahedra, a single spin flip would result in a 3-out-1-in and 3in-1-out spin configuration on two adjoining tetrahedra (Fig. 2.1 left). The center
of a tetrahedron for these positive (negative) defects [1] can be thought of as a
source(sink) of magnetic flux and was thus termed as magnetic monopole (antimonopole) [2, 3] for this solid state system. In this chapter, I discuss the energetics of
these monopoles, how they are predicted to interact with each other, as well as some
of the past searches for these elusive particles in Dysprosium Titanate. Towards
the end of the chapter, a new technique employing a Superconducting QUantum
Interference Device is proposed to look for magnetic monopoles.
To understand how these magnetic defects can act like magnetic monopoles, it
is important to understand the dumbbell model (Fig. 2.1 right) that inspired this
picture. In this model, a Dy spin acting like a magnetic dipole μ can be recast as a
dumbbell of opposite signed magnetic charges ±q m = μ/d with separation d. The
ratio between diamond lattice constant d and a is :d =
√
3/2a = 4.38Å. In the limit
of this separation tending to zero, the dipolar part of the DSIM is reproduced exactly.
The separation between the two charges d is chosen to be the distance between two
diamond lattice vortices, described by the centers of tetrahedra in the pyrochlore
lattice. Casting each dipole as a dumbbell, the center of each tetrahedron will then
contain four dumbbell ends each of charge either +q m or −q m .
The interaction energy V(r ij ) between charges q i and q j (residing on sites i,j,
separated by distance r ij ) can be represented by
© Springer Nature Switzerland AG 2021
R. Dusad, Magnetic Monopole Noise, Springer Theses,
https://doi.org/10.1007/978-3-030-58193-0_2
11