ETD

• Collective modes
• Condensed Matter Physics
• Linear response theory
• Quantum Physics
• Spin ice

Spin ice materials are characterized by magnetic ions residing on a pyrochlore lattice. These ions possess an effective spin-1/2 degree of freedom, arising from the structure of their atomic energy levels. Materials whose magnetic behaviour is accurately captured by classical spin models are referred to as classical spin ice (CSI). Conversely, when quantum mechanics is required for an adequate treatment, the materials are classified as quantum spin ice (QSI).
A defining feature of CSI is the massive frustration arising from the interplay between the lattice geometry and effective antiferromagnetic nearest-neighbour interactions. This leads to an extensively degenerate ground state governed by a "two-in, two-out" rule. Elementary excitations in spin ice take the form of fractionalized magnetic monopole-antimonopole pairs that interact via a magnetic Coulomb potential. In QSI, quantum fluctuations allow these monopoles to propagate coherently and undergo quantum dynamics.
In electronic systems, Coulomb interactions give rise to self-sustained collective density oscillations called plasmons, accurately studied through the random phase approximation (RPA).
In this thesis, we adapt the RPA formalism to QSI materials to demonstrate the existence of collective oscillation modes—magnetic analogues of plasmons—arising from the coherent dynamics of monopoles.