Field Theory of Linear Spin-Waves in Finite Textured Ferromagnets

In the context of an ever-expanding experimental and theoretical interest in the magnetization dynamics of mesoscopic magnetic structures, both in the classical and quantum regimes, we formulate a low energy field theory for the linear spin-waves in finite and textured ferromagnets and we perform its constrained canonical quantization. The introduction of a manifestly gauge invariant Lagrangian enables a straightforward application of the Noether's theorem. Taking advantage of this in the context of a broad class of axisymmetric ferromagnets of special conceptual and experimental relevance, a general expression of the conserved and quantized spin-wave total angular momentum is rigorously derived, while separate conservation and quantization of its orbital and spin components are established for a more restricted class of uniaxial exchange ferromagnets. Further particularizing this general framework to the case of axially saturated magnetic thin disks, we develop a semi-analytic theory of the low frequency part of the exchange-dipole azimuthal spin wave spectrum, providing a powerful theoretical platform for the analysis and interpretation of magnetic resonance experiments on magnetic microdots as further demonstrated in a joint paper [arxiv The Orbital Angular Momentum of Azimuthal Spin-Waves]