Quantum Micromagnetic Theory of Magnons in Finite Nanostructures

TL;DR

This paper develops a quantum field theoretical approach to analyze magnons in finite nanostructures, accounting for arbitrary shapes and nonuniform ground states, extending classical micromagnetic models with quantum operators.

Contribution

It introduces a quantum micromagnetic Hamiltonian formalism for finite nanostructures, enabling detailed spectral analysis of magnons with arbitrary geometries and ground states.

Findings

Derived a quadratic Hamiltonian for magnons in nanostructures.

Diagonalized the Hamiltonian to obtain magnon spectra.

Analyzed temperature and shape effects on magnon fluctuations.

Abstract

This paper presents a quantum field theoretical formalism for studying magnons in finite nanostructures with arbitrary shapes and spatially nonuniform ground states. It extends the classical micromagnetic formalism by introducing a micromagnetic Hamiltonian quantum operator, which incorporates exchange, Dzyaloshinsky-Moriya, anisotropy, magnetostatic, and Zeeman energies. The nonuniformity of the ground state is handled by pointwise aligning the quantization axis of the magnetization field operator with the classical ground state. The Hamiltonian is expanded in the large spin-number limit and truncated to retain only terms quadratic in the components of the magnetization operator transverse to the quantization axis. This quadratic Hamiltonian is used to derive the linear quantum Landau-Lifshitz equation. By diagonalizing this equation under appropriate boundary and normalization conditions, a discrete set of magnon creation and annihilation operators is obtained, enabling a complete description of the magnon spectrum. Finally, the theory is applied to study the effects of temperature and shape on low-temperature thermal equilibrium fluctuations of magnons in thin ferromagnetic nanodisks.