A Collective-Spin Derivation of the Uniform Magnon Hamiltonian in Cavity Magnonics

• URL: http://arxiv.org/abs/2606.13830v1
• Date: Thu, 11 Jun 2026 19:01:24 GMT
• Title: A Collective-Spin Derivation of the Uniform Magnon Hamiltonian in Cavity Magnonics
• Abstract summary: We show that the relevant dynamics can be restricted to the fully symmetric spin sector.<n>Applying the Holstein--Primakoff transformation directly to this total spin yields the usual uniform magnon mode.<n>As a physical consequence, the leading nonlinear correction produces an occupation-dependent reduction of the effective magnon--photon coupling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We present a direct collective-spin derivation of the effective uniform-mode Hamiltonian used in cavity magnonics. Starting from a nearest-neighbor Heisenberg ferromagnet coupled to long-wavelength magnetic fields, we show that the relevant dynamics can be restricted to the fully symmetric spin sector, where the exchange interaction contributes only a constant energy shift and the ferromagnet behaves as a macrospin of length $Ns$. Applying the Holstein--Primakoff transformation directly to this total spin yields the usual uniform magnon mode and its leading nonlinear corrections without first introducing site-resolved bosonic operators. This collective formulation makes explicit the interpretation of the ferromagnet as a synthetic large-spin atom and provides a compact route to the effective Hamiltonians used in driven and Floquet cavity magnonics. As a physical consequence, the leading nonlinear correction produces an occupation-dependent reduction of the effective magnon--photon coupling, providing a simple signature of finite-spin saturation under strong uniform-mode driving.

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