Parametric pumping and kinetics of magnons in dipolar ferromagnets

TL;DR

This paper extends the existing S-theory to include the Gross-Pitaevskii equation, providing a theoretical framework to explain magnon Bose-Einstein condensation observed under microwave pumping in ferromagnets.

Contribution

It introduces a coupled equation approach combining S-theory with the Gross-Pitaevskii equation to analyze magnon dynamics and challenges the role of Zeeman energy in magnon condensation in certain geometries.

Findings

Extended S-theory with Gross-Pitaevskii equation for magnons.

Single condensed mode approximation used in solutions.

Zeeman energy does not induce magnon condensation in parallel pumping geometry.

Abstract

The time evolution of magnons subject to a time-dependent microwave field is usually described within the so-called "S-theory", where kinetic equations for the distribution function are obtained within the time-dependent Hartree-Fock approximation. To explain the recent observation of "Bose-Einstein condensation of magnons" in an external microwave field [Demokritov et al., Nature 443, 430 (2006)], we extend the "S-theory" to include the Gross-Pitaevskii equation for the time-dependent expectation values of the magnon creation and annihilation operators. We explicitly solve the resulting coupled equations within a simple approximation where only a single condensed mode is retained. We also re-examine the usual derivation of an effective boson model from a realistic spin model for yttrium-iron garnet films and argue that in the parallel pumping geometry (where both the static and the time-dependent magnetic field are parallel to the macroscopic magnetization) the time-dependent Zeemann energy cannot give rise to magnon condensation.