Microscopic theory of spin-wave instabilities in parallel-pumped easy-plane ferromagnets

Abstract

Spin-wave instabilities in parallel-pumped easy-plane ferromagnets are investigated using the 5-theory formalism of Zakharov et aI. The parameters in the theory are related to the interaction constants in a microscopic Hamiltonian with exchange anisotropy. A numerical study of two-and five-mode systems shows that the nonequilibrium stationary states are ones where all of the spinwave pair correlation functions have the same phase. It is also found that the phases lock to a common value before the stationary state is reached. From the form of the equations it is argued that a similar result holds for a macroscopic number of modes. Results are presented for the stationary magnon population. The approach to a stationary state in the phase-locked regime is governed by two coupled first-order dilerential equations. %hen the equations are linearized about the fixed points, it is found that the approach to the stationary state involves purely exponential decay just above threshold and damped oscillatory decay at higher power levels. Possible experimental tests of the theory are discussed.

Mechanism for a Chemical Potential of Nonequilibrium Magnons in Parametric Parallel Pumping

“…1, the timeperiodic magnetic field is treated as a classical field in the standard theory. [13][14][15][16][17] Because of this treatment, the standard theory uses an approximation whose validity is uncertain: the factor cos(ω p t) of H pump (t) = gµ B h cos(ω p t) j S z j is replaced by e −iωpt or e iωpt for the magnons-pair creation or annihilation term, respectively. 16,17) In contrast, our theory does not use that approximation because such exponential time dependence appears naturally in the quantized magnetic field.…”

“…Another advantage is the presence of a photon bath. Since the standard theory [13][14][15][16][17] does not consider a photon bath, magnonnumber conservation is always violated by the magnonspair creation and annihilation terms due to the timeperiodic magnetic field, and, as a result, µ = 0. 14,17) In our theory the rates of the pair creation and the pair annihilation satisfy the detailed balance in the nonequilibrium steady state, and, as a result, the effects of their terms are reduced to µ = ω p /2.…”

“…Our Hamiltonian consists of the magnon Hamiltonian of the ferrimagnet, the magnon-photon coupling Hamiltonian due to the time-dependent magnetic field, and the photon Hamiltonian. In contrast to the standard theory, [13][14][15][16][17] the time-periodic magnetic field is treated as a quantized field in our theory. We also argue that our two-sublattice ferrimagnet can be regarded as a minimal model for describing magnon properties of YIG at room temperature.…”

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

“…For the purpose of studying the phenomenon of parametric resonance [24,26,27,28,29,30,31], one usually simplifies the Hamiltonian (A26) by dropping the second line. involving the combination cos(ω 0 t)A k a † k a k ; moreover in the last line one substitutes γ k cos(ω 0 t) → γ k 2 e −iω0t , γ * k cos(ω 0 t) → γ * k 2 e iω0t .…”

Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets

“…Unfortunately, a complete theoretical understanding of this phenomenon is still lacking and there is no theory that can simultaneously describe all stages of the experiment. While the so-called S-theory [11][12][13][14][15][16][17][18] is able to describe the parametric resonance used to populate certain magnon states, it does not properly take magnon-magnon scattering into account and therefore cannot describe the cascade of relaxation processes leading to the formation of a magnon condensate. On the other hand, theories that focus on the condensate usually do not take the pumping dynamics into account and start with some given quasiequilibrium state which can be identified with the ground state of some effective quantum mechanical Hamiltonian [19][20][21].…”