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

Abstract

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion k has two degenerate minima at finite wave-vectors ±q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.PACS. 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties 75.10.JmQuantized spin models -75.30.Ds Spin waves arXiv:1007.3200v3 [cond-mat.quant-gas]

Thermalization of magnons in yttrium-iron garnet: Nonequilibrium functional renormalization group approach

“…Whether or not such a state should be called a Bose-Einstein condensate of magnons seems to be a matter of semantics 40,41 . We have argued previously 26,42 that the experimentally observed strong enhancement of the magnon distribution is not accompanied by superfluidity, because a macroscopic occupation of a certain magnon mode is simply equivalent with a change in magnetic order 43 . In Fig.…”

“…Actually, as reviewed in Appendix A, one can rewrite the kinetic equation in several different forms, depending on the choice of basis and on the re-shuffling of the terms in the Dyson equations. For our purpose, it is most convenient to parametrize the Keldysh block in terms of the distribution matrixĝ by settinĝ 26) where in the non-interacting limit the matrixĝ reduces to the non-interacting distribution matrixĝ 0 given in Eq. (2.18a).…”

“…Note that our Hamiltonian (1.1) does not contain direct two-body interactions between the magnons, so that in the absence of phonons the magnons do not interact. A more realistic model describing the Bose-Einstein condensation of magnons in YIG should also include manybody interactions between the magnons 21,26 . Although these interactions compete with the phonons to thermalize the magnon gas, we focus here on a regime where the dominant thermalization mechanism is due to magnonphonon scattering.…”

Field dependence of magnon decay in yttrium iron garnet thin films

“…11 We would like to point out that it is also precisely the direction along which the minima of the magnon band are located. 13 Therefore, the amplitude of the decay of k = 0 magnon into two magnons at the band minima q m and −q m is zero. This will lead to a rather spectacular violation of the naïve expectation: while kinematic conditions for the decay of k = 0 magnon into ±q m are just met at H c , the corresponding decay amplitude is vanishing.…”

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

“…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]. Phenomenological approaches of the Ginzburg-Landau type also have been used to study the condensation dynamics [22].…”