Bottleneck Accumulation of Hybrid Magnetoelastic Bosons

Dmytro A. Bozhko, Peter Clausen, Gennadii A. Melkov, Victor S. L’vov, Anna Pomyalov, Vitaliy I. Vasyuchka, Andrii V. Chumak, Burkard Hillebrands, and Alexander A. Serga

Phys. Rev. Lett. 118, 237201 – Published 8 June 2017

Abstract

An ensemble of magnons, quanta of spin waves, can be prepared as a Bose gas of weakly interacting quasiparticles. Furthermore, the thermalization of the overpopulated magnon gas through magnon-magnon scattering processes, which conserve the number of particles, can lead to the formation of a Bose-Einstein condensate at the bottom of a spin-wave spectrum. However, magnon-phonon scattering can significantly modify this scenario and new quasiparticles are formed—magnetoelastic bosons. Our observations of a parametrically populated magnon gas in a single-crystal film of yttrium iron garnet by means of wave-vector-resolved Brillouin light scattering spectroscopy evidence a novel condensation phenomenon: A spontaneous accumulation of hybrid magnetoelastic bosonic quasiparticles at the intersection of the lowest magnon mode and a transversal acoustic wave.

Received 7 February 2017

DOI:https://doi.org/10.1103/PhysRevLett.118.237201

Physics Subject Headings (PhySH)

Bosons Ferromagnetism Magnetism Magnons Phonons Spin waves

Ferromagnets

Brillouin scattering & spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dmytro A. Bozhko^1,2,*, Peter Clausen¹, Gennadii A. Melkov³, Victor S. L’vov⁴, Anna Pomyalov⁴, Vitaliy I. Vasyuchka¹, Andrii V. Chumak¹, Burkard Hillebrands¹, and Alexander A. Serga¹

¹Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
²Graduate School Materials Science in Mainz, Kaiserslautern 67663, Germany
³Faculty of Radiophysics, Electronics and Computer Systems, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine
⁴Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel

^*bozhko@physik.uni-kl.de

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Vol. 118, Iss. 23 — 9 June 2017

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Images

Figure 1
(a) Schematic illustration of the experimental setup. The resonator concentrates the applied microwave energy and induces a pumping microwave Oersted field $h_{p}$ oriented along the bias magnetic field $H$ , thus realizing conditions for the parallel parametric pumping. The probing laser beam is focused onto a YIG film placed on top of the microstrip resonator. The light inelastically scattered by magnons is redirected to a Fabry-Pérot interferometer for frequency and intensity analysis. Wave-number-selective probing of magnons with wave vectors $q ∥ H$ is realized by varying the incidence angle $Θ_{q_{∥}}$ between the field $H$ and the probing laser beam. (b) Magnon-phonon spectrum of a $6.7 μ m$ -thick YIG film calculated for $H = 1735 Oe$ . 47 thickness modes with $q ∥ H$ are shown. The upper thick curve shows the most effectively parametrically driven [26] lowest magnon mode with $q ⊥ H$ . The arrow illustrates the magnon injection to the frequency $ω_{p} / 2$ slightly above the ferromagnetic resonance frequency $ω_{FMR}$ .
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Figure 2
Magnon-phonon spectra and their population under different pumping conditions. White dashed lines represent the calculated dispersion relation for the lowest magnon branch ( $q ∥ H$ ), hybridized with a transversal acoustic mode. Strong population of the magnon-phonon hybridization region is clearly visible in the parametrically pumped spectra (a)–(b) measured in the case of a $500 μ m$ –wide pumping area. The width of the population peak is of the order of the wave number resolution of the experimental setup, i.e., $\pm 0.02 \times 1 0^{5} rad {cm}^{- 1}$ . No distinct peculiarities in the thermal spectrum measured for zero pump power are detected (c).
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Figure 3
Temporal dynamics of the magnon gas density. (a) Pronounced accumulation of magnetoelastic bosons is evident for the broad pumping area of $500 μ m$ width. The right panel shows the pumping power dependencies of the quasiparticle density integrated by time. The saturation of the magnetoelastic peak at high pumping powers argues in favor of a relationship between the magnon BEC and the accumulation phenomenon. No accumulation effect is visible in (b) due to a strong leakage of fast magnetoelastic bosons from the narrow pumping area of $50 μ m$ width. The pumping power is significantly decreased due to the increase in the density of a microwave current in the narrow microstrip. In all measurements BLS data are collected in the frequency band of 150 MHz near the bottom of the magnon spectrum [see the shaded area in the right panel of (b)]. The bias magnetic field is $H = 1735 Oe$ .
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Figure 4
Theory of the bottleneck accumulation. (a) Calculated magnon-phonon spectrum near the hybridization region. (b) Interaction amplitudes $T_{q}^{UU}$ , $T_{q}^{LL}$ , and $T_{q}^{UL}$ , normalized by $T_{q}$ , vs the dimensionless distance from the hybridization crossover $o_{q}$ . (c)–(e) Schematic representation of the scattering and cross-scattering four-particle processes in the hybridization region. (f) Solutions of the dimensionless L-MEM density $N_{q}^{L}$ , for different values of the parameter $a$ .
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