Bottleneck accumulation of hybrid bosons in a ferrimagnet

Transcription

1 Bottleneck accumulation of hybrid bosons in a ferrimagnet Alexander A. Serga Fachbereich Physik and Landesforschungszentrum OPTIMAS Technische Universität Kaiserslautern, Germany

2 Magnon computing Concept of magnon spintronics A.V. Chumak et al., ature Phys. 11, 453 (15) Magnon transport plays a central role in magnonics

3 Collaborators Team Kaiserslautern University (Germany) Dmytro Bozhko Vitaliy Vasyuchka Alexander Serga Burkard Hillebrands Taras Shevchenko ational University of Kyiv (Ukraine) Weizmann Institute of Science (Israel) Gennadii Melkov Victor L'vov Anna Pomyalov

4 Magnon gas Magnon as a uanta of spin-wave Energy Momentum Mass Spin s 1 Lifetime ~ 4-7 ns! (Yttrium Iron Garnet, Y 3 Fe 5 O 1 )

5 Magnon-phonon spectrum of in-plane magnetized YIG film Landau-Lifshitz euation: dipolar interaction exchange U - mel +... M magnetoelastic YIG film: 6 µm

6 Magnon-phonon spectrum of in-plane magnetized YIG film Energy and momentum conservation laws f p Parametric pumping by electromagnetic wave at microwave freuency f sw = f p / YIG film: 6 µm Thickness modes having a non-uniform harmonic distribution of dynamic magnetization along the film thickness S.O. Demokritov et al., ature 443, 43 (6) Magnon thermalization due to 4-particle scattering: incoherent magnon gas Bose-Einstein condensate of magnons µ=e min

7 Brillouin light scattering (BLS) spectroscopy Inelastic scattering of photons from spin waves f f f scattered L L sw f L L f sw sw scattered L L sw Intensity of the scattered light is proportional to magnon density magnons f sw, sw Elastically scattered light f L, L Freuency resolution: 5 MHz

8 Time- and wavevector-resolved BLS spectroscopy Time resolution: 1 ns Max wavenumber: Wavenumber resolution: rad/cm 1 3 rad/cm

9 BLS freuency shift (GHz) Thermal magnon-phonon spectrum Wavevector-resolved BLS spectroscopy Anti-Stokes Stokes Wavenumber (x1 5 rad/cm) Hybridization between a phonon mode and magnon modes results in magneto-elastic magnon (MEM) mode

10 Gaseous phase and magnon BEC at the bottom of spin-wave spectrum Pumping pulse

11 (GHz) (GHz) Magnon accumulation in MEM mode (under parametric pumping conditions) Shift of the magnon density peak caused by change of the bias magnetic field H 171 Oe MEM H 165 Oe MEM How magnons accumulate in the BEC and the MEM mode?

12 (GHz) Intercoupling of BEC and MEM Magnon spectrum population at different pumping powers for H 171 Oe f p 681 MHz MEM Calculated magnon spectrum Population of the low energy states at different pumping powers

13 (GHz) Intercoupling of BEC and MEM Magnon spectrum population at different pumping powers for H 171 Oe f p 681 MHz MEM Calculated magnon spectrum Population of the low energy states at different pumping powers

14 (GHz) Intercoupling of BEC and MEM Magnon spectrum population at different pumping powers for H 171 Oe f p 681 MHz BEC MEM Calculated magnon spectrum Population of the low energy states at different pumping powers

15 (GHz) Intercoupling of BEC and MEM Magnon spectrum population at different pumping powers for H 171 Oe f p 681 MHz BEC MEM Calculated magnon spectrum Population of the low energy states at different pumping powers

16 (GHz) Intercoupling of BEC and MEM Magnon spectrum population at different pumping powers for H 171 Oe f p 681 MHz Calculated magnon spectrum BEC MEM The MEM density peak appears before the magnon BEC Population of the low energy states at different pumping powers Formation of the magnon BEC is accompanied by saturation of the MEM peak

17 Accumulation of magnon-phonon hybrid particles Magnon-phonon hybridization area Ratio of magnetic E m and elastic E el energies in the magneto-elastic magnon mode Bottleneck Pure phonon states - no non-linear scattering and thus no connection with upper magnon states Accumulation of the hybridized magnon-phonon states at the bottom of the magnon spectrum

18 Accumulation of magnon-phonon hybrid particles Magnon-phonon hybridization area Barrier Magnon Ratio of highway magnetic - E m current and elastic of magnons E el energies in a phase in the space magneto-elastic to the BEC magnon state mode Bottleneck BEC Pure phonon states - no non-linear scattering and thus no connection with upper magnon states Accumulation of the hybridized magnon-phonon states at the bottom of the magnon spectrum

19 Hamiltonian approach to magnon-phonon hybridization Hamiltonian euation of motion: a i = t H a * b i = t H b * H H H 4 Magnon phonon hybridization Hamiltonian H m * p * * * aa bb ab ab magnons phonons hybridization - magnetoelastic coupling amplitude H T * * 1,34a1aa3a4 T 1,34 - Interaction amplitudes Interaction Hamiltonian of magnon scattering V. L vov and A. Pomyalov, unpublished

20 Magnon-phonon hybridization Linear canonical Bogoliubov transformation for transition to hybridized MEM modes sin cos a cos c c b sin c c c Rotation in the (a, b ) plane allows us to obtain the diagonal uadratic Hamiltonian * * H c c c c 1 m p m p for the upper and lower MEM modes Wavenumber (1 5 rad/cm)

21 1 T 1, Interaction amplitudes T of the upper and lower MEMs T 1, T 1, 34 3 Upper-Upper interaction 4 Lower-Lower interaction 4 Cross Upper-Lower MEMs interaction 4, Wavenumber dependence of interaction amplitudes T, T, T, Dimensionless distance to crossover

22 Statistical description F t T d d F 3 T - Kinetic Euation for the lower MEM mode occupation numbers flux of towards the hybridization region - transition rate - + in the hybridization region,

23 Statistical description, Dimensionless distance to crossover Solution of the kinetic euation (sin ) 1 1 (cos ) (cos ) p p dp a 3 d F t d T F T BEC a BEC

24 Statistical description F t T d d, F 3 T Increase in the magnon BEC population decreases bottleneck effect and explains the saturation phenomenon a BEC BEC BEC Dimensionless distance to crossover

25 Space position (µm) Transport measurements of accumulated hybridized bosons Accumulation of hybridized bosons with non-zero group velocity can be used for spin transport 4 3 vgr Experimental time-space diagram for MEM mode 11 m/s Position of the maximum of a travelling packet of hybridized bosons v m/s gr pumping microstrip 1 ns long pumping pulse Time (ns)

26 Space position (µm) Summary Hybridization between magnons and phonons creates a spectral bottleneck in the system The effects evidence the bottleneck accumulation of the hybridized magnon-phonon bosons at the bottom of the magnon spectrum Developed minimal model describes observed phenomenon of the hybrid bosons accumulation Accumulation of hybridized bosons with non-zero group velocity can be used for spin transport Position of the maximum of a travelling packet of hybridized bosons vgr m/s ns long pumping pulse Time (ns)