Spin Transport using Magneto-elastic Bosons Vitaliy I. Vasyuchka

Transcription

1 Spin Transport using Magneto-elastic Bosons Vitaliy I. Vasyuchka Fachbereich Physik and Landesforschungszentrum OPTIMAS Technische Universität Kaiserslautern Germany

2 Collaborators Team University of Kaiserslautern (Germany) Dmytro Bozhko Andrii Chumak Oleksandr Serha Burkard Hillebrands Taras Shevchenko ational University of Kyiv (Ukraine) Weizmann Institute of Science (Israel) Gennadii Melkov Victor L'vov Anna Pomyalov Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

3 Yttrium Iron Garnet Y 3 Fe 5 O 1 (YIG) Yttrium-Iron Garnet is a marvel of nature. Its role in the physics of magnets is analogous to that of germanium in semiconductor physics, water in hydrodynamics, and uartz in crystal acoustics V. Cherepanov, I. Kolokolov, and V. L vov, The saga of YIG: spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet, Phys. Rep. 9, (1993). Unit cell 48 oxygen atoms 8 octahedral iron atoms (spin 5/ up) 1 tetrahedral iron atoms (spin 5/ down) 1 dodecahedral yttrium atoms Magnetic moment of a unit cell is 10 Bohr magnetons at zero temperature Bulk YIG crystal y z x Wiki Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

4 Yttrium Iron Garnet Y 3 Fe 5 O 1 (YIG) Yttrium-Iron Garnet is a marvel of nature. Its role in the physics of magnets is analogous to that of germanium in semiconductor physics, water in hydrodynamics, and uartz in crystal acoustics V. Cherepanov, I. Kolokolov, and V. L vov, The saga of YIG: spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet, Phys. Rep. 9, (1993). Unit cell 48 oxygen atoms 8 octahedral iron atoms (spin 5/ up) 1 tetrahedral iron atoms (spin 5/ down) 1 dodecahedral yttrium atoms Magnetic moment of a unit cell is 10 Bohr magnetons at zero temperature y z x Wiki Bulk YIG crystal Room temperature ferrimagnet (T С = 560 K) Longest known magnon lifetime (up to 700 ns) Very low phonon damping Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

5 Yttrium Iron Garnet Y 3 Fe 5 O 1 (YIG) Yttrium-Iron Garnet is a marvel of nature. Its role in the physics of magnets is analogous to that of germanium in semiconductor physics, water in hydrodynamics, and uartz in crystal acoustics V. Cherepanov, I. Kolokolov, and V. L vov, The saga of YIG: spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet, Phys. Rep. 9, (1993). Unit cell 48 oxygen atoms 8 octahedral iron atoms (spin 5/ up) 1 tetrahedral iron atoms (spin 5/ down) 1 dodecahedral yttrium atoms Magnetic moment of a unit cell is 10 Bohr magnetons at zero temperature y z x Scientific Research Company Carat, Lviv, Ukraine Single-crystal YIG film Room temperature ferrimagnet (T С = 560 K) Longest known magnon lifetime (up to 700 ns) Very low phonon damping Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

6 Spin waves Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

7 Magnon gas Magnons as uanta of spin waves Energy Momentum Mass Spin s 1 Four- and three-magnon scattering 10 cm -3 magnons at 300 K Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

8 Magnon spectrum of in-plane magnetized YIG film Landau-Lifshitz euation: dipolar interaction exchange interaction Thickness modes having a non-uniform harmonic distribution of dynamic magnetization along the film thickness 6 µm thick YIG film Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

9 Magnon distribution Magnons are bosons (s=1) and similar to other uasi-particles are described in thermal euilibrium by Bose-Einstein distribution with zero chemical potential µ=0 Bose-Einstein distribution µ: chemical potential Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

10 Control of magnon gas density by parametric pumping f p Parametric pumping by electromagnetic wave at microwave freuency µ=0 f p / Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

11 Control of magnon gas density by parametric pumping Energy and momentum conservation laws f p Parametric pumping by electromagnetic wave at microwave freuency 10 0 cm -3 pumped magnons µ=0 Bose-Einstein distribution f p / Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

12 Control of magnon gas density by parametric pumping Energy and momentum conservation laws f p Parametric pumping by electromagnetic wave at microwave freuency 10 0 cm -3 pumped magnons E min >µ>0 Bose-Einstein distribution f p / Magnon thermalization due to 4-particle scattering: incoherent magnon gas Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

13 Bose-Einstein condensation of magnons Energy and momentum conservation laws f p Parametric pumping by electromagnetic wave at microwave freuency 10 0 cm -3 pumped magnons µ=e min Bose-Einstein distribution f p / Magnon thermalization due to 4-particle scattering: incoherent magnon gas S.O. Demokritov et al., ature 443, 430 (006) Bose-Einstein magnon condensate Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

14 Brillouin light scattering spectroscopy Inelastic scattering of photons on magnons: Wavenumber uncertainty! Freuency resolution Stokes Magnon freuency Elastically scattered light anti-stokes Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

15 Wavenumber resolution Wavenumber resolution magnon sin Laser Freuency resolution Max wavenumber Wavenumber resolution rad/cm rad/cm D.A. Bozhko, PhD thesis (017) Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

16 Bose-Einstein magnon condensate arrow pumping area 50 µm pumping pulse BEC A.A. Serga et al., at. Commun. 5, 345 (014) Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

17 Condensation scenarios and phonons Wide pumping area 500 µm pumping pulse Pumping power 40 W??? BEC D.A. Bozhko et al., Phys. Rev. Lett. 118, 3701 (017) Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

18 Condensation scenarios and phonons Wide pumping area 500 µm pumping pulse Pumping power 40 W MEM??? BEC Why and how uasi-particles accumulate in the magneto-elastic mode (MEM)? Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

19 (GHz) Intercoupling of BEC and MEM in a parametrically populated magnon gas Magnon spectrum population at different pumping powers H 1710 Oe f p MHz Calculated magnon spectrum MEM MEM peak appears below the threshold of magnon BEC formation Population of the low energy states at different pumping powers Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

20 (GHz) Intercoupling of BEC and MEM in a parametrically populated magnon gas Magnon spectrum population at different pumping powers H 1710 Oe f p MHz Calculated magnon spectrum MEM MEM peak appears below the threshold of magnon BEC formation Population of the low energy states at different pumping powers Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

21 (GHz) Intercoupling of BEC and MEM in a parametrically populated magnon gas Magnon spectrum population at different pumping powers H 1710 Oe f p MHz Calculated magnon spectrum BEC MEM MEM peak appears below the threshold of magnon BEC formation Population of the low energy states at different pumping powers Formation of the magnon BEC is accompanied by saturation of the MEM peak Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

22 (GHz) Intercoupling of BEC and MEM in a parametrically populated magnon gas Magnon spectrum population at different pumping powers H 1710 Oe f p MHz Calculated magnon spectrum BEC MEM MEM peak appears below the threshold of magnon BEC formation Population of the low energy states at different pumping powers Formation of the magnon BEC is accompanied by saturation of the MEM peak Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

23 (GHz) Intercoupling of BEC and MEM in a parametrically populated magnon gas Magnon spectrum population at different pumping powers H 1710 Oe f p MHz Calculated magnon spectrum BEC MEM MEM peak appears below the threshold of magnon BEC formation Population of the low energy states at different pumping powers Formation of the magnon BEC is accompanied by saturation of the MEM peak Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

24 Magnon bottleneck and 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 magneto-elastic bosons at the bottom of the magnon spectrum Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

25 Magnon bottleneck and 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 magneto-elastic bosons at the bottom of the magnon spectrum Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

26 Hamiltonian approach to magnon-phonon hybridization Hamiltonian euation of motion: a i = t H a * b i = t H b * H H H H 4 Magnon phonon hybridization Hamiltonian m * p * * * aa bb ab ab hybridization, magnons phonons - coupling amplitude m p - magnon dispersion law - phonon dispersion law H T * * 1,34a1aa3a4 T 1,34 - interaction amplitudes Interaction Hamiltonian of magnon scattering Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

27 Magnon-phonon hybridization Transition to hybridized MEM modes using linear canonical Bogolyubov transformation (rotation by the angle in the (a, b ) plane) c sin cos a cos c c b sin c c 1 cos 1, 1 p m, Diagonal uadratic Hamiltonian for the upper and lower MEM modes * * H cc cc 1 m p m p Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

28 Interaction amplitudes T 1,34 of the upper and lower MEMs 1 T 1, 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 Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

29 Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017 Statistical description, 3 T F T - flux of towards the hybridization region - - transition rate in the hybridization region - + d F t d - balance euation for the lower MEM mode occupation numbers - BEC 5 5, The dimensionless lower-mem and upper-mem densities:

30 Statistical description F t T d d F 3 T - balance euation for the lower MEM mode occupation numbers flux of towards the hybridization region - transition rate - + in the hybridization region, Taking into account the euations for T d d cos 3a cos sin BEC 1 p m cos 1, 1 5 BEC,, a Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

31 Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017 Bottleneck accumulation Dimensionless distance to crossover Solution of the kinetic euation (sin ) 1 1 (cos ) (cos ) p p dp a BEC BEC a 3 T F T d F t d, relative population of the BEC state 83

32 Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017 Bottleneck accumulation Increase in the magnon BEC population decreases bottleneck effect and explains the MEM saturation phenomenon BEC BEC 3 T F T d F t d BEC a, Dimensionless distance to crossover 83 D.A. Bozhko et al., Phys. Rev. Lett. 118, 3701 (017)

33 Transport measurements Group velocities of magnon-phonon bosons in hybridization area Experimental time-space diagram for BEC and MEM 1 Position of the maximum of a travelling packet of hybridized bosons v gr1 00 m/s 1 BEC Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

34 Transport measurements Group velocities of magnon-phonon bosons in hybridization area Experimental time-space diagram for BEC and MEM 1 v gr 1100 m/s Position of the maximum of a travelling packet of hybridized bosons v gr1 00 m/s 1 BEC Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017

35 Space position (µm) Summary Observed effects evidence the bottleneck accumulation of hybridized magneto-elastic bosons at the bottom of the magnon spectrum Developed minimal model ualitatively describes the observed phenomena Transport measurements give an information about spectral positions of accumulated uasi-particles Accumulated hybridized bosons with non-zero group velocity can be used for spin transport Bottleneck accumulation can occur in any multicomponent gas-mixture of interacting uasiparticles with different scattering amplitudes Position of the maximum of a travelling packet of hybridized bosons v 00 m/s 00 ns long pumping pulse Time (ns) gr Vitaliy Vasyuchka SPICE Young Research Leaders Workshop Mainz, August 017