1. EMMI Workshop, Münster 19.02.2009 V.E. Demidov, O. Dzyapko, G. Schmitz, and S.O. Demokritov Münster, Germany G.A. Melkov, Ukraine A.N. Slavin, USA V.L. Safonov, USA Group of NonLinear Magnetic Dynamics Bose-Einstein condensation of quasi-equilibrium magnons at RT http://www.uni-muenster.de/Physik/AP/Demokritov/ Magnons??? Ground state of a FM: S z =Ns z Excited states: S z =Ns z -1, S z =Ns z -2, S z =Ns z -3, … 1 magnon, 2 magnons, 3 magnons,… => magnons are Bose-particles H

2. EMMI Workshop, Münster 19.02.2009 classical gas quantum gas BEC Condition of BEC transition: Thermodynamics of BEC: Bose-Einstein-Condensation of atoms

3. EMMI Workshop, Münster 19.02.2009 Magnons in ferromagnetic films YIG (yttrium-iron-garnet) Transparent ferromagnet Films 5  m thick No domains H= 700 Oe

4. EMMI Workshop, Münster 19.02.2009 Magnons in ferromagnetic films YIG (yttrium-iron-garnet) Transparent ferromagnet Films 5  m thick No domains H= 700 Oe Three contributions to the magnon energy: Zeeman, exchange, and dipole- dipole

5. EMMI Workshop, Münster 19.02.2009 (Thermo)dynamic of magnons In equilibrium: Magnons are quasi-particles with variable N.

6. EMMI Workshop, Münster 19.02.2009 (Thermo)dynamic of magnons In equilibrium: Magnons are quasi-particles with variable N. In equilibrium E min > 0. No BEC possible.

7. EMMI Workshop, Münster 19.02.2009 (Thermo)dynamic of magnons In quasi-equilibrium: Two important time scales: In YIG: Under external influence magnon gas first thermalizes itself to a quasi-equilibrium with and then relax as a whole. at any temperature In equilibrium: We can change N Magnons are quasi-particles with variable N. In equilibrium E min > 0. No BEC possible.

8. EMMI Workshop, Münster 19.02.2009 Strategy to reach BEC of magnons 1. Inject ultracold magnons (parametric pumping) 2. Wait and see what happens with magnon distribution Magnons created by microwaves and detected by light scattering with time (and space) resolution H

9. EMMI Workshop, Münster 19.02.2009 BLS spectroscopy A well defined wavevector Optic Photon Photon Magnon Intensity is proportional to the population number

10. EMMI Workshop, Münster 19.02.2009 BLS spectroscopy A well defined wavevector Optic Photon Photon Magnon Intensity is proportional to the population number

11. EMMI Workshop, Münster 19.02.2009 Integrated BLS spectrum f min f0f0 Integration over wavevectors BLS-intensity ~ n × DOS

12. EMMI Workshop, Münster 19.02.2009 Experimental setup for time-resolved measurements Stroboscopic time-of-flight technique

13. EMMI Workshop, Münster 19.02.2009 Mechanisms of magnon thermalization Two-magnon scattering Impurity-scattering, linear effect (independent of the magnon density) Elastic, k-thermalization Four-magnon scattering: Nonlinear effect (increase with increasing density) Inelastic, , k-thermalization Thermalization keeps the number of particles constant Happens if the number of pumped magnon is high enough

14. EMMI Workshop, Münster 19.02.2009 Magnon kinetics and formation of condensate Magnons are gathered at the point in the phase space corresponding to the minimum frequency. The distribution is narrowed with time. k ll kk BLS t 0 

15. EMMI Workshop, Münster 19.02.2009 Pumped magnons (step-like pumping) P = 4 W Time development of magnon distribution Known DOS: fit with Bose-statistics with non-zero

16. EMMI Workshop, Münster 19.02.2009 Time dependence of the chemical potential For high pumping power one can reach the critical density of magnons J. Appl. Phys. ´07. Stationary state due to spin-lattice relaxation

17. EMMI Workshop, Münster 19.02.2009 Pumped magnons (step-like pumping) max. value P = 5.9 W Time development of magnon distribution Known DOS: fit with Bose-statistics. At 300 ns critical density:

18. EMMI Workshop, Münster 19.02.2009 Pumped magnons (step-like pumping) P = 5.9 W Time development of magnon distribution Known DOS: fit with max. value Bose-statistics. At 300 ns critical density:

19. EMMI Workshop, Münster 19.02.2009 Experiments with ultimate resolution The addition to the critical density is of  – type (width is <1.5 mK, i.e. <10 -5 kT). A condensate is created! Condensate: a lot of spins precess in phase. “normal” measurements measurements with ultimative frequency resolution HWHM = 30 MHz Nature ’06  =500 ns

20. EMMI Workshop, Münster 19.02.2009 Detection of the coherent magnetic precession Appl. Phys. Rev. Lett., 08 The radiation of the precessing spins is detected Pump magnons. Analyze the ringing of the sample using MW spectrum-analyzer.

21. EMMI Workshop, Münster 19.02.2009 Spectrum of magnetic precession BLS ultimate resolution Appl. Phys. Rev. Lett., 08 The measured width corresponds to 0.3 mK, i.e. 2  10 -6 kT

22. EMMI Workshop, Münster 19.02.2009 Radiation due to condensate Frequency of the radiation depends on the applied field, it is independent of the pumping freqeuncy

23. EMMI Workshop, Münster 19.02.2009 Critical index Kalafati & Safonov predicted (1993) P rad  (P p -P cr ) 2 for BEC of magnons, Provided two condensates (at k min and at – k min ) are coherent Fit: P rad  P p -P cr ) 2 Sweeping pumping power just above the BEC threshold

24. EMMI Workshop, Münster 19.02.2009 Noise pumping Up to now coherent pumping (albeit with different frequency) Can it be the reason for the condensation? Check: incoherent pumping with variable bandwidth (BW). Threshold of pumping grows proportionally to BW of the pumping field (agreement with the theory) Threshold of BEC is almost independent of BW

25. EMMI Workshop, Münster 19.02.2009 The birth and death of the condensate BLS t 0  Magnons are pumped just for 30 ns. Delay (ns) Lifetime is determined by interaction with the lattice: fpfp f min

26. EMMI Workshop, Münster 19.02.2009 Thermalization at different densities P = 2.5 W P = 3 W P = 5 W “Lifetime” depends on the magnon density

27. EMMI Workshop, Münster 19.02.2009 EXPERIMENT: The measured decay rate increases with pumping power (total magnon density) Scattering from the bottom of the spectrum Phys. Rev. Lett. ´08.

28. EMMI Workshop, Münster 19.02.2009 Light scattering from magnons Number of magnons decays The decay rate is determined by the livetime: BLS-intensity from incoherent magnons BLS-intensity from coherent magnons For incoherent magnons we are sensitive to For coherent magnons we are sensitive to

29. EMMI Workshop, Münster 19.02.2009 Doubling of the decay rate

30. EMMI Workshop, Münster 19.02.2009 Scattering intensity Maximum scattering intensity Experimental confirmation of the temporal coherency of the condensate

31. EMMI Workshop, Münster 19.02.2009 Study with k-resolution Instead integrating the signal over (k ll, k  ) k-resolved measurements are performed. Goal: investigation of magnon kinetics during the formation of the condensate and spatial coherence properties of the condensate.

32. EMMI Workshop, Münster 19.02.2009 Magnons are gathered at the point in the phase space corresponding to the minimum frequency. The distribution is narrowed with time. k ll kk Switch on the k-resolution again

33. EMMI Workshop, Münster 19.02.2009 Spatial coherence of the condensate The width of the magnon cloud in the k-space first decreases and then saturates. The corresponding coherence length can be determined:  =  /  k  || = 6  m   > 10  m The coherence length is anisotropic, reflecting the anisotropy of the magnon spectrum.

34. EMMI Workshop, Münster 19.02.2009 Spatial coherence of the condensate The width of the magnon cloud in the k-space first decreases and then saturates. The corresponding coherence length can be determined:  =  /  k  || = 6  m   > 10  m The coherence length is anisotropic, reflecting the anisotropy of the magnon spectrum.

35. EMMI Workshop, Münster 19.02.2009 Outlook Creation of two condensate close to each other to investigate the interaction of two condensates.

36. EMMI Workshop, Münster 19.02.2009 Summary Kinetics of quasi-equilibrium magnons is studied Quasi-equilibrium gas of magnons with chemical potential  ≠ 0 is created BEC of magnons is found at room temperature Spatial coherence length reflects the anisotropy of the magnon spectrum http://www.uni-muenster.de/Physik/AP/Demokritov/