Ground state and excitations in BEC of magnons M nster V.E. Demidov, - PowerPoint PPT Presentation

Ground state and excitations in BEC of magnons M ünster V.E. Demidov, O. Dzyapko, P. Nowik-Boltyk, S.O. Demokritov G.A. Melkov Kiev, Ukraine A.N. Slavin USA V L Safonov V.L. Safonov USA USA B. Malomed Israel N.G. Berloff, H. Salman Cambridge Group of N on L inear M agnetic D ynamics

Ground state and excitations in BEC of magnons M ünster V.E. Demidov, O. Dzyapko, P. Nowik-Boltyk, S.O. Demokritov G.A. Melkov Kiev, Ukraine Spin waves  magnons A.N. Slavin USA V L Safonov V.L. Safonov USA USA B. Malomed Israel N.G. Berloff, H. Salman Cambridge Magnons??? Ground state of a FM: Ground state of a FM: S z =Ns z Excited states: S z =Ns z -1, S z Ns z 1, S z Ns z 2, S z Ns z 3, … S z =Ns z -2, S z =Ns z -3, … 1 magnon, 2 magnons, 3 magnons,…  magnons are Bose-particles Courtesy: Prof. C. Patton Carry transverse magnetization y g

Bose-Einstein-Condensation of atoms classical gas classical gas quantum gas BEC quantum gas BEC Condition of BEC transition: C diti f BEC t iti Th Thermodynamics of BEC: d i f BEC 1 2  23   3.31 3.31 n kT kT N N         E E c m exp 1     kT m 23  N kT    ( ( , ) ) 2 2 T N T N E E c c 3.31  min c c

Magnons in ferromagnetic films YIG (yttrium-iron-garnet) Transparent ferromagnet Films 5-10  m thick No domains No domains 5 5 H= 700 Oe k||H 4 y (GHz) 3 f i f min Frequency 2 cm  5 1   0.35 10 k Three contributions to the Three contributions to the m m 1 magnon energy: Zeeman, exchange, and dipole- dipole p 0 0 4 5 5 5.0x10 1.0x10 1.5x10 Wavevector (1/cm) Scattering amplitude depends on wavevector

Magnons in ferromagnetic films YIG (yttrium-iron-garnet) YIG ( tt ium i n n t) Transparent ferromagnet 5 Films 5-10  m thick H= 700 Oe No domains No domains k k H H 4 Hz) uency (GH f 0 Frequ 3 3  m m    2 k||H E h GHz eff e min f f       100 100 10 10 k k mK mK eV eV min B 2 1 2 3 4 5 6 10 10 10 10 10 10 2 2  Wavevector (1/cm) W t (1/ ) 23  cm  3.31 5 1   0.35 10 kT N k c m m

(Thermo)dynamic of magnons In equilibrium: In uilib ium: Magnons are quasi-particles with variable N (T) . In equilibrium with the lattice ( F = F min ).    0 E   min min Therefore: Therefore: F F    0  at any temperature N E min > 0. No BEC possible No BEC possible. In quasi-equilibrium: In quasi equilibrium: We can change N We can change N   Two important time scales: ss sp s ph p In YIG: In YIG:     10 50 ns sp  ss         ss 0 2 0.2 0 5 0.5 s s sp

Experimental setup for BEC observation Magnons created by microwaves and detected by light scattering with time and space resolution Two thresholds: #1 #1: pumping itself i it lf #2: BEC

Mechanisms of magnon thermalization Two-magnon scattering Impurity-scattering, linear effect       (independent of the magnon density (independent of the magnon density 1 2  Elastic, k -thermalization k k 1 2 Four-magnon scattering: Nonlinear effect (increase with increasing density)              1 2 3 4 Inelastic,  , k -thermalization    k k k k 1 2 3 4 M Magnon-magnon scattering keeps the number of particles constant tt i k th b f ti l t t

Magnon thermalization (step-like pumping) 8 P=0.7 W  0 t ion (a.u.) 6  =50 ns n populati 4 lation  =40 ns Magnon non popul 2  =30 ns 2 f f p 0 0 Magn  =0 ns 200 200 0 f min 2,0 150 (thermal) Time (ns) 2,5 100 F 3,0 r e f q u u f f min 50 e e T 3,5 3 5 0 0 n n i f f c y ( G p 4,0 0 H z ) 4,5 Th Thermalization happens li ti h 2,0 2 0 2 5 2,5 3 0 3,0 3 5 3,5 4 0 4,0 Frequency (GHz) „wave-like“

Thermalization time 10 P = 0.7 W 300 200 230 ns 230 ns 60 ns 60 ns 8 time (ns) f @ ulation min ation 6 6 200 200 non popula gnon popu rmalization t f @ min 100 4 Magn Mag Ther 3.2GHz × 100 100 @ 2 f =3.2 GHz @ 0 0 0 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2 3 10 10 Pumping power (W) Time (ns) Time (ns) Thermalization time depends on the pumping power/magnon density At high magnon densities is below 50 ns. Phys. Rev.Lett. ´07.

Mechanisms of magnon thermalization Two-magnon scattering Impurity-scattering, linear effect       (independent of the magnon density (independent of the magnon density 1 2  Elastic, k -thermalization k k 1 2 Under external influence magnon gas in YIG first Four-magnon scattering: Nonlinear effect thermalizes itself to a quasi-equilibrium q q (increase with increasing density)              (and then relax as a whole, 1 2 3 4 Inelastic,  , k -thermalization    if pumping is switched off) k k k k 1 2 3 4 Magnon-magnon scattering keeps the number of particles constant Magnon magnon scattering keeps the number of particles constant Thermalization happens fast if the number of magnons is high enough enough

Brillouin Light Scattering Momentum conservation law: the geometry defines the spin-wave wavevector Energy conservation law: change of the photon’s frequency 5 cy (GHz) Frequenc 4 3 2 0,0 0,5 1,0 1,5 2,0 5 cm -1 ) Wavevector (10 Wavevector (10 cm )

Brillouin Light Scattering Momentum conservation law: the geometry defines the spin-wave wavevector Energy conservation law: change of the photon’s frequency 5 cy (GHz) Frequenc 4 3 2 0,0 0,5 1,0 1,5 2,0 5 cm -1 ) Wavevector (10 Wavevector (10 cm )

BLS spectroscopy equency 2 f P MW Photon Fre Magnons agnon 5 GHz) f P Ma Population n requency ( 4 Fr f 0 4 4 6x10 3x10 4 0 -1 k k , cm 4 -3x10 -6x10 6x10 BLS-intensity ~ n × DOS 3 f min 2 0 0 0.0 0.5 0 5 1 0 1.0 1 5 1.5 2 0 2.0 Wavevector (10 5 cm -1 )

Pumped magnons (step-like pumping)  /h   200 ns 1.70 GHz 0,6 , 1.96 GHz 1.96 GHz 400 ns 400 ns 2.04 GHz 600 ns  0 t 2.07 GHz 800 ns 2 08 GHz 2.08 GHz 1000 ns 1000 P = 4 W nts/ms 0,4 Theory: y Time development of Time development of sity, coun  /h  2.10 GHz magnon distribution     n  Known DOS: fit  max value max. value Intens 0 2 0,2 with Bose statistics with Bose-statistics with    non-zero max 0,0 1 0 1,0 1 5 1,5 2 0 2,0 2 5 2,5 3 0 3,0 3 5 3,5 4 0 4,0 Frequency, GHz

Time dependence of the chemical potential E min P = 5.9 W  0 t ntial P = 4.5 W P = 2.5 W P = 4 W ical Pote Stationary state Stati nar state Chem due to spin-lattice relaxation 0 200 400 600 800 1000 t, ns For high pumping power one can reach the critical density of magnons density of magnons

Pumped magnons (step-like pumping)  /h   100 ns n/d 2.05 GHz 200 ns 200 ns 2.10 GHz 300 ns  0 t 2 max. value 400 ns ms counts/m 500 500 ns P = 5.9 W Time development of Time development of ntensity, magnon distribution     1 n  Known DOS: fit  30 30 In with Bose-statistics. Bose statistics At 300 ns critical density:      0 max max 1,0 1 0 1 5 1,5 2 0 2,0 2 5 2,5 3 0 3,0 3,5 3 5 4 0 4,0 Frequency, GHz

Experiments with ultimate resolution  =500 ns 2,1          n f n f The addition to the critical The addition to the critical C density is of  – type (width is <1.5 mK, 1,4 , i.e. <10 -5 kT). HWHM = 30 MHz A condensate is created! d d! 0,7 Condensate: a lot of spins precess in phase. 0 0 0,0 2 3 4 Nature 443 430 ’06

The condensate is doubly degenerate  i t          C    ψ , , ψ , , ik z ψ , , ik z  y z t y z t e y z t e e 0 0   y c n n e u q e r n F o o n g a n M o i t t a l u p o P BEC-condensates k z k y

Detection of the coherent magnetic precession Condensate: a lot of spins precess in phase . The precessing spins should radiate at f min p g p min Pump magnons. Pump magnons. Analyze the ringing of the sample using MW spectrum-analyzer.

Spectrum of magnetic precession 1,0 BLS The measured width 0,8 .u. corresponds to wer, a. 0.3 mK, i.e. 2  10 -6 kT 0,6 tral pow Very high temporal coherence of the 0,4 HWHM condensate condensate Spect =5 MHz =5 MHz 0,2 0,0 -100 -80 -60 -40 -20 0 20 40 60 80 100 Appl Phys Rev Lett 92 162510 08‘ Appl. Phys. Rev. Lett. 92 162510 08 Frequency shift MHz Frequency shift, MHz