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

Ground state and excitations in BEC of magnons

V.E. Demidov, O. Dzyapko, P. Nowik-Boltyk, S.O. Demokritov

Münster

G.A. Melkov Kiev, Ukraine A.N. Slavin USA V L Safonov USA V.L. Safonov USA

• B. Malomed Israel

N.G. Berloff, H. Salman Cambridge

Group of NonLinear Magnetic Dynamics

Ground state and excitations in BEC of magnons

V.E. Demidov, O. Dzyapko, P. Nowik-Boltyk, S.O. Demokritov

Münster Spin waves  magnons

G.A. Melkov Kiev, Ukraine A.N. Slavin USA V L Safonov USA V.L. Safonov USA

• B. Malomed Israel

N.G. Berloff, H. Salman Cambridge

Magnons??? Ground state of a FM: Ground state of a FM: Sz=Nsz Excited states: Sz=Nsz-1, Sz=Nsz-2, Sz=Nsz-3, … Sz Nsz 1, Sz Nsz 2, Sz Nsz 3, … 1 magnon, 2 magnons, 3 magnons,… magnons are Bose-particles Carry transverse magnetization

Courtesy: Prof. C. Patton

y g

classical gas quantum gas BEC

Bose-Einstein-Condensation of atoms

classical gas quantum gas BEC C diti f BEC t iti Th d i f BEC Condition of BEC transition: Thermodynamics of BEC:

1 n E    

2 23

3.31 kT N  

exp 1 E kT         

( ) T N E 

3.31

c

kT N m

23 2 c

m N kT 

min

( , )

c c

T N E  

2

3.31

c



Magnons in ferromagnetic films

YIG (yttrium-iron-garnet)

Transparent ferromagnet Films 5-10 m thick No domains

5

No domains

4 5

k||H

H= 700 Oe

3

f i

y (GHz) 5 1

0.35 10

m

k cm  

2

fmin

Frequency

Three contributions to the

m 1

Three contributions to the magnon energy: Zeeman, exchange, and dipole- dipole

5.0x10

4

1.0x10

5

1.5x10

5

Wavevector (1/cm)

p Scattering amplitude depends on wavevector

Magnons in ferromagnetic films

YIG ( tt ium i n n t) YIG (yttrium-iron-garnet)

Transparent ferromagnet Films 5-10 m thick No domains

5

k H

H= 700 Oe

No domains

4 Hz)

k H

3

f

uency (GH min

2 100 10 E h GHz k mK eV     

eff e

m m 

3

f

k||H

Frequ

100 10

B

k mK eV    

10

1

10

2

10

3

10

4

10

5

10

6

2

f

W t (1/ )

min

2

5 1

0.35 10

m

k cm  

Wavevector (1/cm)

2 23

3.31

c

kT N m  

(Thermo)dynamic of magnons

In uilib ium:

 

min

E 

In equilibrium:

F 

Magnons are quasi-particles with variable N (T). In equilibrium with the lattice (F=Fmin). Therefore:

min

at any temperature

F N     

Therefore: Emin > 0. No BEC possible

In quasi-equilibrium:

We can change N No BEC possible.

In quasi equilibrium:

Two important time scales: In YIG:

ph s

ss



sp



We can change N

ss



sp



In YIG:

10 50 0 2 0 5

ss

ns s       

p

0.2 0.5

sp

s    

Experimental setup for BEC observation

Magnons created by microwaves and detected by light scattering with time and space resolution

Two thresholds: #1 i it lf #1: pumping itself #2: BEC

Mechanisms of magnon thermalization

Two-magnon scattering

Impurity-scattering, linear effect (independent of the magnon density

  

(independent of the magnon density Elastic, k-thermalization

1 2 1 2

k k    

Four-magnon scattering: Nonlinear effect

(increase with increasing density)

     

Inelastic, ,k-thermalization

1 2 3 4 1 2 3 4

k k k k          

M tt i k th b f ti l t t Magnon-magnon scattering keeps the number of particles constant

Magnon thermalization (step-like pumping)

8

P=0.7 W

=50 ns

6

ion (a.u.)

t 

lation

=40 ns

4

n populati =30 ns

non popul

2 200 2

Magnon

f

=0 ns

(thermal) Magn

2,0 2,5 3,0 3 5 50 100 150 200

f f

Time (ns) F r e q u e n

fmin

fp f

i

Th li ti h

2 0 2 5 3 0 3 5 4 0

3,5 4,0 4,5

f

T u e n c y ( G H z )

p

fmin

Thermalization happens „wave-like“

2,0 2,5 3,0 3,5 4,0

Frequency (GHz)

Thermalization time

10

P = 0.7 W 60 ns 230 ns

300 200 6 8

60 ns 230 ns

min

f

ation @ 200 ulation

time (ns)

4 6 non popula 200

min

f

gnon popu @ 100

rmalization t

2 Magn

f =3.2 GHz

@ 100 Mag

3.2GHz × 100

@

Ther

10

2

10

3

Time (ns) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Pumping power (W)

Thermalization time depends on the pumping power/magnon density At high magnon densities is below 50 ns.

Time (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 Elastic, k-thermalization

1 2 1 2

k k    

Four-magnon scattering: Nonlinear effect

(increase with increasing density)

     

Under external influence magnon gas in YIG first thermalizes itself to a quasi-equilibrium

Inelastic, ,k-thermalization

1 2 3 4 1 2 3 4

k k k k          

q q (and then relax as a whole, if pumping is switched off) 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)

4

Frequenc

3 0,0 0,5 1,0 1,5 2,0 2

Wavevector (10

5 cm

• 1)

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)

4

Frequenc

3 0,0 0,5 1,0 1,5 2,0 2

Wavevector (10

5 cm

• 1)

Wavevector (10 cm )

BLS spectroscopy

equency

2fP MW Photon

5

GHz) Magnons fP

agnon

n Fre

4

requency (

Ma

Population

Fr

f0

• 6x10

4 -3x10 4 0

3x10

4 6x10 4

k k , cm

• 1

3

BLS-intensity ~ n×DOS

6x10

0 0 0 5 1 0 1 5 2 0 2

fmin

0.0 0.5 1.0 1.5 2.0

Wavevector (105 cm-1)

Pumped magnons (step-like pumping)

0,6 1.70 GHz 1.96 GHz

 200 ns

400 ns

/h

t 

, 1.96 GHz 2.04 GHz 2.07 GHz 2 08 GHz 400 ns 600 ns 800 ns 1000

P = 4 W Time development of

0,4 Theory: 2.08 GHz

nts/ms

1000 ns

Time development of magnon distribution Known DOS: fit

 

n 

0 2 y

/h2.10 GHz

max value

sity, coun

with

 



Bose statistics with

0,2

• max. value

Intens

Bose-statistics with non-zero

max

  

1 0 1 5 2 0 2 5 3 0 3 5 4 0 0,0 1,0 1,5 2,0 2,5 3,0 3,5 4,0

Frequency, GHz

Time dependence of the chemical potential

Emin

ntial P = 4 W P = 2.5 W P = 4.5 W P = 5.9 W

t 

Stati nar state

ical Pote

Stationary state due to spin-lattice relaxation

Chem 200 400 600 800 1000

For high pumping power one can reach the critical density of magnons

t, ns

density of magnons

Pumped magnons (step-like pumping)

n/d 2.05 GHz

 100 ns

200 ns

/h

2 2.10 GHz

ms

200 ns 300 ns 400 ns 500

t 

• max. value

counts/m

500 ns

P = 5.9 W Time development of

1

ntensity,

30

Time development of magnon distribution Known DOS: fit

 

n 

In

30

with

 



Bose statistics

1 0 1 5 2 0 2 5 3 0 3 5 4 0

Bose-statistics. At 300 ns critical density:

max

  

1,0 1,5 2,0 2,5 3,0 3,5 4,0

Frequency, GHz

max

 

Experiments with ultimate resolution

2,1

   

C

n f n f 

The addition to the critical

=500 ns

1,4

   

The addition to the critical density is of – type (width is <1.5 mK, , i.e. <10-5kT). d d!

HWHM = 30 MHz

0,7 A condensate is created! 0 0 Condensate: a lot of spins precess in phase. 2 3 4 0,0

Nature 443 430 ’06

The condensate is doubly degenerate

     

 

ψ , , ψ , , ψ , ,

C

i t ik z ik z

y z t y z t e y z t e e

    

 



n c y

• n

F r e q u e n

M a g n

• t

i

• n

P

• p

u l a t

BEC-condensates

kz ky

Detection of the coherent magnetic precession

The precessing spins should radiate at fmin Condensate: a lot of spins precess in phase. p g p

min

Pump magnons. Pump magnons. Analyze the ringing of the sample using MW spectrum-analyzer.

Spectrum of magnetic precession

1,0 0,8

.u.

BLS

The measured width

0,6

wer, a.

corresponds to 0.3 mK, i.e. 210-6kT

0,4

tral pow HWHM =5 MHz

Very high temporal coherence of the condensate

0,2

Spect =5 MHz

condensate

• 100 -80 -60 -40 -20

20 40 60 80 100 0,0

Frequency shift MHz

Appl Phys Rev Lett 92 162510 08‘

Frequency shift, MHz

• Appl. Phys. Rev. Lett. 92 162510 08

Critical index

Sweeping pumping power just above the BEC threshold Kalafati & Safonov predicted (1993)

2

10

• 6

Fit: Prad Pp-Pcr)2 Prad (Pp-Pcr)2

for BEC of magnons

10 er (W)

g due to double degeneracy of the spectrum and

10

• 7

ated powe

spectrum and phase-locking between to components of the

10

• 8

Radi

components of the condensate

0.1 1 10

• 9

P -P (W)

Pp Pcr (W)

Study with k-resolution

Instead integrating the signal over (kll, k) g (

ll, )

k-resolved measurements are performed performed. Goal: investigation of magnon kinetics magnon kinetics during the formation

• f the condensate and

spatial coherence properties of the condensate condensate.

Magnon kinetics in the phase space

20 700ns   

BLS

20 700ns 

t 0 

k

H

kll

Magnons are gathered at the point in the phase di t th i i f

• Phys. Rev. Lett. 101 257201 ´08.

space corresponding to the minimum frequency.

Spatial coherence of the condensate

The width of the magnon cloud in the k-space first d d th decreases and then saturates. The corresponding p g coherence length can be determined:

 = /k

Spatial coherence of the condensate

The width of the magnon cloud in the k-space first d d th decreases and then saturates. The corresponding p g coherence length can be determined:

 = /k || = 6 m  > 10 m

h h l h The coherence length is anisotropic, reflecting the anisotropy of the magnon anisotropy of the magnon spectrum.

Phase-locking between the k and -k components

CW measurements Two components of the condensate are phase locked The pase-locking is b bl d t th probably due to the defect-mediated coupling In addition to regular periodic structure stationary vortices stationary vortices are observed

Correlation of the k and -k components

CW measurements The amplitude of the modulation grows faster than the total density. The pase locking is The pase-locking is due a nonlinear interaction between the components of the components of the condensate

Vortices in the condensate

2 2

     

     

 

ψ , , ψ , , ψ , ,

C

i t ik z ik z

y z t y z t e y z t e e

    

 



 

2 2 ||

2 2

yy zz t C s

i U iP J m m

     

                      



  

   

2 eff t s s

P i r

 

          

   

eff t s s  

   

Scientific Reports, in press

Spatio-temporal evolution of the condensate

Experiment

     

, , ,

ik z ik z

z t z t e z t e

 

    

Theory

The nonlinearly coupled equations, written for amplitudes of the right- ( ) and left-traveling

k 

( ) and left traveling ( ) waves, combininig basic features of the Gross-Pitaevskii and complex Ginzburg Landau models

k k  

complex Ginzburg-Landau models.

B.Malomed et al., Phys. Rev. B 81 024418 ´10 y

Sound in the condensate

Condensate is created by the microwave pumping via dielectric microwave pumping via dielectric resonator It is disturbed by radio-field using a narrow wire The wire excites waves propagating in narrow wire the condensate

Sound in the condensate



 

Theory based on the GPE and the known spectrum of The wire excites waves propagating in

tan

ph

v k    

magnons. the condensate

Sound in the condensate



 

Theory based on the GPE and the known spectrum of The wire excites waves propagating in

tan

ph

v k    

magnons. the condensate

Summary

• Doubly degenerated Bose-Einstein condensate of

magnons is created at room temperature

• Coherence properties of the condensate as well its

sp ti t mp l d n mics studi d spatio-temporal dynamics are studied

http://www.uni-muenster.de/Physik/AP/Demokritov/