Andrey Grachev, Alexandr Sadovnikov, Evgeny Beginin

Saratov State University

BLOCH OSCILLATIONS AND TUNABLE SPIN-WAVE TRANSPORT IN ARRAYS OF MAGNETIC STRUCTURES

MOTIVATION

Kotel'nikov Institute of

Radio Engineering and

Electronics of

Russian Academy of

Sciences

arato

MS

agnonics

v

1Saratov State University, 410012, Saratov, Russia

Andrew.A.Grachev@gmail.com

532 nm

Fp2

laser

Fp1

Scan

Sample

fs fas

scattering spetra2D BLS spin-wave intensity map

YIG

Brillouin light scatteringspetroscopy(0-300 GHz)

(BLS) Demokritov S.O. et al. //

Phys. Rep. 2001. V. 348. P. 441.

EXPERIMENT

Signal generatorAnritsu

MG3692С

PNA Network Analyzer

AgilentE8352C

YIG

H = 0-1.8 T0

Microwave spetroscopy(0-67 GHz)

џ The planar microstructures based on thin ferrimagnetic films of yttrium iron garnet (YIG) opens a promising alternative to signal processing by spin waves in beyond-CMOS computing technology, based on magnonic networks with low-level energy consumption.

џ We report here on dipolar spin-wave coupling in the lateral topology of adjacent YIG stripes. We propose control of spin-wave coupling characteristics by variation of the static magnetization angle. The functionality of the proposed magnonic coupler was verified with micromagnetic simulation of spin-wave propagation along adjacent stripes. By the means of micromagnetic numerical simulation, the transmission spectra of SW were calculated. It was shown that lateral magnonic stripes can be used as a functional unit in planar magnonic networks as a directional coupler, spin-wave multiplexer, and microwave powerdivider. Using Brillouin light scattering spectroscopy we experimentally demonstrated spin-wave transport along bilateral magnonic stripes.

GGG

BLS STUDY OF SPIN-WAVE PROPAGATION

3MUMAX

SIMULATION

џ We propose control of spin-wave coupling characteristics by variation of the static magnetization angle. The functionality of the proposed magnonic coupler was verified with micromagnetic simulation of spin-wave propagation along adjacent stripes.

џ Using Brillouin light scattering spectroscopy we experimentally demonstrated spin-wave transport along bilateral magnonic stripes.

CONCLUSION

200 mm

x

probing laser light

Spin Wave

x

z

yj

Hmssw

GGG

YIGYIG

YIG

d

w

t

Hbvmsw

Pin

Pout1Pout2 Pout3

MULTI-CHANNEL DIRECTIONAL COUPLER

4pM =1750 G (saturation magnetization) 0

t=10 mm (YIG film thickness)

d = 40 mm (distance between stripes )

y

BLS intensity (arb.units)0 1

0 1.0 2.0 3.0

y-co

ordi

nate

(m

m)

4.0

x-coordinate (mm)

(a)790395

-3950

-790

0 1.0 2.0 3.0 4.0

(b)790395

-3950

-790H0

oj = -15

0 1.0 2.0 3.0 4.0

(c)790395

-3950

-790H0

oj = 15

0395790

-790-395

S1

S2

S3

(a)

Intensity (arb.units)0 1

0 1.0 2.0 3.0 4.0

y-co

ordi

nate

(m

m)

0395790

-790-395

S1

S2

S3

(b)

0 1.0 2.0 3.0 4.0x-coordinate (mm)

0395790

-790-395

S1

S2

S3

(c)

0 1.0 2.0 3.0 4.0

0395790

-790-395

S1

S2

S3

(d)

0 1.0 2.0 3.0 4.0

H0

oj=15

H0

oj=0

H0

oj=0

H0

oj = 15

φ = 0°

0 395 790-395-790

1185

1190

1195

H (

Oe)

in

t

ΔH int

φ = 15°φ = 30°

y-coordinate (mm)

DH

int

4.0

01.02.03.0

0 20 40 60 80 100 120j (deg)

DH

(O

e)in

t

y-coordinate

1180

The intensity distribution in the case of p r o p a g a t i o n o f s u r f a c e magnetostatic waves (left column) and backward-volume magnetostatic waves (right column) with rotation of the bias angle j. It can be seen that when the angle j is rotated about the x axis, a transformation of the spatial intensity distribution in the side bars S is observed, in 1,3

particular, a decrease in intensity in the stripe S . 3

2 2( , ) x zI x y m m= +

The profiles of internal magnetic field H of three coupled magnetic stripes in case int

of varying the bias angle φ. It is seen that with increasing bias angle, the magnitude of the internal magnetic field is transformed in each stripe. We introduce the parameter ΔH = H - H , which determines the difference of the internal fields in int int2 int1,3

the stripes S and S or S . 2 1 3

An experimental study of the spatial dynamics of the MSSW was carried out using the Brillouin light spectroscopy of magnetic materials. In figures (a-c) shows spatial maps of the intensity of the spin wave I BLS

with a change in the bias angle j. It can be seen that when the angle j is rotated about the y axis, a transformation of the spatial intensity distribution in the side bars S is observed, in particular, a 1,3

decrease in intensity in the stripe S . 3

F. Lederer, G.I. Stegeman, D.N. Christodoulides et al., Phys. Rep., 463, 1 26 (2008).

2+C(A +A )+γ|A | A = 0n+1 n-1 n nβAn+

dAn

dzi

β - wavenumber in single microstrip

C = π/2L( f ) - coupling between 2 stripes

γ - nonlinear parameter

A - amplitude in n-th stripen

x-co

ord

inate

, m

m

z-coordinate, mm

YIG

YIG

YIG

GGG-substrate4

3

2

0 2.0 4.0 6.0 8.0

YIG 1

YIG 0

-1

-2

-3

-4

YIG

YIG

YIG

YIG

0.0

1.0

2.0

40 m

m140 m

m

NUMERICAL MODEL

Nonlinear discrete Schrödinger equation

k =β-2C cos(k d) - dispersionz x

2∂kx

2∂ kz 2D= = 2Cd cos(k d) - difraction parameter x

dβ2d|φ|

2, where β(ω, ω ) and ω (|φ| ), m m

2ω -(ω +hωm 2

) = -(ωm 2 -2|β|S) e , S - film thickness

γ=

22

π0

137

147

π/2k d┴

-1k , cm||

D>0

D<0

Isofrequency curveMSSW(FEM simulation)

D

γ

BV

MS

WM

SS

W

Bright soliton Dark soliton

γD>0

γD>0

γD<0

γD<0

Bright solitonDark soliton

0

...

f=5.6 GHz

4pM = 1750 G0

H = 1200 Oe0

S = 10 mm

d = 180 mm

Bias magnetic field

Magnetization saturation

YIG thickness

Period (in x-direction)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

f = 5.4 GHz

z-coordinate (mm)

z-coordinate (mm)

z-coordinate (mm)

z-coordinate (mm)

0

4.4

x-co

ord

inate

(m

m)

1.1

2.2

3.3

4.4

x-co

ord

inate

(m

m)

1.1

2.2

3.3

0

4.4

x-co

ord

ina

te (

mm

)

1.1

2.2

3.3

0

4.4

x-co

ord

ina

te (

mm

)

1.1

2.2

3.3

0

P = -10 dBmin

P = 5dBmin

P = 15 dBmin

P = 30 dBmin

1.01.52.02.53.03.5

00.5

0 0,5 1,0 1,5 2,0 2,5 3,0 3,5Nor

mal

ized

bea

m w

idth

(ar

b. u

n.)

z-coordinate (mm)

Power sweep

-10 dBm

5 dBm

15 dBm

30 dBm

A =0.010

A =0.0250

00 1 2 3 4

5

10

15

20

25

wav

egui

denu

mbe

r

z-coordinate, mm

10

15

20

25

wav

egui

denu

mbe

r

0

5

z-coordinate, mm

Numerical simulation

BLS EXPERIMENTBVMSW

Bright discrete soliton formation

0 1 2 3 4

Transverse position (mm)0 10 20 30 40

BLS

inte

nsity (

arb

.un.)

z-coordinate (mm)

x-co

ord

inate

(m

m)

0

2.25

0 4

z-coordinate (mm)

x-c

oord

inate

(m

m)

0

2.25

0 4

P = 5dBmin

P = 32 dBmin

Transverse position (mm)0 10 20 30 40

BLS

inte

nsity (

arb

.un.)

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

BLS EXPERIMENT

f = 5.5 GHzPower sweep MSSW