Near-Field diffraction of spin waves

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Submitted on 11 Oct 2019

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Near-Field diffraction of spin waves

Vincent Vlaminck, Nicolas Loayza, Vincent Castel, Daniel Stoeffler, Matthieu

Bailleul, Benjamin Youngfleisch, Axel Hoffmann

To cite this version:

Vincent Vlaminck, Nicolas Loayza, Vincent Castel, Daniel Stoeffler, Matthieu Bailleul, et al.. Near-Field diffraction of spin waves. Colloque Louis Néel XIX, May 2019, Toulouse, France. 2019. �hal-02310439�

Motivations

► Shaping spin wave beams in continuous layers

From special design of constricted microwave antennae [1-3]

► Diffraction model for all spin wave modes

Analytical understanding of the spin wave interference

mechanisms from Fresnel’s near-field diffraction [3]

Near-field diffraction of spin waves

Authors

Contact : vincent.vlaminck@imt-atlantique.fr

Co

lloqu

e

Lou

is

Ne

el

14

-17

Mai 2019

T

oul

ouse

Vincent VLAMINCK

1,2

Nicolas LOAYZA

2

Vincent CASTEL

1

Daniel STOEFFLER

3

Matthieu BAILLEUL

3

BenjaminYoungfleisch

4,5

Axel Hoffmann

4

1

_{IMT- Atlantique}

Campus de Brest

Département Micro Ondes

Technopole Brest-Iroise

CS83818

29238 Brest Cedex 03

2

_USFQ

Universidad San Francisco de

Quito,

Colegio de Ciencias e Ingeneria

Quito, Ecuador

3

_IPCMS

Institut de Physique et Chimie des

Matériaux de Strasbourg,

UMR 7504 CNRS

Université de Strasbourg

Funding

ANR-11-LABX-0058_NIE

References

[1] P. GRUSZCEKI et al.,

Sci. Rep. 6, 22367 (2016)

[2] H. S. KÔRNER et al.,

Phys. Rev. B 96, 100401 (2017)

[3] N. LOAYZA et al.,

Phys. Rev. B 98, 144430 (2018)

[4] O. Büttner et al.,

Phys. Rev. B 61, 11576 (2000)

[5] T. Brächer et al.,

Phys. Rev. B 95, 064429 (2017)

[6] B. A. Kalinikov,

Fizika, No. 8, pp. 42-56 (1981)

► Anisotropic dispersion

Each direction (

q

_k

) corresponds to a distinct k [4]

Conclusions

► Excellent agreement between a Fresnel approach and micromagnetic simulations for MSFVW

► Spin wave spectroscopy in continuous layers possible with sharply constricted antenna

► Near-field diffraction model for in-plane modes to be validated with micromagnetic simulations

MuMax 3

Fresnel model

f=5.15GHz - µ

₀

H

_ext

=308mT

k

_res

= 6,17 rad/µm - L

_att

=13,8µm

MuMax 3

f=5.25GHz - µ

₀

H

_ext

=308mT

Fresnel model

k

_res

= 7,98 rad/µm - L

_att

=14,5µm

► Diffraction of isotropic circular waves

(

from 3 rectangular apertures)

Fixed frequency and applied field a single resonant k

𝐿

_𝑎𝑡𝑡

=

1

𝛼𝜔

𝜕𝜔

𝜕𝑘

𝜔 𝐻, 𝑘 =

𝜔

_𝐻

+ 𝜂𝑘

2

𝜔

_𝐻

+ 𝜂𝑘

2

+ 𝜔

_𝑀

𝑃(𝑘)

−

𝑙

2

D

s

G+

S

G-r

y

x

l

x,y

𝑙

2

m

CPW

= m

S

- m

G-

- m

G+

෥

𝑚

_𝑖

𝐷, 𝑠 = න

−

₂

𝑙

𝑙

2

𝑑𝑦 න

−

𝑤

₂

𝑖

𝑤

_𝑖

2

𝑑𝑥

1

𝑟

_𝑖

𝑒

−

_𝐿

𝑟

𝑖

𝑎𝑡𝑡

𝑒

𝑖𝑘 𝑟

𝑖

► Spin wave spectroscopy in continuous YIG films

No need to structure a spin wave guide

► Discrete mapping of MSFVW modes

Via inductive technique with a smaller probe [3]

k

_II

k=0

_k

I

f

_osc

D=4mm

D=8mm

D=12mm

m

₀

H

_ext

= 308 mT

2 mm

D

s

2 mm

D

s

𝜔 𝐻, 𝑘, 𝜃

_𝑀

, 𝜃

_𝑘

=

𝜔

_𝐻

+ 𝜂𝑘

2

𝜔

_𝐻

+ 𝜂𝑘

2

+ 𝜔

_𝑀

𝐹(𝑘, 𝜃

_𝑘

, 𝜃

_𝑀

)

𝑃 𝑘 = 1 −

1 − 𝑒

−𝑘𝑡

𝑘𝑡

► Both h

_in

and h

_out

excites spin waves [5]

y

z

x

Isotropic out-of-plane modes (MSFVW) [3]

Near-field diffraction model for in-plane modes

► In-plane modes diffraction pattern adapted from Eq. 34 of [6]

( Ԧ𝑟, 𝜃

_𝑀

) = න

−∞

+∞

𝑑𝑦′ න

−∞

+∞

𝑑𝑥′

ℵ

𝑖𝑛

Ԧ𝑟 − Ԧ𝑟

′

_{. ℎ}

𝑖𝑛

Ԧ𝑟

′

. cos 𝜃

𝑀

+

+ℵ

_𝑜𝑢𝑡

Ԧ𝑟 − Ԧ𝑟

′

. ℎ

_𝑜𝑢𝑡

Ԧ𝑟

′

𝑒

−

𝑟− Ԧ

_𝐿

Ԧ

𝑟′

𝑎𝑡𝑡

𝑒

−𝑖𝑘 Ԧ

𝑟− Ԧ

𝑟′

෥

𝑚

ℵ

_𝑖𝑛

= 𝑖𝜔

_𝑀

𝜔 − 𝜔

_𝐻

+ 𝜂𝑘

2

+ 𝜔

_𝑀

1 − 𝑃 𝑘

;

ℵ

_𝑜𝑢𝑡

= −𝜔

_𝑀

𝜔 − 𝜔

_𝐻

+ 𝜂𝑘

2

+ 𝜔

_𝑀

𝑃 𝑘 𝑠𝑖𝑛

2

𝜃 − 𝜃

_𝑀

;

𝐿

_𝑎𝑡𝑡

=

2

𝛼 2𝜔

_𝐻

+ 𝜔

_𝑀

𝜕𝜔

𝜕𝑘

Ԧ𝑟 − Ԧ𝑟

′

_{, 𝜃}

𝑀

k

_I

4 mm

k

_II

k [rad.µm

-1

_]

ǁ𝑗(

𝑘

)

k

_I

k

_II

M

k

y

[m

m]

k

_x

[mm]

Isofrequencies

𝑘( Ԧ𝑟 − Ԧ𝑟

′

, 𝜃

_𝑀

)

k(q

_k

-q

_M

)

h

_in

h

_out

x [µm]

h

e x c

[a.u

.]

𝜇

₀

𝐻

_𝑒𝑥𝑡

= 308 𝑚𝑇

𝜇

0

𝑀

𝑒𝑓𝑓

= 136 𝑚𝑇

𝐴

_{𝑒𝑥𝑐ℎ}

= 4 𝑝𝐽. 𝑚

−1

k

_x

[mm]

k

y

[mm]

f [GHz]

M

k

_x

[mm]

k

_y

[mm]

𝜇

₀

𝐻

_𝑒𝑓𝑓

= 0.2 𝑇

𝜇

₀

𝑀

_𝑠

= 0.17 𝑇

𝐴

_{𝑒𝑥𝑐ℎ}

= 3.5 𝑝𝐽. 𝑚

−1

f [GHz]

𝐹 𝐻, 𝑘, 𝜃

_𝑘

, 𝜃

_𝑀

= 1 − 𝑃𝑐𝑜𝑠

2

𝜃

_𝑘

− 𝜃

_𝑀

+

𝜔

𝑀

𝑃(1 − 𝑃)

𝜔

_𝐻

+ 𝜂𝑘

2

𝑠𝑖𝑛

2

𝜃

𝑘

− 𝜃

𝑀

t

_YIG

= 30 nm ; µ

₀

M

_s

=196mT ; µ

₀

H

_K

=60mT

Affiliations

4

_MSD-ANL

Material Science Division

Argonne National Laboratory

Argonne, Illinois, USA

5

_{University of Delaware}

Dept. of Physics and Astronomy

Newark, Delaware, USA

f

_res

=7.80 GHz – µ

₀

H

_ext

=0.2T

q

_M

=0

_M

s

q

M

=p/6

_M

q

M

=p/4

q

M

=p/3

s

M

_s

M

_s

f

_res

=7.80 GHz – H

_ext

=0.2T

q

_M

=0

M

_s

f =7.62 GHz

M

_s

_M

_s

H

_ext

=0.2T -

q

_M

=90°

f =7.55 GHz

f =7.65 GHz