Interactions, fields and dynamics in ferromagnets - Iramis

Interactions, fields and dynamics in ferromagnets - Iramis

Interactions, fields and dynamics in ferromagnets Bob McMichael Center for Nanoscale Science and Technology, National Institute of Standards & Technol...

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Interactions, fields and dynamics in ferromagnets Bob McMichael Center for Nanoscale Science and Technology, National Institute of Standards & Technology, Gaithersburg, MD

 Interactions  Spin waves in extended structures  Ferromagnet dynamics in nanostructures

Acknowledgements

Han Jong Chia

Meng Zhu

Mark Stiles Mike Donahue Don Porter Tom Silva Justin Shaw Hans Nembach

Brian Maranville Caroline Ross Joy Cheng Vivian Chuang Sudook Kim Ward Johnson David Abraham

Brian Soe

Magnetization

Exchange interaction

Temperature

µ B Bexch >> k BT Bexch >> 300 T

Interactions Dipole-dipole (magnetostatic) (demagnetization)

Exchange

Eexchange = ∫ d 3r v

2 A  2 2 ∇ M + ∇ M + ( ∇M z )  ( ) ( ) x y 2   Ms 

Em =

µ0  1 −(r − r′)∇′·M (r′) (r − r′)M (r′)·n′  3 3 2 ′ ′ + d r M ( r )· d r d r  ∫s′ 2 ∫v 4π  ∫v′ | r − r′ |3 | r − r′ |3 

http://math.nist.gov/oommf

• Public domain • Extensible • Domain calcs • Dynamics calcs • Field calcs • Mailing list • Standard problems

2 µm

Field = 0.2 T

20 nm thick

10 µm Elapsed time = 2.1 ns

Spin waves

Propagation direction Precession direction

Propagation direction

M v 1.1 T

1.1 T “Demag” field Film: H demag = − M

Permalloy, Ni80Fe20 500 nm

20 nm thick

Internal Field (T)

500 nm

Uniform Applied Field

H

1.0 T

0.4 T/µm Field gradient 1.2 T

500 nm

500 nm

20 nm thick

Resonant slice calculation

Line width ≈ 2

Internal Field (T)

Applied field gradient Non-uniform dipolar field

ω α ≈ 4 mT γ

Field gradient = 0.4 T/µm

10 nm Resonant slice

Calculated frequency response

Distrubution of local fields

a Internal Field (T)

b

c a d

b i

c j

e

i

j

k

d k

e

Trapping spin waves

Resonant slice?

NMR, EPR, Weak interactions:

Off resonance

Off resonance

Happl

Ferromagnets, Strong interactions:

Spin waves on resonance

Off resonance

Happl

a Internal Field (T)

a

Edge modes & trapped spin waves

~50 T/µm

See also C. Hammel Thurs AM 0

20

40

60

80

100

Conclusions

Ferromagnet dynamics • Interactions, interactions, interactions! • No resonant slice. • Localized mode in low-field regions

a

Internal Field (T)

b

c a b

d

c i

j

e

i

j

d

k

e k