Spin Excitations and Spin Damping in

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Spin Excitations and Spin Damping in Ultrathin
Ferromagnets D. L. Mills Department of
Physics and Astronomy University of
California Irvine, California
Collaborators R. B.Muniz and
A. T. Costa Instituto de
Fisica Universidade Federal de
Fluminense Niteroi, Brazil

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• Experimental methods for probing spin dynamics
• In ultrathin magnetic films
• Ferromagnetic resonance (FMR) Examines
• only

spin motions.
2. Brillouin light scattering (BLS) (Inelastic
scattering of photons) Examines
, small on the scale of the
Brillouin zone.
3. Inelastic Neutron Scattering Problems!
(i). Not surface sensitive. (ii). Neutrons
cant excite spin excitations in materials
of interest Neutron kinetic energy 30
meV, spin wave energy scale 300
meV. 4. Spin Polarized Electron Energy Loss
Spectroscopy (SPEELS) (i). High surface
sensitivity (ii). Lots of beam energy
(several eV) (iii). Cross section small.

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Expectations for Spin Wave Spectrum of an N
Layer Ferromagnetic Film
The Heisenberg Model
Spin Wave Excitations 1. Write down equation of
motion for
2. Seek solutions of the form
where
lies in the 2D Brillouin zone.
Conclusion For each value of
one has N
spin wave eigenmodes, each with
infinite lifetime.
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Heisenberg Model Description of the Spin Wave
Spectrum of a Five Layer Ferromagnet
For the materials of interest currently,
this picture is qualitatively wrong!
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• Our Approach
• Place ultrathin, few layer film on a semi
  infinite
• substrate.
• 2. Use empirical tight binding description of
  electronic
• structure, with nine bands for each
  material.
• Parameters obtained from fits to electronic
• structure calculations.
• 3. Ferromagnetism driven by intra atomic Coulomb
• interactions, with strength taken from
• photoemission data on exchange splitting
• (F. Himpsel, J. Magn. Mag. Mat. 102, 261
  (1991))
  )
• 4. Mean field, self consistent calculation of
  ground
• state, with moments allowed to vary on a
  layer
• by layer basis.

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• The Fe Monolayer on W(110) Comparison
• Between Local Density of States in GGA Based
• Density Functional Calculation (black) and
• Tight Binding Description.
• T. Costa, R. B. Muniz, J. X. Cao, R. Wu and
• D.L. Mills (to be published)

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Spin Excitations In Ultrathin 3d Ferromagnetic
Films The Case of Fe (5 layers) on W(110) A.
T. Costa, R. B. Muniz, and D. L. Mills, Phys.
Rev. B66, 224435 (2001).
Qx0.05
Qx0.20
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Farther out in the Brillouin Zone
Qx0.4
Qx0.6
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• Another Example Eight Layers of Co on Cu(100)
• T.Costa, R. B. Muniz and D. L. Mills,
• Phys. Rev. B70, 54406 (2004)

Q0.3
Q0.6
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An Experiment Spin Polarized Electron Loss
Spectroscopy (SPEELS)
Specular Direction
Spin Wave Excitation Angular Momentum
Conservation Requires a Spin Flip
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An Example of Electron Loss Spectroscopy Surface
Phonons on the Ni (100) Surface
Experiment M. L. Xu, B. M. Hall, S. Y. Tong, M.
Rocca. H. Ibach and J. E. Black, Phys.
Rev. Letters 54, 1171 (1985). Theory B. M.
Hall and D. L. Mills, Phys. Rev. B54, 1171 (1985).
What do we expect for spin waves? Theory
says sSW/sPh 10-3 . (M. P. Gokhale, A. Ormeci
and D. L. Mills, Phys. Rev. B46, 8978 (1992))
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SPEELS Studies of Spin Waves in
Ultrathin Ferromagnets Co on Cu(100) R.
Vollmer, M. Etzkorn, P. S. Anil Kumar, H. Ibach,
and J. Kirschner, Phys. Rev. Letters 91, 147201
(2003)
Spin Dependence of the Excitation Process
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Comparison Between Theory and Experiment A.
Dispersion Relation of Single Loss Feature
B. Linewidth and Lineshape
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The Limit of Zero Wave Vector

• It is crucial to understand the spin damping in
• ultrathin films at long wavelengths this
  controls
• realizable switching speeds in devices.
• A measure of spin damping Ferromagnetic
• resonance linewidths.
• The Question Are damping mechanisms the same
• In ultrathin ferromagnets as in bulk materials?
• Bulk Ferromagnets Damping at Q 0 is a spin
• orbit based mechanism (Goldstone theorem).
• Ultrathin Ferromagnets Two mechanisms not
• operative in the bulk
• Spin pumping Intrinsic.
• Two magnon scattering Extrinsic.

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• Calculations of FMR Spectra and Linewidths
• T. Costa, R. B. Muniz and D. L. Mills (to be
• Published)

1. Co2 on Cu(100)
2. Co2Cu2Co2 on Cu(100)
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Comparison Between Theory and Experiment
The Case of Fe on Au(100)

Data R. Urban, G.Woltersdorf and B.
Heinrich, Phys. Rev. Letters 87,217204 (2001).
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Data on Trilayers Quantum Interference
Effects The Data (K. Lenz, T. Tolinski, J.
Lindner, E. Kosubek, and K. Baberschke, Phys.
Rev. B69, 14422 (2004).
Theory
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Concluding Remarks

• For large wave vector spin wave excitations
• in ultrathin ferromagnets, the Heisenberg
  model
• description fails qualitatively. The reason
  is a
• breakdown of the adiabatic approximation.
• An effective Heisenberg Hamiltonian can be
  used
• to describe static phenomenon (domain
  walls) but
• not spin excitations at large wave vectors.
• 2. Our approach provides a quantitative
  description of
• spin excitations and their (intrinsic)
  damping
• throughout the two dimensional Brillouin
  zone,
• from the FMR regime to the large wave vectors
• explored in the electron energy loss studies.