Spin Excitations and Spin Damping in

Ultrathin Ferromagnets

D. L. MillsDepartment of Physics and Astronomy

University of CaliforniaIrvine, California

Collaborators:

R. B.Muniz and A. T. Costa Instituto de Fisica Universidade Federal de Fluminense Niteroi, Brazil

Experimental methods for probing spin dynamics

In ultrathin magnetic films:

1. Ferromagnetic resonance (FMR): Examines only 0// Q

spin motions.

2. Brillouin light scattering (BLS): (Inelastic scattering of photons): Examines

15// 10 cmQ

, small on the scale of the

Brillouin zone.

3. Inelastic Neutron Scattering : Problems! (i). Not surface sensitive. (ii). Neutrons can’t 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.

Expectations for Spin Wave Spectrum of an N Layer Ferromagnetic Film:

The Heisenberg Model:

)','(),()',;'( ////, ','

////

// //

llSllSllllJHll ll

Spin Wave Excitations:

1. Write down equation of motion for ),( // llS

2. Seek solutions of the form

))(exp()(),( //////

tQilQilsllS llQ

where //Q

lies in the 2D Brillouin zone.

Conclusion: For each value of //Q

one has N

spin wave eigenmodes, each with infinitelifetime.

Heisenberg Model Description of the SpinWave Spectrum of a Five Layer Ferromagnet:

For the materials of interest currently, thispicture is qualitatively wrong!

Our Approach:

1. 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.

5. Random Phase Approximation applied to description of spin dynamics.

The Fe Monolayer on W(110); ComparisonBetween Local Density of States in GGA BasedDensity Functional Calculation (black) andTight Binding Description.

A.T. Costa, R. B. Muniz, J. X. Cao, R. Wu andD.L. Mills (to be published)

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).

Qx=0.05

Qx=0.20

Farther out in the Brillouin Zone:

Qx=0.4

Qx=0.6

Another Example : Eight Layers of Co on Cu(100)

A. T.Costa, R. B. Muniz and D. L. Mills, Phys. Rev. B70, 54406 (2004)

Q=0.3

Q=0.6

An Experiment : Spin Polarized Electron Loss Spectroscopy (SPEELS)

Specular DirectionII KE

,

SS KE

,

SWSW Q//,

SWIS EE SWIS QKK //////

Spin Wave Excitation: Angular Momentum Conservation Requires a Spin Flip

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 saysSW/Ph ~ 10-3 . (M. P. Gokhale, A. Ormeci andD. L. Mills, Phys. Rev. B46, 8978 (1992))

SPEELS Studies of Spin Waves in UltrathinFerromagnets; 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:

Comparison Between Theory and Experiment:

A. Dispersion Relation of Single Loss Feature:

B. Linewidth and Lineshape:

The Limit of Zero Wave Vector:

It is crucial to understand the spin damping inultrathin films at long wavelengths; this controlsrealizable switching speeds in devices.

A measure of spin damping: Ferromagnetic resonance linewidths.

The Question: Are damping mechanisms the sameIn ultrathin ferromagnets as in bulk materials?

Bulk Ferromagnets: Damping at Q = 0 is a spin orbit based mechanism (Goldstone theorem).

Ultrathin Ferromagnets: Two mechanisms notoperative in the bulk:

1. “Spin pumping”: Intrinsic.

2. Two magnon scattering: Extrinsic. R. Arias and D. L. Mills, Phys. Rev. B60, 7395 (1999), D. L. Mills and S. M. Rezende, p. 27 of Spin Dynamics in Confined Structures II, (Springer Verlag, Heidelberg, 2002).

Calculations of FMR Spectra and Linewidths:

A. T. Costa, R. B. Muniz and D. L. Mills (to bePublished)

1. Co2 on Cu(100):

2. Co2Cu2Co2 on Cu(100):

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).

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:

Concluding Remarks:

1. 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.