1. Spin Wave Model to study multilayered magnetic materials Sarah McIntyre

2. Why study spin waves? Atomic level precision materials Well defined interfaces Magnetic properties of buried interfaces difficult to measure Probe via spin waves

3. Ferromagnetism Spins align parallel Exchange interaction Resultant magnetic field Low anisotropy

4. Antiferromagnetism Spins align antiparallel Not net magnetic field High anisotropy

5. Ferromagnetic resonance mode

9. Excited modes

10. Model Lattice

11. Hamiltonian

12. Equations of motion Commutators of the Hamiltonian; Assume plane wave solution;

13. Dipole sums Slow to converge

14. Dipole sums Rapidly convergent form

15. Mode Profiles in a Ferromagnetic Film

16. Multilayers

17. Pinning of the FMR mode

18. Frequency shifts due to an interface

22. Future Work Fine tuning experimental parameters Fit to data sets from experiment Value for exchange at the interface?