1. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Traian PETRISOR Master 2 Internship Internship Coordinator Ursula EBELS Magnetization dynamics at high frequencies FMR using an inductive method

2. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 1 Motivation MRAM, Magnetic Random Access Memories; RF oscillators; Importance of magnetization dynamics in new devices: High Frequency Characterization of Materials for the mentioned applications Replacement of the classical FMR techniques with a broadband measurement;

3. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Magnetization Dynamics M   H eff precession Equation of motion: 2

4. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 precession frequencies are in the GHz range, while relaxation proccesses are of the order of ns; precession damping M H eff   Magnetization Dynamics Landau-Lifschitz-Gilbert equation: 3

5. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Ferromagnetic Resonance Excitation: External radio frequency magnetic field uniform oscillation mode; FMR: 4

6. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 The Coplanar Waveguide Critical parameters in determining Z:-central line width; -gap width; -substrate dielectric constant; -line conductivity. 5

7. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 What do we measure in a FMR experiment? 6

8. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 for small oscillations, we have harmonic solutions for m x : so that: if we consider for the radio frequency field we have a harmonic behaviour: What do we measure in a FMR experiment? 7

9. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Transmission Line Theory Telegrapher’s Equations: V and I are traveling waves having a propagation constant, TEM(Transverse Electric and Magnetic Fields) mode of propagation characteristic impedance 8

10. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 9

11. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 in order to perform an FMR experiment and obtain , we have two basic requirements: 1)Radio frequency pumping field, h rf ; 2)Measurement of  Z ; Solution: use of the Vector Network Analyzer (VNA) The Vector Network Analyzer 10

12. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 The Vector Network Analyzer Incident Transmitted Reflected IncidentTransmitted Reflected S 21 S 22 S 12 S 11 a1a1 b2b2 b1b1 a2a2 the S-parameters are determined by measuring the incident, reflected and transmitted power; at high frequencies it is difficult to measure voltages and currents, → use of S-parameters 11

13. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Using the S-Parameters Localized impedance 12

14. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 The Vector Network Analyzer Calibration in order to make relevant measurements the Network Analyzer has to be calibrated; Calibration Process:-determination of the systematic sources of errors by measuring known standards (SOLT); - mathematical removal of the errors from subsequent measurements; - shifting the reference planes of the measurement; we find 25ps Delay Line 13

15. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 pre-existing Coplanar Waveguides with 100nm thick Py lines on top; the lines were fabricated from Cu/Ta on high resistivity Si substrate; designed to have a Zc=50  → TEM propagation mode; the lines did not show the expected behavior, non-TEM propagation mode; The Studied Samples Access port 900µm 14 central line width: 5µm; Py line width: 4µm

16. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 pre-existing Coplanar Waveguides with 100nm thick Py lines on top; the lines were fabricated from Cu/Ta on high resistivity Si substrate; designed to have a Zc=50  → TEM propagation mode; the lines did not show the expected behavior, non-TEM propagation mode; The Studied Samples Access port 900µm 15

17. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Measurement Protocol in an FMR Experiment Reference measurement, no precession Signal measurement, precession Substraction of the two contributions 16

18. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Extraction of dynamic susceptibility the results are not in agreement with the theoretical behaviour; Reason: we did not take into account propagation effects, we used the localized impedance model; 17

19. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 the results are in agreement with theoretical behaviour; Extraction of dynamic susceptibility 18

20. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Conclusion After phase correction the results are in good agreement with expected behaviour. 19

21. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Perspectives Improvement of the coplanar waveguides: - change of geometry; - oxyde layer between substrate and lines; Access port 900µm Extraction of the dynamic susceptibility using the equivalent circuit approach; Removing access port contribution from measurements by performing different calibration (ex. TRL, LL); Characterization of different materials and structures. 20

22. Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 Acknowledgments 21 I would like to express my gratitude towards Ursula EBELS for her constant help and support during the entire period of the internship and to Bernard VIALA and Jean-Philippe MICHEL for their patience and support in preparing this presentation