Magnetization dynamics at high frequencies FMR using an

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

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

Magnetization Dynamics Equation of motion: Heff q M F precession Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 2

Magnetization Dynamics Landau-Lifschitz-Gilbert equation: Heff q M F precession damping • precession frequencies are in the GHz range, while relaxation proccesses are of the order of ns; Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 3

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

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

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

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

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

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The Vector Network Analyzer • in order to perform an FMR experiment and obtain c, we have two basic requirements: 1) Radio frequency pumping field, hrf ; 2) Measurement of DZ ; 3) Solution: use of the Vector Network Analyzer (VNA) Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 10

The Vector Network Analyzer • at high frequencies it is difficult to measure voltages and currents, → use of S-parameters • the S-parameters are determined by measuring the incident, reflected and transmitted power; a 1 Incident S 21 Transmitted b 2 S 11 Reflected S 22 b 1 a 2 Transmitted S 12 Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 11 Incident

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

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; 25 ps Delay Line • we find Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 13

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

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

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

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

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

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

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

Acknowledgments 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 Lucian Prejbeanu Spin dynamics workshop, Corfu, october 2005 21