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Magnetization dynamics at high frequencies FMR using an inductive method. Traian PETRISOR Master 2 Internship Internship Coordinator Ursula EBELS. Motivation. Importance of magnetization dynamics in new devices:. MRAM, Magnetic Random Access Memories; RF oscillators;.

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Presentation Transcript
slide1

Magnetization dynamics at high frequencies

FMR using an inductive method

Traian PETRISOR

Master 2 Internship

Internship Coordinator

Ursula EBELS

slide2

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;

1

slide3

Magnetization Dynamics

Heff

q

M

F

Equation of motion:

precession

2

slide4

Magnetization Dynamics

Heff

q

M

F

Landau-Lifschitz-Gilbert equation:

damping

precession

  • precession frequencies are in the GHz range, while relaxation proccesses
  • are of the order of ns;

3

slide5

Ferromagnetic Resonance

  • uniform oscillation mode;

Excitation: External radio frequency

magnetic field

FMR:

4

slide6

The Coplanar Waveguide

Critical parameters in determining Z:-central line width;

-gap width;

-substrate dielectric constant;

-line conductivity.

5

slide8

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

7

slide9

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,

8

slide11

The Vector Network Analyzer

  • in order to perform an FMR experiment and obtain c, we have two
  • basic requirements:
  • Radio frequency pumping field, hrf ;
  • Measurement of DZ ;
  • Solution: use of the Vector Network Analyzer (VNA)

10

slide12

The Vector Network Analyzer

S21

Transmitted

Incident

a1

b2

S11

Reflected

Reflected

S22

b1

a2

S12

Transmitted

Incident

  • 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;

11

slide13

Using the S-Parameters

Localized impedance

12

slide14

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;

25ps Delay Line

  • we find

13

slide15

The Studied Samples

  • 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=50W→TEM propagation mode;

900µm

Access port

Access port

  • central line width: 5µm; Py line width: 4µm
  • the lines did not show the expected behavior, non-TEM propagation mode;

14

slide16

The Studied Samples

  • 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=50W→TEM propagation mode;

900µm

Access port

Access port

  • the lines did not show the expected behavior, non-TEM propagation mode;

15

slide17

Measurement Protocol in an FMR Experiment

Signal measurement, precession

Reference measurement, no precession

Substraction of the two contributions

16

slide18

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

slide19

Extraction of dynamic susceptibility

  • the results are in agreement with theoretical behaviour;

18

slide20

Conclusion

  • After phase correction the results are in good agreement with expected behaviour.

19

slide21

Perspectives

900µm

Access port

Access port

  • Improvement of the coplanar waveguides:
  • - change of geometry;
  • - oxyde layer between substrate and lines;
  • 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

slide22

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

21