lucian prejbeanu spin dynamics workshop, corfu, october 2005 traian petrisor master 2 internship...

Lucian PrejbeanuSpin dynamics workshop, Corfu, october 2005

Traian PETRISORTraian PETRISORMaster 2 Internship

Internship Coordinator

Ursula EBELSUrsula EBELS

Magnetization dynamics at high frequenciesMagnetization dynamics at high frequenciesFMR using an inductive methodFMR using an inductive method


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;


Magnetization Dynamics

)( 0 effHMt

M

M

Heff

precession

exbiasdipolaneff HHHHH

),,,( exbiasdipolan HHHHf

Equation of motion:

2


t

MM

MHM

t

M

Seff

)( 0

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

precession damping

M

Heff

Magnetization Dynamics

Landau-Lifschitz-Gilbert equation:

3


Ferromagnetic Resonance

),,,( exbiasdipolan HHHHf

Excitation: External radio frequency magnetic field

rfh

• uniform oscillation mode;

int extFMR:

rfhm

χ

4


The Coplanar Waveguide

Critical parameters in determining Z:-central line width; -gap width;

-substrate dielectric constant; -line conductivity.

5


What do we measure in a FMR experiment?

tdV

dzdmd x 0 SB

dzt

mddV x

0

6


• for small oscillations, we have harmonic solutions for mx:

tjxx emtm )(

tjrfrf ehth )(

• so that:

rfxxx hm • if we consider wIhrf 2

Iw

dj

dz

dVxx

20

• for the radio frequency field we have a harmonic behaviour:

What do we measure in a FMR experiment?

7


Transmission Line Theory

Telegrapher’s Equations:

)()()(

)()()(

zVCjGdz

zdI

zILjRdz

zdV

• V and I are traveling waves having a propagation constant,

))(( CjGLjRj

TEM(Transverse Electric and Magnetic Fields) mode of propagation

• characteristic impedance

CjG

LjRZc

8


)()()(

zILjRdz

zdV

)(2

)( 0 xxw

djjLR

Iw

dj

dz

dVxx

20

9


• in order to perform an FMR experiment and obtain , we have two basic requirements:

1) Radio frequency pumping field, hrf ;2) Measurement of Z ;

Solution: use of the Vector Network Analyzer (VNA)

The Vector Network Analyzer

10


The Vector Network Analyzer

Incident Transmitted

Reflected

IncidentTransmitted

Reflected

S21

S22

S12

S11

DUT

a1

b2

b1 a2

• 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

01

01

02

02

2

112

2

222

1

221

1

111

a

a

a

a

a

bS

a

bS

a

bS

a

bS

11


Using the S-Parameters

12

1212

S

SZcZ

Localized impedance

Incident

dTransmitteS 12

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;

fS 212

• we find ps5.20

25ps Delay Line

13


• 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 Access port900µm

14

•central line width: 5µm; Py line width: 4µm


• 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


15


Measurement Protocol in an FMR Experiment

Reference measurement, no precession Signal measurement, precession

Substraction of the two contributions

t

MM

MHM

t

M

Seff

)( 0

16


Extraction of dynamic susceptibility

ref

ref

a S

S

S

SZcKjZ

12

12

12

12 1122

• 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;

12

1212

S

SZcZ

17


• the results are in agreement with theoretical behaviour;

ref

ref

a S

S

S

SZcKjZ

12

12

12

12 1122

Extraction of dynamic susceptibility

jeSS 1212

)()( fef ja

18


Conclusion

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

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;

CjG

LjRZc

))(( CjGLjR

• Removing access port contribution from measurements by performing different calibration (ex. TRL, LL);

• Characterization of different materials and structures.

20


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

lucian prejbeanu spin dynamics workshop, corfu, october 2005 traian petrisor master 2 internship...

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