Presentation of Licentiate in Physics Engineering of Francisco Almeida

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Magnetic characterization of Fe/57FeSi/Fe trilayers

Francisco Almeida, student from Faculdade de Ciências da Universidade de Lisboa (Erasmus exchange)ESTÁGIO PROFISSIONALIZANTE – LICENCIATURA EM ENGENHARIA FÍSICA

Promotor:-Prof. Dr. José Carvalho Soares (FCUL)

Magnetic thin films group:-Dr. Bart Croonenborghs-Dr. Johan Meersschaut-Dr. Dominique Aernout-Dr. Caroline L’Abbé

Coordenators:

-Prof. Dr. Andre Vantomme (IKS, KUL)-Dr. Johan Meersschaut (IKS, KUL)

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Overview• Motivation

– Magnetic multilayers, interlayer exchange coupling and Giant Magnetic Resistance

– Debate on the coupling behaviour of Fe/FeSi trilayers

• Techniques used– Molecular Beam Epitaxy

– Vibrating Sample Magnetometry• Numerical analysis: Simulating and fitting the acquired data

– Structural characterization through several techinques• Conversion Electron Mossbauer Spectroscopy

• High Resolution X-Ray Diffraction

• Rutherford Backscattering Spectroscopy

• Results– Coupling evolution throughout different thicknesses

– Quality of samples

• Conclusions

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MotivationInterlayer exchange coupling

Bilinear antiferromagnetic ( = 180º) coupling between two ferromagnetic layers

1 1 2 1 cosE J m m J

Energy related to the interlayer exchange coupling:

Analogy to Heisenberg type exchange:

1 2ˆ 2JS S

SH

(Bilinear form Hamiltonian)

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MotivationGiant Magnetoresistivity

• Interlayer coupling gives enhances Magnetoresistivity

• Giant Magnetoresistivity is the underlying principle of a variety of sensors and magnetic recording

– Discovered in 1988 in Fe/Cr magnetic multilayers1

– First seen in Fe/Cr/Fe trilayers2 in 1989

1 Baibich, M.N.; Broto, J.M.; Van Dau, F.N. - “Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices”, Phys. Rev. Lett. 61, 2472 (1988)

2 Binash, G.; Grunberg, P.; Saurenbach, F. - “Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange”, Phys. Rev. B 39, 4828 (1989)

GMR plot from Fert, A.; Grunberg, P.; Barthelemy, A. – “Layered magnetic structures: interlayer exchange coupling and giant magnetoresistance”, J. Mag. M. Mat. 1, 140 (1995)

R R R

R R

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Interlayer exchange couplingPhenomenological energy expression

Bilinear (AF) coupling

0 1 cosE J J

Biquadratic coupling

22 cosJ 3

3 cos ...J Energy power expansion1 on cos

1 Slonczewski, J. C. – “Overview of interlayer exchange theory”; Journal of Magnetism and Magnetic Materials, 150, 13 (1995)

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Interlayer exchange couplingThe RKKY approximation

• Ruderman-Kittel-Kasuya-Yosida indirect exchange

• Indirect exchange coupling mediated through conduction electrons

• Good approximation for coupling mechanism in metallic spacer trilayers

2D decay:

22

sin 2

2FD

RKKY

F

k LJ

k L

3D (general case) decay:

3

cos 2 FRKKY

k rJ

r

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Interlayer exchange couplingThe RKKY approximation

Exchange coupling oscillating as a function of a metallic spacer thickness, for several different potencial barrier values:

a) V = 0.

b) V = 0.3EF.

c) V = 0.6EF.

d) V = 0.9EF.

(From Ferreira et al,

J. Phys.: Cond. Matt. 6, L619 (1994) )

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Interlayer exchange couplingTemperature and thickness dependence

• Insulator spacers:– Monotonous increase with temperature (thermally activated)

– Exponential decay with the thickness

• Conducting metal spacers:– Weak J1 and stronger J2 temperature dependence

– Coupling strength oscillates with thickness (RKKY-type damped oscillation.)

• Semiconductors:– Possible coupling behaviour depends on band-gap (i.e., state population near Fermi level)

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Interlayer exchange couplingDebate on the coupling behaviour of Fe/FeSi

trilayers• Different groups show contradicting results

– Oscillatory or exponential coupling thickness dependence?

Bürgler, D.A.; Gareev, R.R. et al - J. Phys. : Condensed Matter 15 S443 (2003)

de Vries, J.J.; de Jonge, W.J.M. et al – Phys. Rev. Lett. 78, 3023 (1997)

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Samples grown through Molecular Beam Epitaxy

• Samples consisting of Fe/57FeSi/Fe– Varying FeSi thickness

– Aiming at Fe0.5Si0.5 stoichiometry

• Trilayers grown epitaxially on an MgO substrate– Fe (100) axis parallel to MgO (110)

– P~10-10 mBar, T = 150ºC

3.12%s

s

a am

a

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• Intended system is MgOsubst\Fe80 A\57Fe0.5Si0.5\Fe40 A\Aucap

• Thicknesses checked through X-Ray reflectivity

• All samples grew with the correct Fe thicknesses, except for C1207 (bottom Fe layer too thick)

• The phase of the iron in the spacer was checked through CEMS, and the Fe in the spacer is in a non-magnetic environment (no Zeeman splitting observed)

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Sample L(57FeSi) [Å] C1205 8 C1206 10 C1207 12 C1208 14 C1209 16 C1210 18 C1211 20 C1212 22 C1213 24 C0906 26 C1214 28 C1215 30

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Vibrating Sample Magnetometry

• Measurement of total sample magnetization for low and high temperatures

• Physical principle: Faraday Law

• Suited for magnetic thin films

BdV t

dt

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Vibrating Sample MagnetometryMeasuring hysterysis curves

Characterizing magnetic materials through:

-Saturation field (MS)

-Remanent field (MR)

-Coercivity (HC)

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Numerical analysisSimulation through energy minimization

• Finding the energy minimum

• No analytical general solution

• Numerical approximations

4

2 2(1) (2)4 1 1 1 2 2 2cos sin cos sinE K t K t

1 1 2 2cos cosM H t t

21 2 1 2 2 1cos cosJ J

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Numerical analysisSimulation of biquadratic coupling

2

1 2R

tM

t t

t1

t2

(pinned)

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Numerical analysisSimulation of bilinear coupling

2 1

1 2R

t tM

t t

t1

t2

(pinned)

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Numerical analysisAutomatically fitting the data

• Fitting allows to measure:– Bilinear coupling J1 and biquadratic coupling J2

– Cubic crystalline anisotropy K4

– Ferromagnetic layers thicknesses (t1, t2)

– Angle of magnetisation projection (mismatch from axis)

• Information on “easy” and “hard” axis projections

• Grid Local Search for non-linear least squares fit– Local 2 minimization

– Parameter error bars

[100] Fe // [110] MgO

easy

hard

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ResultsCoupling strength

• Possible to obtain a trend of the coupling strength as function of temperature and thickness

• General tendency of decreasing coupling with temperature and spacer thickness

• Strong temperature dependency for both bilinear and biquadratic coupling

• Sample C1210 (with an 18 Å FeSi spacer) looses the interlayer coupling at RT

• Samples with a spacer thicker than ~20 Å are simply not coupled

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ResultsCoupling strength – C1208 (14 Å FeSi)

• Use of “easy” and “hard” axis measurements allows to estimate anisotropy

• Cubic anisotropy decreases with temperature, from 36 kJ.m-3 to 32 kJ.m-3

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-1.0

-0.5

0.0

0.5

1.0(11) (Hard axis)

tspacer

= 16 A, t1 = 40 A, t

2 = 80 A

J1 = -0.5863 mJ/m2

J2 = -0.0612 mJ/m2

K4 = 32000 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1208 - 290 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]-0.4 -0.2 0.0 0.2 0.4

-1.0

-0.5

0.0

0.5

1.0(10) (Easy axis)

tspacer

= 14 A, t1 = 40 A, t

2 = 80 A

J1 = -0.5863 +- 0.0053 mJ/m2

J2 = -0.06125 +- 0.0011 mJ/m2

K4 = 32000 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1208 - 290 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/M S)

Field [T]

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Coupling strength – C1208 (14 Å FeSi)

-0.4 -0.2 0.0 0.2 0.4

-1.0

-0.5

0.0

0.5

1.0(10) (Easy axis)

tspacer

= 14 A, t1 = 40 A, t

2 = 80 A

88.5 % effective coupling

J1 = -1.0485 ± 0.0041 mJ/m2

J2 = -0.2421 ± 0.0056 mJ/m2

K4 = 35000 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1208 - 20 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]-0.4 -0.2 0.0 0.2 0.4

-1.0

-0.5

0.0

0.5

1.0 (10) (Easy axis)tspacer

= 14 A, t1 = 40 A, t

2 = 80 A

J1 = -0.7546 ± 0.0149 mJ/m2

J2 = -0.1048 ± 0.0045 mJ/m2

K4 = 33000 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1208 - 220 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]

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Coupling strength – C1208 (14 Å FeSi)

0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

-J1

-J2

Bilinear and biquadratic coupling

Co

up

ling

str

en

gth

[mJ/

m2 ]

Temperature [K]

0 50 100 150 200 250 3000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Saturation field temperature dependence

Sa

tura

tion

fie

ld [T

]

T [K]

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Coupling strengthLoose spins model (Slonczewski et al)

21, ,0

2J T ca f T f T

22

1,0 , 2 , 22

J T J T ca f T f T f T

Interlayer coupling mediated through “loose spins” in the spacer

1sinh 1 2

, ln

sinh 2

B

B

B

US k T

f T k TU

Sk T

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Coupling strengthLoose spins model fit to data

0 50 100 150 200 250 3000.00

0.05

0.10

0.15

0.20

0.25

0.30 C1208 data theory

C1208 - Slonczewski fit

c = 0.118 a [A] = 2.86

U1/k [K] = 98.9173 U2/k [K] = 362.974

-J2

[mJ/

m2 ]

T [K]

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C1208 (14 Å FeSi)A strange effect

-0.4 -0.2 0.0 0.2 0.4

-1.0

-0.5

0.0

0.5

1.0

Loop shape change with temperature

220 K 110 K 20 K

Ma

gn

etis

atio

n (

M/M

S)

Applied field [T]0 50 100 150 200 250 3000.0

0.1

0.2

0.3

0.4

0.5

Remanence raise at low temperatures

Remanence temperature dependence

33% Remanence - Bilinear interlayer coupling

Re

ma

ne

nce

T [K]

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C1208 (14 Å FeSi)Antiferromagnetic fraction (AFF)

• Introducing a normal ferromagnetic term allows to reproduce the measured loops, without loss of continuity in the coupling J1 and J2

0 50 100 150 200 250 3000.85

0.90

0.95

1.00

Antiferromagnetically coupled fraction of the sample

AF

F

T [K]

0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

-J1

-J2

Bilinear and biquadratic coupling

Co

up

ling

str

en

gth

[mJ/

m2 ]

Temperature [K]

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Thinner samples (C1205 and C1206)Difficulties in finding solutions

• AFF function quickly drops just below RT or at even higher temperatures– This drop multiplies the number of possible solutions of the system

– Complexity of fitting procedure dramatically increases

– Adopted fitting method does not have enough sensitivity

• Only some measurements, at room temperature, might be fitted and used for analysis

• Possible coupling strength distribution causes smeathering of measured data (also seen in other samples, but with a weaker effect and only at low temperature)

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-0.8 -0.4 0.0 0.4 0.8

-1.0

-0.5

0.0

0.5

1.0(10) (Easy axis)

tspacer

= 10 A, t1 = 40 A, t

2 = 80 A

J1 = -1.5167 ± 0.0033 mJ/m2

J2 = -0.3979 ± 0.0004 mJ/m2

K4 = 32000 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1206 - 290 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]

-0.8 -0.4 0.0 0.4 0.8

-1.0

-0.5

0.0

0.5

1.0(10) (Easy axis)

tspacer

= 10 A, t1 = 40 A, t

2 = 80 A

J1 = -1.5308 ± 0.0042 mJ/m2

J2 = -0.4073 ± 0.0032 mJ/m2

K4 = 32000 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1206 - 270 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]

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-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9

-1.0

-0.5

0.0

0.5

1.0(10) (Easy axis)

tspacer

= 8 A, t1 = 40 A, t

2 = 80 A

90.6% effectively coupled

J1 = -0.4494 ± 0.0288 mJ/m2

J2 = -0.6151 ± 0.0099 mJ/m2

K4 = 33600 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1205 - 200 K (Alternate solution)

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-1.0

-0.5

0.0

0.5

1.0(10) (Easy axis)

tspacer

= 8 A, t1 = 40 A, t

2 = 80 A

J1 = -0.3770 ± 0.0558 mJ/m2

J2 = -0.6773 ± 0.0816 mJ/m2

K4 = 33600 J/m3

Mbulk

= 1.76014e+006 J(T.m3)

C1205 - 200 K

No

rma

lize

d M

ag

ne

tiza

tion

(M

/MS)

Field [T]

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Coupling strengthAll samples

• C1208 is representitive of what occurs in most coupled samples

• Thinner samples have a much stronger coupling strength

• AFF tends to reduce below unity at higher temperatures and less, as the thickness decreases

• Bilinear coupling saturates, and in some cases, decreases at low temperature

• Biquadratic coupling generally saturates at low temperatures

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0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

18 A

16 A

14 A

12 A

Bilinear coupling with varying thickness

-J1

[mJ/

m3 ]

T [K]

12 13 14 15 16 17 180

50

100

150

200

250

Transition temperature to partialferromagnetic coupling

Tra

nsi

tion

tem

pe

ratu

re [K

]

Thickness [A]

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5 10 15 20 25 30-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Coupling thickness dependence

Pinholes

A

A

Co

up

ling

str

en

gth

[mJ/

m2 ]

thickness [A]

-J1

-J2

Exponential decay fit Exponential decay fit

0

d

J d J e

J0 = Maximum value (null thickness)

= Coeherence length

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Conclusions

• The chosen method for analysis of magnetisation loops obtained through VSM is efficient, but its efficiency depends on the quality of the measurements

• Ambiguous fitting solutions for some of the samples must be resolved through an alternate analysis method

• The best model to explain the temperature dependent coupling behaviour is the loose spins model (Slonczewski et al), although this system has some peculiarities

– The stoichiometry should be close to Fe0.5Si0.5, but there might be an excess of Si in the spacer.

– Still ongoing work in adjusting the model to exact the results on a loose spins model interpretation is being done.

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References• Baibich, M.N.; Broto, J.M.; Van Dau, F.N. - “Giant Magnetoresistance of (001)Fe/(001)Cr

Magnetic Superlattices”, Phys. Rev. Lett. 61, 2472 (1988)

• Binash, G.; Grunberg, P.; Saurenbach, F. - “Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange”, Phys. Rev. B 39, 4828 (1989)

• Fert, A.; Grunberg, P.; Barthelemy, A. – “Layered magnetic structures: interlayer exchange coupling and giant magnetoresistance”, J. Mag. M. Mat. 1, 140 (1995)

• Ferreira, M.S.; Edwards, D.M. – “The nature and validity of the RKKY limit of exchange coupling in magnetic trilayers”; J. Phys.: Cond. Matt. 6, L619 (1994)

• Bürgler, D.A.; Gareev, R.R. – “Exchange coupling of ferromagnetic films across metallic and semiconducting interlayers”; J. Phys. : Condensed Matter 15 S443 (2003)

• Sloncsewski, J.C. – “Origin of biquadratic exchange in magnetic multilayers”; J. Appl. Phys. 73, 5957 (1993)

• de Vries, J.J.; de Jonge, W.J.M. – “Exponential Dependence of the Interlayer Coupling on the Spacer Thickness in MBE-grown Fe/SiFe/Fe Sandwiches”; Phys. Rev. Lett. 78, 3023 (1997)

• Strijkers, G.J.; de Jonge, W.J.M. – “Origin of Biquadratic Exchange in Fe\Si\Fe”

Presentation of Licentiate in Physics Engineering of Francisco Almeida

Education

Transcript of Presentation of Licentiate in Physics Engineering of Francisco Almeida