presentation of licentiate in physics engineering of francisco almeida
DESCRIPTION
This seminar was presented to show the results of my research on magnetic thin films for my Licentiate diploma in Physics Engineering. This is a subset (although the biggest portion) of the analysis performed. (note: the two last slides are not part of the actual presentation).TRANSCRIPT
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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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Samples grown through Molecular Beam Epitaxy
• 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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Samples grown through Molecular Beam Epitaxy
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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Thinner samples (C1205 and C1206)Difficulties in finding solutions
-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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Thinner samples (C1205 and C1206)Difficulties in finding solutions
-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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Coupling strengthAll samples
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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Coupling strengthAll samples
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”