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Presentation of Licentiate in Physics Engineering of Francisco Almeida

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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 …

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).


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  • 1. Magnetic characterization of Fe / 57 FeSi / Fe trilayers Francisco Almeida, student from Faculdade de Ci ê ncias da Universidade de Lisboa ( Erasmus exchange ) EST Á GIO PROFISSIONALIZANTE – LICENCIATURA EM ENGENHARIA F Í SICA
    • Promotor:
    • Prof. Dr. Jos é Carvalho Soares (FCUL)
    • Magnetic thin films group:
    • Dr. Bart Croonenborghs
    • Dr. Johan Meersschaut
    • Dr. Dominique Aernout
    • Dr. Caroline L’Abb é
    • Coordenators:
    • -Prof. Dr. Andre Vantomme (IKS, KUL)
    • Dr. Johan Meersschaut (IKS, KUL)
  • 2. 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
  • 3. Motivation Interlayer exchange coupling Bilinear antiferromagnetic (  = 180 º ) coupling between two ferromagnetic layers Analogy to Heisenberg type exchange: (Bilinear form Hamiltonian) Energy related to the interlayer exchange coupling:
  • 4. Motivation Giant 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 multilayers 1
      • First seen in Fe/Cr/Fe trilayers 2 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)
  • 5. Interlayer exchange coupling Phenomenological energy expression 1 Slonczewski, J. C. – “Overview of interlayer exchange theory”; Journal of Magnetism and Magnetic Materials, 150 , 13 (1995) Bilinear (AF) coupling Biquadratic coupling Energy power expansion 1 on
  • 6. Interlayer exchange coupling The 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: 3D (general case) decay:
  • 7. Interlayer exchange coupling The RKKY approximation
    • Exchange coupling oscillating as a function of a metallic spacer thickness, for several different potencial barrier values:
    • V = 0.
    • V = 0.3E F .
    • V = 0.6E F .
    • V = 0.9E F .
    • (From Ferreira et al ,
    • J. Phys.: Cond. Matt. 6 , L619 (1994) )
  • 8. Interlayer exchange coupling Temperature and thickness dependence
    • Insulator spacers:
      • Monotonous increase with temperature (thermally activated)
      • Exponential decay with the thickness
    • Conducting metal spacers:
      • Weak J 1 and stronger J 2 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)
  • 9. Interlayer exchange coupling Debate on the coupling behaviour of Fe/FeSi trilayers
    • Different groups show contradicting results
      • Oscillatory or exponential coupling thickness dependence?
    de Vries, J.J.; de Jonge, W.J.M. et al – Phys. Rev. Lett. 78 , 3023 (1997) B ü rgler, D.A.; Gareev, R.R. et al - J. Phys. : Condensed Matter 15 S443 (2003)
  • 10. Samples grown through Molecular Beam Epitaxy
    • Samples consisting of Fe/ 57 FeSi/Fe
      • Varying FeSi thickness
      • Aiming at Fe 0.5 Si 0.5 stoichiometry
    • Trilayers grown epitaxially on an MgO substrate
      • Fe (100) axis parallel to MgO (110)
      • P~10 -10 mBar, T = 150 º C
  • 11. Samples grown through Molecular Beam Epitaxy
    • Intended system is MgO subst Fe 80 A 57 Fe 0.5 Si 0.5 Fe 40 A Au cap
    • 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)
  • 12. Samples grown through Molecular Beam Epitaxy
  • 13. Vibrating Sample Magnetometry
    • Measurement of total sample magnetization for low and high temperatures
    • Physical principle: Faraday Law
    • Suited for magnetic thin films
  • 14. Vibrating Sample Magnetometry Measuring hysterysis curves
    • Characterizing magnetic materials through:
    • Saturation field ( M S )
    • Remanent field ( M R )
    • Coercivity ( H C )
  • 15. Numerical analysis Simulation through energy minimization
    • Finding the energy minimum
    • No analytical general solution
    • Numerical approximations
  • 16. Numerical analysis Simulation of biquadratic coupling t 1 t 2 (pinned)
  • 17. Numerical analysis Simulation of bilinear coupling t 1 t 2 (pinned)
  • 18. Numerical analysis Automatically fitting the data
    • Fitting allows to measure:
      • Bilinear coupling J 1 and biquadratic coupling J 2
      • Cubic crystalline anisotropy K 4
      • Ferromagnetic layers thicknesses ( t 1 , t 2 )
      • 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
  • 19. Results Coupling 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
  • 20. Results Coupling 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
  • 21. Coupling strength – C1208 (14 Å FeSi)
  • 22. Coupling strength – C1208 (14 Å FeSi)
  • 23. Coupling strength Loose spins model (Slonczewski et al ) Interlayer coupling mediated through “loose spins” in the spacer
  • 24. Coupling strength Loose spins model fit to data
  • 25. C1208 (14 Å FeSi) A strange effect
  • 26. 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 J 1 and J 2
  • 27. 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)
  • 28. Thinner samples (C1205 and C1206) Difficulties in finding solutions
  • 29. Thinner samples (C1205 and C1206) Difficulties in finding solutions
  • 30. Coupling strength All 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
  • 31. Coupling strength All samples
  • 32. Coupling strength All samples J 0 = Maximum value (null thickness)  = Coeherence length
  • 33. 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 Fe 0.5 Si 0.5 , 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.
  • 34. 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)
    • B ü rgler, 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 FeSiFe”
  • 35. Rutherford Backscattering Spectrometry (inacabado…)
    • Nuclear technique suited for thin films characterization :
      • Concentration and depth sensitive (profiling through ion energy loss)
    • Rutherford scattering cross-section (CM approximation)
      • Useful for concentration or stoichiometry measurements
  • 36. Rutherford Backscattering Spectrometry Stoichiometry of the Fe 1-x Si x spacer layer (inacabado…)
    • Use of low beam energy, normal incidence geometry and increased detection solid angle for maximizing the cross-section
    Sample 0° 80° He + Detector