Thin Film Magnetism: The Reflectometric Approach

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Thin Film MagnetismThe Reflectometric Approach

• Dénes Lajos Nagy

KFKI Research Institute for Particle and Nuclear
Physicsand Eötvös Loránd University , Budapest,
Hungary
Thin Films as Seen by Local Probes ERASMUS
Intensive Programme Frostavallen (Höör), Sweden,
2-12 May, 2002
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Outline

• A brief survey of thin film magnetism
• exchange coupling in multilayers
• magnetic anisotropy in thin films
• Principles of reflectometry
• Polarised neutron reflectometry (PNR)

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Outline

• Synchrotron Mössbauer reflectometry (SMR)
• depth selectivity
• electronically allowed and forbidden reflections
• time-integral and time-differential SMR
• Antiferromagnetically coupled multilayers
• the spin-flop transition
• domain formation, ripening and coarsening
• Summary

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Exchange coupling in multilayers

• Within a single layer rigid ferromagnetic
  coupling.

• J1 gt 0 ferromagneticJ1 lt 0 antiferromagnetic
  coupling M(H) is linear up to
  saturation

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Exchange coupling in multilayers

• J2 lt 0 preferred 90 orientation M(H) is
  nonlinear around saturation

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Magnetic anisotropy in thin films

• Magnetocrystalline anisotropy The crystal
  electric field splits the orbital levels.
  Therefore, the spin-orbit coupling leads to
  preferred orientation of the magnetisation (easy
  axes).

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Magnetocrystalline anisotropy in thin films

• Volume anisotropy The anisotropy energy follows
  the symmetry of the crystal lattice. In case of
  thin films, this leads to in-plane anisotropy.
  The in-plane symmetry may be, e.g.
• uniaxial, e.g. Fe(211) grown on MgO(110),
• fourfold, e.g. Fe(110) grown on MgO(001),
• etc.

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Magnetic anisotropy in thin films

• Surface and interface anisotropy The symmetry of
  the crystal is broken at the surface and at
  interfaces leading to an axial component of the
  crystal electric field with its axis
  perpendicular to the surface or the interface.
  Via spin-orbit coupling, this leads to a
  preferred out-of-plane magnetisation.
• Deformation anisotropy The relaxation of the
  lattice at the surface or the lattice mismatch at
  epitaxial interfaces results in this kind of
  anisotropy via magnetoelastic effects.

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Magnetic anisotropy in thin films

• The layer thickness and temperature dependence of
  the exchange coupling and anisotropy leads to a
  variety of magnetic and domain structures in thin
  films and multilayers at different layer
  thickness, temperature and magnetic field. The
  competition of in-plane and out-of-plane
  anisotropy may lead to the spin-reorientation
  transition.
•   

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Reflection geometry depth selectivity
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Neutron, X-ray and Mössbauer reflectometry

• Specular reflected beam The intensity rapidly
  decreases for ? gt ?c with increasing scattering
  vector Q  2k  sin ?.

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Neutron, X-ray and Mössbauer reflectometry

• In a stratified medium reflected and refracted
  beams appear at each interface ? interference.
• The reflected intensity R(Q) ?r(Q)?2 bears
  information on the depth profile of the index of
  refraction n(z). In frames of a given model for
  the stratified system, n(z) can be reconstructed
  from R(Q), e.g., with the method of the
  characteristic matrices.

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Neutron, X-ray and Mössbauer reflectometry
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Neutron reflectometrythe scattering amplitudes
for neutron spin perpendicular to
magnetisationspin-flip scattering!
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X-ray and Mössbauer reflectometrythe scattering
amplitudes
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Mössbauer reflectometry the optical model
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Polarised neutron scattering (H. Zabel)
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Polarised neutron scattering (H. Zabel)
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Polarised neutron reflectometry (H. Zabel)
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Polarised neutron reflectometry (H. Zabel)
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Polarised neutron reflectometry (H. Zabel)
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Polarised neutron reflectometry (H. Zabel)
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Polarised neutron reflectometry (H. Zabel)
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Mössbauer reflectometry why at synchrotrons?

• Due to the small (1-2 cm) size of the sample and
  the small (1-10 mrad) angle of grazing incidence,
  the solid angle involved in a Mössbauer
  reflectometry experiment is 10-5 Þ only 1 photon
  from 106 is used in a conventional source
  experiment. In contrast, the highly collimated SR
  is fully used.
• The linear polarisation of the SR allows for an
  easy determination of the magnetisation direction.

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Arrangement of an SMR experiment
Q/2Q-scan qz-scan
w-scan qx-scan
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Depth selective phase analysis with SMR

• By changing ? around ?c one can adjust the
  depth at which the thin film is sampled.
  Example oxidised 57Fe films (V.G. Semenov et al.)

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Electronically allowed and forbidden reflections
Float glass/57Fe(22.5 Å)/56Fe(22.5 Å)/57Fe(22.5
Å)15/Al(90 Å)
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Time-integral and time-differential SMR

• Time-integral SMR total number of delayed
  photons from t1 to t2 as a function of ? (delayed
  ?2? scan).
• t1 deadtime, bunch quality
• t2 bunch-repetition time
• As a rule, a ?2? scan of the prompt photons
  (i.e., conventional x-ray reflectometry) is
  recorded along with a time integral SMR scan.

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Time-integral and time-differential SMR

• Time-differential SMR time response measurement
  in a fixed ?2? geometry. hyperfine
  interaction ? quantum beats
• Full SMR
• prompt ?2? scan
• delayed time integral ?2? scan
• a set of time response reflectivity measurements
• All these data should be evaluated
  simultaneously.

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The bulk spin flop in AF-coupled multilayers

• Fourfold in-plane magnetocrystalline anisotropy.
• All layer magnetisations are aligned along the
  same easy axis.
• At a moderate increasing magnetic field parallel
  to the easy axis in which the layer
  magnetizations lay, all magnetisations jump to
  the perpendicular easy direction.
• The new alignment is retained in remanence.

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Bulk spin flop in an epitaxialMgO(001)57Fe(26Å)/
Cr(13Å)20 multilayer
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Magnetisation and SMR field dependence of
aMgO(100)57Fe(26Å)/Cr(13Å)20 multilayer during
the bulk spin flop
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Formation of patch domains...
in Greek mythology
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Antiferromagnetic multilayer leaving magnetic
saturation
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Formation of two kinds of domains
z
y
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Domain formation on leaving saturation
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From saturation to remanencethe domain ripening

• The correlation length of the domains immediately
  after their formation is equal to the lateral
  structural correlation length of the multilayer
  (terrace length, 50 nm). Still, in remanence we
  observe mm-size domains. Why?
• The driving force of the spontaneous change of
  the domain size in decreasing field is the
  domain-wall energy. The sign of the size change
  depends on the scaling law of the domain-wall
  density inclusions (µ x) Þ decreasing domain
  size chessboard (µ 1/x) Þ increasing domain size

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Domain ripening the final state

• The correlation length of the primary domains in
  remanence is determined by the domain-wall-energy-
  driven and coercivity-limited spontaneous growth
  (ripening). Ripening takes place when the applied
  magnetic field is decreased from the saturation
  region to zero.

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Domain ripening off-specular SMR
Decreasing the field and having left the
saturation region, the AF peak appears with
increasing intensity. In Hext 0.3 T the domain
size is x 500 nm. On decreasing the field to 0,
the domain size increases tox 2.6 mm. Domain
ripening is an irreversible process the domain
size no longer changes in increasing or
decreasing field.
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Formation of very large domains (coarsening)

• After ripening, the domain size in remanence is
  expected to be always about 500 nm 5 mm.
• This is not the case! The domain size is a
  complicated function of the magnetic prehistory.
  Under favourable conditions, even much larger
  domains (up to mm?) may be formed.

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Spin-flop-induced domain coarsening (SMR)
MgO(001)57Fe(26Å)/Cr(13Å)20 2Q _at_ AF reflection
Correlation lengthx 1/Dqx
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Spin-flop induced domain coarsening (PNR)
7 mT
14.2 mT
35 mT
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Domain coarsening on spin flop

• Coarsening on spin flop is an explosion-like
  90-deg flop of the magnetization annihilating
  primary 180-deg walls. It is limited neither by
  an energy barrier nor by coercivity.
  Consequently, the correlation length of the
  secondary patch domains x may become comparable
  with the sample size.

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Domain coarsening during spin flop
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Summary

• Reflectometry is a powerful tool for studying the
  depth profile of the scattering length density in
  thin films.
• The scattering length density is sensitive to the
• electron density (non-resonant x-rays),
• kind of the isotopes, as well as the strength and
  direction of the magnetisation (thermal
  neutrons),
• electron density, as well as the strength and
  orientation of the hyperfine interactions
  (nuclear resonant / Mössbauer x-rays).

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Summary

• In neutron reflectometry, the antiferromagnetic
  structure of a coupled magnetic multilayer
  results in half-order Bragg-peaks.
• In polarised neutron reflectometry (PNR) with
  spin analysis
• the field- (and neutron-spin-) parallel
  (ferromagnetic) magnetisation of a magnetic
  multilayer results in non-spin-flip scattering,
• the field- (and neutron-spin-) perpendicular
  (antiferromagnetic) magnetisation of a magnetic
  multilayer results in spin-flip scattering.

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Summary

• In (synchrotron) Mössbauer reflectometry (SMR),
  the antiferromagnetic structure of a coupled
  magnetic multilayer results in half-order
  Bragg-peaks, provided that (for 1/23/2 SMR) the
  magnetisation is parallel to the photon
  propagation direction.
• Off-specular (diffuse) reflectivity is sensitive
  to the in-plane autocorrelation of the scattering
  length density. Off-specular reflectivity
  measured at a half-order reflection maps the
  antiferromagnetic domain structure of a coupled
  magnetic multilayer (both for PNR and SMR).

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