Impulsive electron scattering

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Impulsive electron scattering

• Maarten Vos
• Thanks to
• Co-workers Cameron Bowles
• Anatoli Kheifets
• Michael Went
• Funding Australian Research Council

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Impulsive Collisions

• Collision mechanism very simple
• Plane wave impulse approximation valid
• Binary collisions, remainder of target is
  spectator.
• In short billiard ball physics
• Why study these simple collisions?
• We can learn something about the target!
• Three examples
• -Electron Momentum Spectroscopy from Si crystals
• -scattering of polarized electrons
• -scattering of electrons from nuclei

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K1, E1
Energy Conservation E0 - e E1 E2 Momentum
Conservation K0 q k1 k2
K0, E0
K2, E2
Particle in target with momentum q, binding
energy e before the collision
-EMS coincidence measurement, we know K0, E0,
K1, E1, K2, E2 and determine probability that
target particle (electron) has momentum q and
energy e. -Compton scattering we know K0, E0,
K1, E1 but not E2, k2 One still get some
information about target particle with mass m E0
- E1 ( k0 k1 ) 2 / 2m ( k0 k1 ) q / m
If target mass m large (scattering from atom)
then E0 - E1 small
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EMS of Si single crystal
First example

• Goal Illustrate the relation between crystal
  momentum and real momentum

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Under normal operating conditions we measure
target electrons with momentum px0 pz0, py
c(f1-f2) If we use the deflectors then we can
rotate the analyzers and measure target
elec-trons with momentum pxa, pzb, py
c(f1-f2)
What happens if we measure along lines that
differ by a reciprocal lattice vector?
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Dashed lines no significant density
expected Full line expected density proportional
to line thickness
Energy(eV)
Typical EMS results Band structure has more
branches than we observe. All bands below the
Fermi level are occupied. So where can we see
the other bands?
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010
Line b sifted by 101 Line c shifted by 200
Reciprocal Lattice Si (BCC)
001
100
Solid lines free electron approximation Dashed
lines LMTO band structure calc.
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lt010gt direction 101 offset
lt010gt direction
lt010gt direction 200 offset
G
G
G
G
G
G
G
G
X
X
X
X
X
X
X
a b
c
E(G2,5)
0
E(X4)
2.8
Binding Energy (eV)
E(X1)
7.8
E(G1)
11.9
1.2 0 1.2
1.2 0 1.2
1.2 0 1.2
py(a.u.)
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Band 1
Band 2
Band 3
Band 4
Dashed unoccupied
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line a no shift line b 100 shift line c
110 shift line d 111 shift
Solid lines free electron approximation Dashed
lines LMTO band structure calc.
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lt110gt direction 001 offset
lt110gt direction 111 offset
lt110gt direction
G
G
G
G
G
G
X
X
X
X
X
X
G
G
G
G
X
X
X
X
E(G2,5)
0
2.8
E(X4)
Binding Energy (eV)
E(X1)
7.8
11.9
E(G1)
0.87 0 0.87
0.87 0 0.87
0.87 0 0.87
0.87 0 0.87
py (a.u.)
lt110gt
lt001gt
1.7 a.u.
origin
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Measurements for noble metals
With increasing Z diffraction becomes more and
more important and it becomes more and more
difficult to determine which band is occupied in
which Brillouin zone
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Spin effects
second example

• Can we obtain information about spin densities?
• Cross section for electron-electron scattering
• K k0 - k1, S k0 k2, q1,2 angle between
  projectile and target electron spin
• Cross section 0 if projectile and target have
  same spin orientation and SK!
• This applies for both left and right detectors
• Cross section of electron-nucleus scattering
• depends on spin due to spin-orbit interaction.
• As angular momentum is different for scattering
  to left and right, count
• rate will fluctuate out of phase for both
  detectors

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Determine Polarization using Au foil
left
right
Polarisation close to 20 using a 830nm laser
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Anisotropy of a magnetised Fe sample
Compton Profile
Compton profile is measured by varying E1 E0 - E1
(k0 k1)2 / 2m q (k0 k1)2
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It looks like many of the electrons at 0.5E0 are
due to electron- nucleus collision rather than
electron-electron collisions!
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How is this possible? It is highly unlikely for
an elastically scattered electron to lose 25 keV
by inelastic excitations in a thin (100 Å) thick
film Idea 1 Purely experimental electrons
with energy of 50 keV are detected Idea
2 More Physics Bremsstrahlung is emitted when
electron is accelerated (i.e. deflected over a
large angle) by the nucleus and 25 keV electron
enters analyser
Channel plate
Secondary electron
Ñn
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Spin asymmetry averaged over both detectors is
close to the magentic Compton profile as obtained
from circular polarised X-ray scattering using a
synchrotron. (Our measurement is not on an
absolute scale (yet)) The momentum resolution
from an electron scattering experiment should be
better than that from X-ray measurements, but
multiple scattering effects will be worse.
0
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Scattering from atoms
third example

• -Can we resolve the energy transfer
• Energy transfer (k0-k1)2 / 2M with M mass of
  atom,
• usually considered infinite in electron
  scattering.
• -Is the plain wave impulse approximation valid?
• Calculated energy transfer of the order of 1 eV
• -What kind of information do we obtain?

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K
K
Graphite anisotropic (layered) material.
Evaporate 1 Å of Au on thin graphite
film. Measured with momentum transfer along and
perpendicular to the graphite planes. -two peaks
(after Au evaporation). -separation of peaks
close to calculated one for C-Au. -C peak broader
than Au peak (Doppler broadening resolved for
C) -C peak width depends on orientation.
(vibrational anisotropy resolved) -C peaks
asymmetric, peak position depends on orientation
(failure impulse approximation).
Au
a
C
b
Energy Loss (eV)
40 keV elastic scattering Scattering angle 450
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These effects are not restricted to electron
scattering
Neutron scattering at ISIS M P Paoli et al 1988
J. Phys. C Solid State Phys. 21 3633 (1988)
High energy photoemission at SPRING-8 Y. Takata
et al, Phys. Rev. B 75, 233404 (2007)
Difference in peak shift and peak asymmetry are
interpreted as a failure of the impulse
approximation. Its validity depends on the
scattering time.
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-Increased scattering angle from 450 to 1200,
improving the peak separation 6-fold. -Peak
separations now very well described by
calculations assuming collision between free
particles. -Area ratio is more problematic.
(discrepancies up to 20-30), using calculated
cross sections including screening effects etc.
(we use ELSEPA package from Salvat et al)
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Summary -EMS of Silicon crystals was used to
illustrate the relation between crystal momentum
and real momentum. More extensive description
Phys. Rev. B 73 085207 (2006) -It appears
possible to measure magnetic Compton profiles
using electron scattering, but separation of
electron-electron and electron-nucleus collision
not as straight forward as expected. (Thesis
Cameron Bowles, paper to be submitted)
-Electron-nucleus collision can, at high
momentum transfer, also be described as a
collision between free particles. Graphite
story Phys. Rev. B 74 205407 (2006) Large angle
elastic scattering Applied Physics letters 90
072104 (2007) -electron Rutherford
backscattering possible new analytical technique?
Simple impulsive collisions can teach us a lot
of interesting physics