Download - The Muppet’s Guide to: The Structure and Dynamics of Solids Neutron Diffraction and Magnetism
The Muppet’s Guide to:The Structure and Dynamics of Solids
Neutron Diffraction and Magnetism
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Neutron ScatteringNeutron scattering is more complicated than x-rays because neutrons are defined both by their wavevector, k, and spin, s.
They can be polarised - ±S
Scattering cross section will depend on both the neutron-nuclear (structure) and the nuclear spin interaction with any magnetic moments
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Atomic Nuclear Factor - StructureVery strong interaction because it is the same force that
bind the nucleus together
Approximate the scattering potential as a Fermi pseudo potential:
22
V b rm
As r0 ~10-15 m the interaction is essentially point like
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Atomic Nuclear Factor - StructureThe spatial density distribution of the nucleus is an infinitesimal point with respect to the neutron wavelength.
Thus, nuclear scattering factor for neutrons is a constant and independent of q.
No sinq/l correction
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X-ray and Neutron comparison:
q exp q r exp q T N j jj T
A b i i
T
q q exp q r exp q Tj jj
A fi i
Neutrons:
X-rays:
Neutrons: Point like, isotope dependent, sensitive to light elements. Contrast varied by isotope substitution.
X-rays: Extended scatters, depends only on number of electrons – can’t ‘see’ light elements. Contrast change through anomalous scattering
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Contrast MatchingUnlike x-rays the neutron cross section is isotope dependent.
Isotope b1H, Hydrogen -3.7406(11)2H, Deuterium 6.671(4)3H, Tritium 4.792(27)
Controlled mixing of 1H and 2H allows contrast to be changed. Very powerful technique for soft condensed matter.
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Magnetic Interactions…The magnetic moment of the neutron interacts with the magnetic moment of any unpaired electrons within a crystal - and this probes the magnetic structure.
energy associated with the neutron magnetic moment, mN in the internal field of the ion, H
SPIN ORBIT
V curlp
n ni B ir Hr
r
r
r2 2
2
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magnetic scattering amplitude for an ion is related to the Fourier Transform of the total magnetisation density, M(r)::
As the magnetism arises from unpaired electrons in outer shells and not the nucleus there is a
dependence on intensity, similar to the sin( ) q / l
used for x-rays
3M q M r exp q ri d r
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Scattering in Reciprocal Space
T
q q exp q r exp q Tj jj
A f i i Peak positions and intensity tell us about the structure:
Peak PositionPeriodicity within the
sample
Peak Width Extent of periodicity
Peak Intensity Atomic positions
Underlying translational symmetry
Particle / Grain size
Order / disorder
T
q exp q r exp q Tj jj
A b i i
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Magnetic Super-Structures
Ferromagnetic:Magnetic and charge have the same unit cell
aa
c
c
Anti-Ferromagnetic: Magnetic and charge have the different unit cells. Magnetic cell double nuclear cell.
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RuSrGdCuO Powder
Magnetic Diffraction Peaks
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Conventional Wisdom
X-raysEnergies typically keV
(Elastic scattering)Scatters from electrons
(High Z materials)Strongly absorbed
Good for imagingHigh FluxHigh resolution
Everyone knows that x-rays are good for studying structure
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Magnetic X-ray Scattering
e spinf r R q f
arg exp[ ]Ch eV
f R q r iq r dr Z
argCh e spinff f
Recall the atomic scattering factor:
Atomic scattering length:
arg ( ) ( )ik r ik r iQ rch e fi
V V
f k V k e V r e V r e
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From and e- to a magnetic atom
M. Blume and D. Gibbs, Phys. Rev. B 37 1779-1789 (1988)
S(q) is the FT of time averaged spin density and L(q) the corresponding FT of the orbital density
2Total ef r R q i L q A S q B
mc
ˆ ˆ ˆ ˆ ˆ ˆB q q q q q q
A and B are vectors which contain the polarisation dependences….
ˆ ˆA q q
As electrons are orbiting a nucleus we need to include orbital as well as spin components in the magnetic term.
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Magnetic X-ray Scattering
M. Blume and D. Gibbs, Phys. Rev. B 37 1779-1789 (1988) & F. de Bergevin PRL 39A(2) 1972
2Total ef r R q i L q A S q B
mc
The maximum intensity is about 2counts / min above the background
Counts in 225 mins. or 3¾hrs Data set takes 4 days to collect
Pre-factor relates reduces magnetic scattering intensity by ~106.
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Realistic Magnetic X-ray scattering
Make electronic interactions sensitive to the magnetic moment.
X-ray Magnetic Circular Dichroism (XMCD)2 step process that couples circular polarised x-rays to a the absorption processes in a magnetic material
X-ray analogue to the Kerr effect
2Total ef r R q i L q A S q B
mc
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Electronic resonancesA core electron is excited and creates a spin polarised photoelectronExchange split final states act as a filter of the spin
Magnetic sensitivity comes through the spin-orbit coupling and exchange and has strong polarisation dependence (MOKE)
Courtesy W. Kuch, Freie Universität Berlin
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XMCD Examples at Resonant Edges
From Magnetism by J. Stöhr and H.C. Siegmann, Springer