Ab-initio výpocty magnetismu clusteru a nanostruktur:

Transkript

Ab-initio výpočty
magnetismu clusterů a nanostruktur:
Proč a jak?
Ondřej Šipr
Fyzikálnı́ ústav Akademie věd České republiky, Praha
http://www.fzu.cz/~ sipr
16. března 2010 / Odborný seminář Nové technologie LS 2010
Osnova
Magnetismus: Kdo je kdo, co je co
Motivace: Proč nanosystémy ?
Magnetismus volných a adsorbovaných clusterů — srovnánı́
Rentgenová absorpčnı́ spektroskopie snadno a rychle
Součtová pravidla pro XMCD spektroskopii: důvěřuj, ale prověřuj
Osnova
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Osnova
Where does magnetism come from?
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Classically: Magnetic field is something produced by moving
electric charges that affects other moving charges
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Special relativity: Magnetism is a fictitious force needed to
guarantee Lorentz invariance when charges move
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One observer may perceive a magnetic force where a moving
observer perceives only an electrostatic force
Dealing with magnetism in the framework of Dirac equation
(instead of Schrödinger equation) is ideologically simple
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Magnetický moment
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Magnetický moment µ je mı́rou snahy zmagnetizovaného
objektu orientovat se v souhlau s vnějšı́m magnetickým polem
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Moment sı́ly τ působı́cı́ na magnetický moment
v magnetickém poli:
τ = µ×H
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Potenciálnı́ energie magnetického momentu v magnetickém
poli:
U = −µ · H
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Přı́klad: Pro uzavřenou smyčku
µ = µ0 I S
Magnetický moment
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τ = µ×H
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poli:
U = −µ · H
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µ = µ0 I S
Magnetický moment
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τ = µ×H
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poli:
U = −µ · H
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µ = µ0 I S
Magnetický moment
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τ = µ×H
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poli:
U = −µ · H
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µ = µ0 I S
Two ways of moving an electron
(A quick and dirty introduction to magnetism)
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Orbiting
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Spinning
Orbital magnetic moment
Classical expression for magnetic moment:
µorb = µ0 I S
=⇒
µorb = − µB S
where µB is Bohr magneton
µB ≡
eµ0 ~
2me
and L is angular momentum devided by ~.
For electron orbiting around an atom, the z-component of orbital
magnetic moment is thus
(z)
µorb = − mℓ µB ,
where mℓ is the magnetic quantum number.
Orbital magnetic moment
Classical expression for magnetic moment:
µorb = µ0 I S
=⇒
µorb = − µB S
where µB is Bohr magneton
µB ≡
eµ0 ~
2me
and L is angular momentum devided by ~.
For electron orbiting around an atom, the z-component of orbital
magnetic moment is thus
(z)
µorb = − mℓ µB ,
where mℓ is the magnetic quantum number.
Spin magnetic moment
Electron spin: Picture of a rotating charged sphere fails. . .
µorb = − µB L
vers.
µspin = − 2 µB S
L is angular momentum connected with orbital motion
S is angular momentum connected with “spinning”
For electron around an atom, the z-component of spin-related
angular momentum is
S (z) = ±
1
~ ,
2
hence we get for a z-component of spin-related magnetic moment
(z)
µspin = ± µB .
Spin magnetic moment
Electron spin: Picture of a rotating charged sphere fails. . .
µorb = − µB L
vers.
µspin = − 2 µB S
L is angular momentum connected with orbital motion
S is angular momentum connected with “spinning”
For electron around an atom, the z-component of spin-related
angular momentum is
S (z) = ±
1
~ ,
2
hence we get for a z-component of spin-related magnetic moment
(z)
µspin = ± µB .
Magnetická anizotropie
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Magnetické vlastnosti materiálů závisı́ na směru (orientaci)
Energie systému závisı́ na směru spontánnı́ magnetizace
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Různé zdroje (druhy) magnetické anizotropie
Magnetická anizotropie
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Magnetické vlastnosti materiálů závisı́ na směru (orientaci)
Energie systému závisı́ na směru spontánnı́ magnetizace
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Různé zdroje (druhy) magnetické anizotropie
Tvarová magnetická anizotropie
Energie interakce mezi dipóly:
Edip−dip
1 X 1
= −
2πµ0
rij3
i 6=j
"
(rij · µi )(rij · µj )
µi · µj − 3
rij2
Protáhlé nebo planárnı́ objekty se snažı́
orientovat magnetizaci rovnoběžně
s rovinou.
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Magnetokrystalická anizotropie
Orientace magnetizace ve směru preferovaném geometrickou
strukturou krystalu
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U normálnı́ch (3D) látek obvykle malá
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U povrchů, vrstev, clusterů může být vysoká
strukturou krystalu
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strukturou krystalu
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Konkurenčnı́ boj anizotropiı́
Tvarová anizotropie chce magnetizaci orientovat “in-plane”,
magnetokrystalická anizotropie působı́ (zde) “out-of-plane”,
výsledek závisı́ na tom, kdo je silnějšı́.
Osnova
Magnetism of Fe atom
Magnetic properties of atoms are governed by Hund rules
Electron configuration: 3d 6 4s 2
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Spin magnetic moment: µspin = 4 µB
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First P
Hund rule: Total atomic spin quantum number
S = ms is maximum (as long as it is compatible with
Pauli exclusion principle)
Orbital magnetic moment: µorb = 2 µB
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Second
P Hund rule: Total atomic orbital quantum number
L = mℓ is maximum (as long as it is compatible with
Pauli exclusion principle and first Hund rule)
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First P
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Second
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First P
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Second
Magnetism of bulk Fe crystal
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Generally: Magnetism is suppressed in the bulk
(with respect to atomic case)
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Intuitively: Electron are not free to orbit around atoms
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Spin magnetic moment is µspin ≈ 2.2 µB per atom
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Orbital magnetic moment is quenched (outright zero in
non-relativistic case)
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Surfaces are magnetism-friendly
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Atoms at surfaces exhibit some atomic-like
characteristics
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Spin magnetic moment is larger than in bulk; for Fe it is
µspin ≈ 2.5–3.0 µB per atom
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The orbital magnetic moment is increased by an even larger
percentage, µorb ≈ 0.07–0.12 µB per atom
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characteristics
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characteristics
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Magnetism of iron: summary
atom
surface
bulk
µspin = 4 µB
µspin = 2.5–3.0 µB
µspin = 2.2 µB
µorb = 2 µB
µorb = 0.07–0.12 µB
µorb = 0.05 µB
A co anizotropie malých systémů ?
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Magnetická anizotropie vrstev je řádově většı́ než anizotropie
krystalů
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Magnetická anizotropie clusterů je (až) řádově většı́ než
anizotropie vrstev.
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⇒ Kdož máš zájem na vysoké anizotropii, vrhni se na
nanostruktury
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krystalů
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anizotropie vrstev.
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nanostruktury
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krystalů
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anizotropie vrstev.
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nanostruktury
K čemu je anizotropie dobrá ?
Obracet směr spinu je energeticky řádově snažšı́ než přidávat či
odebı́rat elektrony −→ spintronika !
Why all the fuss with µorb ?
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µorb is small but important !
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It is a manifestation of spin-orbit coupling, which is the
mechanism behind the magnetocrystalline anisotropy
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Under certain assumptions, magnetocrystalline anisotropy
energy (MAE) can be estimated as
k
∆EMAE = const × µorb − µ⊥
orb
k
where µorb and µ⊥
orb are orbital magnetic moments for two
perpendicular directions of the magnetization M
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k
orb
k
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k
orb
k
Osnova
Clusters: Who they are?
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Free clusters — giant molecules, surrounded by vacuum
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Supported clusters — adsorbed on a surface
Clusters: Who they are?
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Free clusters — giant molecules, surrounded by vacuum
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Supported clusters — adsorbed on a surface
Comparing free and supported clusters
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How do the magnetic properties change if clusters are
deposited on a substrate ?
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Take analogous systems (identical sizes, identical geometries)
and have a look
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Focus rather on the trends than on particular values
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and have a look
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and have a look
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Calculational procedure for supported clusters
Impurity Green function method
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Calculate electronic structure of the “host” system (clean
surface)
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Supported clusters are treated as a perturbation to the clean
surface and the
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Green’s function of the new system (cluster plus substrate) is
obtained by solving the Dyson equation.
Focus on planar FeN on Ni(001) and CoN clusters on Au(111)
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surface)
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surface and the
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surface)
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surface and the
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surface)
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surface and the
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Shapes of clusters (free or supported)
FeN / Ni(001)
CoN / Au(111)
Only nearest-neighbor substrate atoms are shown.
Average magnetic moments
2.3
Co
3.1
supported
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Supported
clusters: nearly
monotonous decay
of µspin and µorb
with N
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Free clusters:
quasi-oscillations,
quite large
amplitides
2.2
in Co spheres
3.0
2.9
2.8
2.1
2.0
1.9
spin
spin
in Fe spheres
spin
1.8
Fe
2.7
spin
1.7
supported
1.6
2.6
2
4
6
8
10
2
Number of atoms in cluster
4
6
8
0.9
0.5
0.8
supported
supported
0.7
0.2
in Co spheres
in Fe spheres
0.3
orb
0.4
Fe
orb
orb
Co
0.6
orb
0.5
0.4
0.3
0.1
0.2
0.0
2
4
6
8
10
2
4
6
8
Average magnetic moments
2.3
Co
free
supported
3.1
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Supported
clusters: nearly
monotonous decay
of µspin and µorb
with N
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Free clusters:
quasi-oscillations,
quite large
amplitides
2.2
in Co spheres
3.0
2.9
2.8
2.1
2.0
1.9
spin
spin
in Fe spheres
spin
1.8
Fe
2.7
spin
free
supported
1.7
1.6
2.6
2
4
6
8
10
2
4
6
8
0.9
0.5
free
supported
0.7
0.2
in Co spheres
in Fe spheres
orb
0.4
0.3
free
supported
0.8
Fe
orb
orb
Co
0.6
orb
0.5
0.4
0.3
0.1
0.2
0.0
2
4
6
8
10
2
4
6
8
3.0
2.8
2.6
2.4
2.2
B]
2.2
Co
supported
2.0
2
3
4
5
6
7
1.8
spin
2
3
4
5
6
7
8
9
in Co spheres [
Fe
supported
3.2
spin
in Fe spheres [
B]
Effect of coordination on µspin
1.6
2.0
0
2
4
Number of neighboring Fe atoms
0
2
4
Number of neighboring Co atoms
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µspin decreases if coordination number increases
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Estimates of µspin possible for large clusters
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For free clusters, big scatter of data
6
3.0
2.8
2.6
2.4
2.2
B]
2.2
Co
supported
2.0
2
3
4
5
6
7
1.8
spin
2
3
4
5
6
7
8
9
in Co spheres [
Fe
supported
3.2
spin
in Fe spheres [
B]
1.6
2.0
0
2
4
0
2
4
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6
3.0
2.8
2.6
2.4
2.2
B]
2.2
Co
supported
2.0
2
3
4
5
6
7
1.8
spin
2
3
4
5
6
7
8
9
in Co spheres [
Fe
supported
3.2
spin
in Fe spheres [
B]
1.6
2.0
0
2
4
0
2
4
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6
3.0
2.8
2.6
2.4
2.2
B]
2.2
Co
supported
2.0
2
3
4
5
6
7
1.8
spin
2
3
4
5
6
7
8
9
in Co spheres [
Fe
supported
3.2
spin
in Fe spheres [
B]
1.6
2.0
0
2
4
0
3.0
2.8
2.6
2.4
2
4
6
B]
2.2
Co
free
2.0
1.8
spin
in Co spheres [
Fe
free
3.2
spin
in Fe spheres [
B]
2.2
1.6
2.0
0
2
4
0
2
4
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6
Comparison between free and supported clusters: summary
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Substrate acts as an adult supervisor for the free clusters
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It suppresses the tendency of magnetic moments to oscillate
with cluster size
It makes µspin to depend linearly on the coordination number
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For free clusters, this trend appears as well but only for
spherical and/or larger clusters
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with cluster size
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with cluster size
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Osnova
Clusters and magnetism: Problems . . .
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Magnetic properties of large assemblies of clusters are
macroscopic: no principal problems with measuring them
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To understand nanomagnetism, one needs to study individual
small systems
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Magnetization of individual clusters (of just few atoms)
cannot be measured by macroscopic methods
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Recent progress in studying magnetism of clusters is, to a
large extent, associated with spectroscopy
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small systems
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small systems
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small systems
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X-ray absorption spectroscopy howto
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X-rays go in, x-rays go out, absorption coefficient is measured
as a function the energy of the incoming x-rays
x-rays in
x-rays out
sample
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Most of the absorption goes on account of the photoelectric
effect on core electrons
X-ray absorption spectroscopy howto
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X-rays go in, x-rays go out, absorption coefficient is measured
as a function the energy of the incoming x-rays
x-rays in
x-rays out
sample
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Most of the absorption goes on account of the photoelectric
effect on core electrons
Absorption via core electron excitation
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By tuning the energy of incoming x-rays,
electrons from one core level only
participate
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Chemical selectivity
Dipole selection rule
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Angular-momentum selectivity
(whether they are s, p, d states. . . )
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participate
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participate
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participate
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Absorption edges (Absorpčnı́ hrany)
hrana
excitovaný elektron
K
L1
L2
L3
1s
2s
2p1/2
2p3/2
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Zvyšuje-li se energii fotonů, absorpčnı́ koeficient klesá
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Vzroste-li energie tak, že může dojı́t k excitovánı́ dalšı́ho
vnitřnı́ho elektronu, absorpčnı́ koeficient se skokem zvýšı́
hrana
K
L1
L2
L3
1s
2s
2p1/2
2p3/2
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hrana
K
L1
L2
L3
1s
2s
2p1/2
2p3/2
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Jemná struktura absorpčnı́ hrany: EXAFS a ti druzı́
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Nı́zké energie fotoelektronu (do ∼50 eV)
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XANES (X-ray Absorption Near Edge Structure)
NEXAFS (Near Edge X-ray Absorption Fine Structure)
Vysoké energie fotoelektronu (∼100–1000 eV)
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EXAFS (Extended X-ray Absorption Fine Structure)
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Určovánı́ struktury, zejména nekrystalických látek
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XMCD howto
XMCD (X-ray Magnetic Circular Dichroism):
sample is magnetized, measure the difference between absorption
of left and right circularly polarized x-rays
photon helicity
x-rays
parallel
magnetization
antiparallel
µXMCD = µ(+) − µ(−)
XMCD howto
XMCD (X-ray Magnetic Circular Dichroism):
sample is magnetized, measure the difference between absorption
of left and right circularly polarized x-rays
photon helicity
x-rays
parallel
magnetization
antiparallel
µXMCD = µ(+) − µ(−)
L2,3 edge of magnetic systems
L3
EF
L2,3-edge XANES
6
L3
isotropic
absorption
4
2p3/2
2p1/2
XMCD sum rules:
By adding, subtracting and
dividing the peak areas,
chemically-specific µspin , µorb
and µorb /µspin can be obtained
L2
2
0
2
L2,3-edge XMCD
L2
(transition metals)
0
difference
(+)
(-)
-
-2
-4
-10
0
10
20
30
energy [eV]
Z
Z
(d)
(d)
(∆µL3 − 2∆µL2 ) dE
∼
(∆µL3 + ∆µL2 ) dE
∼
µspin + 7Tz
(d)
3nh
(d)
µorb
(d)
2nh
L3
EF
L2,3-edge XANES
6
L3
isotropic
absorption
4
2p3/2
2p1/2
XMCD sum rules:
L2
2
0
2
L2,3-edge XMCD
L2
(transition metals)
0
difference
(+)
(-)
-
-2
-4
-10
0
10
20
30
energy [eV]
Z
Z
(d)
(d)
(∆µL3 − 2∆µL2 ) dE
∼
(∆µL3 + ∆µL2 ) dE
∼
µspin + 7Tz
(d)
3nh
(d)
µorb
(d)
2nh
L3
EF
L2,3-edge XANES
6
L3
isotropic
absorption
4
2p3/2
2p1/2
XMCD sum rules:
L2
2
0
2
L2,3-edge XMCD
L2
(transition metals)
0
difference
(+)
(-)
-
-2
-4
-10
0
10
20
30
energy [eV]
Z
Z
(d)
(d)
(∆µL3 − 2∆µL2 ) dE
∼
(∆µL3 + ∆µL2 ) dE
∼
µspin + 7Tz
(d)
3nh
(d)
µorb
(d)
2nh
What can XMCD do for us?
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Through the sum rules, XMCD can inform about µspin and
µorb separately
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For compounds, magnetic state of each element can be
explored separately
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Employing sum rules on experimental data may require
substantial theoretical input
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µorb separately
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explored separately
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µorb separately
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explored separately
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Problems with sum rules
Approximations involved in its derivation:
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Transition to a well-defined single band
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Core hole neglected
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...
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Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
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Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
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Core hole neglected
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...
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Core hole neglected
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...
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Core hole neglected
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...
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Core hole neglected
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...
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Core hole neglected
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...
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Tz term: A feature, not a bug !
3
IA
(∆µL3 − 2∆µL2 ) dE =
µspin + 7Tz
nh
integrated isotropic absorption spectrum
d component of the local spin magnetic moment
number of holes in the d band
d component of magnetic dipole operator
IA
µspin
nh
Tz
Tz =
Z
D
T̂z
E
=
1
2
[σ − 3r̂(r̂ · σ)]z
Tz is a measure of the asphericity of spin magnetization
µspin can be obtained only in combination with 7Tz !
3
IA
(∆µL3 − 2∆µL2 ) dE =
µspin + 7Tz
nh
IA
µspin
nh
Tz
Tz =
Z
D
T̂z
E
=
1
2
[σ − 3r̂(r̂ · σ)]z
3
IA
(∆µL3 − 2∆µL2 ) dE =
µspin + 7Tz
nh
IA
µspin
nh
Tz
Tz =
Z
D
T̂z
E
=
1
2
[σ − 3r̂(r̂ · σ)]z
Osnova
Does Tz term really matter ?
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For bulk systems it is usually negligible
◮
For surfaces, monolayers or wires, absolute value of 7Tz is
about 20 % of µspin
◮
For investigating trends of µspin within a series of systems,
what matters is how Tz varies from one system to another
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If variations in Tz are small, neglect of Tz causes just an
overall shift of the deduced µspin
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Could Tz vary in such a way that the overall trends
of µspin +7Tz and µspin would be quite different ?
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To find out wheter Tz may turn nasty or not
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Take a series of supported clusters of different sizes
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For each cluster size, evaluate average of d components
of µspin
N
1 X (j)
µspin
N
j=1
and of [µspin + 7Tz ]/nh
(j)
(j)
N
1 X µspin + 7Tz
(j)
N
n
j=1
◮
h
Compare how µspin and [µspin + 7Tz ]/nh depend on the
cluster size
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of µspin
N
1 X (j)
µspin
N
j=1
(j)
(j)
N
1 X µspin + 7Tz
(j)
N
n
j=1
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h
cluster size
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of µspin
N
1 X (j)
µspin
N
j=1
(j)
(j)
N
1 X µspin + 7Tz
(j)
N
n
j=1
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h
cluster size
◮
◮
of µspin
N
1 X (j)
µspin
N
j=1
(j)
(j)
N
1 X µspin + 7Tz
(j)
N
n
j=1
◮
h
cluster size
Systems
Clusters: FeN , CoN
Substrates: Ni(001), Au(111)
Clusters on Au(111)
N=1–7
Clusters on Ni(001)
N=1–9
Results: µspin and [µspin + 7Tz ]/nh
0.9
0.8
0.7
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
1
3
5
7
9
[
B]
3.2
spin
3.0
2.8
Fe on Ni
1 3 5 7 9
no. of Fe atoms N
FeN /Ni(001)
CoN /Ni(001)
FeN /Au(111)
CoN /Au(111)
B]
0.7
(
0.7
+ 7 Tz) / nh [
0.8
0.8
spin
0.9
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
1
3
5
7
9
1
3
5
7
9
2.1
B]
2.0
[
[
B]
3.2
spin
spin
3.0
1.9
2.8
Fe on Ni
1.8
Co on Ni
1 3 5 7 9
no. of Fe atoms N
1 3 5 7 9
no. of Co atoms N
FeN /Ni(001)
CoN /Ni(001)
FeN /Au(111)
CoN /Au(111)
1
3
5
7
B]
9
1
3
5
7
5
7
B]
[
B]
1.9
spin
spin
3.0
2.8
1.8
3
3.4
2.0
[
B]
[
0.7
1
3.2
spin
0.8
9
2.1
Fe on Ni
0.9
(
spin
+ 7 Tz) / nh [
B]
0.7
(
0.7
+ 7 Tz) / nh [
0.8
0.8
spin
0.9
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
3.2
3.0
Co on Ni
Fe on Au
2.8
1 3 5 7 9
no. of Fe atoms N
1 3 5 7 9
no. of Co atoms N
1 3 5 7
no. of Fe atoms N
FeN /Ni(001)
CoN /Ni(001)
FeN /Au(111)
CoN /Au(111)
B]
+ 7 Tz) / nh [
spin
0.8
0.7
0.8
0.6
0.4
(
B]
0.9
(
spin
+ 7 Tz) / nh [
B]
0.7
(
0.7
+ 7 Tz) / nh [
0.8
0.8
spin
0.9
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
0.2
7
9
1
3
5
7
9
1
2.1
1.9
spin
spin
3.0
spin
7
1
2.8
3.2
3.0
Co on Ni
3
5
7
2.1
B]
[
B]
[
B]
[
2.0
1.8
5
3.4
3.2
Fe on Ni
3
B]
5
2.0
[
3
spin
1
Fe on Au
1.9
1.8
Co on Au
2.8
1 3 5 7 9
no. of Fe atoms N
1 3 5 7 9
no. of Co atoms N
1 3 5 7
no. of Fe atoms N
FeN /Ni(001)
CoN /Ni(001)
FeN /Au(111)
1 3 5 7
no. of Co atoms N
CoN /Au(111)
B]
+ 7 Tz) / nh [
spin
0.8
0.7
0.8
0.6
0.4
(
B]
0.9
(
spin
+ 7 Tz) / nh [
B]
0.7
(
0.7
+ 7 Tz) / nh [
0.8
0.8
spin
0.9
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
0.2
7
9
1
3
5
7
9
1
2.1
1.9
spin
spin
3.0
spin
7
1
2.8
3.2
3.0
Co on Ni
3
5
7
2.1
B]
[
B]
[
B]
[
2.0
1.8
5
3.4
3.2
Fe on Ni
3
B]
5
2.0
[
3
spin
1
Fe on Au
1.9
1.8
Co on Au
2.8
1 3 5 7 9
no. of Fe atoms N
1 3 5 7 9
no. of Co atoms N
1 3 5 7
no. of Fe atoms N
FeN /Ni(001)
CoN /Ni(001)
FeN /Au(111)
1 3 5 7
no. of Co atoms N
CoN /Au(111)
CoN /Au(111): Tz changes the picture completely !
0.8
◮
For CoN on Au(111), trends of µspin and
of [µspin + 7Tz ]/nh are exactly opposite.
◮
Ignoring variations in Tz would lead to a false
estimate of how µspin per atom depends on
the cluster size
0.6
0.4
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
0.2
1
3
5
7
2.0
spin
[
B]
2.1
1.9
1.8
Co on Au
1 3 5 7
no. of Co atoms N
0.8
◮
◮
the cluster size
0.6
0.4
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
0.2
1
3
5
7
2.0
spin
[
B]
2.1
1.9
1.8
Co on Au
1 3 5 7
no. of Co atoms N
0.8
◮
◮
the cluster size
0.6
0.4
(
spin
+ 7 Tz) / nh [
B]
no Tz
with Tz
0.2
1
3
5
7
2.0
spin
[
B]
2.1
1.9
1.8
Co on Au
1 3 5 7
no. of Co atoms N
Sum rules themseleves can be checked
L2,3-edge XANES
6
L3
◮
Calculate the spectra theoretically
◮
Aply XMCD sum rules
◮
Compare µspin and µorb derived
from XMCD spectra with moments
calculated directly
◮
Upper integration boundary Ecut
chosen so that there are exactly
10 electron states up to Ecut in the
d band
isotropic
absorption
4
L2
2
L2,3-edge XMCD
0
2
0
difference
(+)
(-)
-
-2
-4
-10
0
10
20
energy [eV]
30
L2,3-edge XANES
6
L3
◮
◮
Aply XMCD sum rules
◮
calculated directly
◮
d band
isotropic
absorption
4
L2
2
L2,3-edge XMCD
0
2
0
difference
(+)
(-)
-
-2
-4
-10
0
10
20
energy [eV]
30
L2,3-edge XANES
6
L3
◮
◮
Aply XMCD sum rules
◮
calculated directly
◮
d band
isotropic
absorption
4
L2
2
L2,3-edge XMCD
0
2
0
difference
(+)
(-)
-
-2
-4
-10
0
10
20
energy [eV]
30
L2,3-edge XANES
6
L3
◮
◮
Aply XMCD sum rules
◮
calculated directly
◮
d band
isotropic
absorption
4
L2
2
L2,3-edge XMCD
0
2
0
-2
Ecut
-4
-10
0
10
difference
(+)
(-)
20
energy [eV]
30
Validity of sum rules
0.045
(
spin
orb
/ nh
orb
/(
spin
+ 7Tz)
FeN / Ni(001)
directly
0.035
0.05
spin
0.045
/(
spin
orb/nh
+ 7Tz)
per Fe atom
per Fe atom
0.7
per Fe atom
0.04
0.8
0.03
(
orb
+ 7Tz)/nh
0.055
+ 7Tz) / nh
0.04
0.6
0.025
2
4
6
number of Fe atoms
8
2
4
6
number of Fe atoms
8
2
4
6
8
number of Fe atoms
◮
Trends of the “effective moments” (µspin + 7Tz )/nh and
µorb /nh are reproduced well enough
◮
Applying sum rules to supported clusters in principle makes
sense
◮
However, beware of the Tz term (see above)
0.045
(
spin
orb
/ nh
orb
/(
spin
+ 7Tz)
FeN / Ni(001)
0.035
0.05
spin
0.045
/(
spin
orb/nh
+ 7Tz)
per Fe atom
per Fe atom
0.7
directly
from XAS
per Fe atom
0.04
0.8
0.03
(
orb
+ 7Tz)/nh
0.055
+ 7Tz) / nh
0.04
0.6
0.025
2
4
6
number of Fe atoms
8
2
4
6
number of Fe atoms
8
2
4
6
8
number of Fe atoms
◮
◮
sense
◮
0.045
(
spin
orb
/ nh
orb
/(
spin
+ 7Tz)
FeN / Ni(001)
0.035
0.05
spin
0.045
/(
spin
orb/nh
+ 7Tz)
per Fe atom
per Fe atom
0.7
directly
from XAS
per Fe atom
0.04
0.8
0.03
(
orb
+ 7Tz)/nh
0.055
+ 7Tz) / nh
0.04
0.6
0.025
2
4
6
number of Fe atoms
8
2
4
6
number of Fe atoms
8
2
4
6
8
number of Fe atoms
◮
◮
sense
◮
0.045
(
spin
orb
/ nh
orb
/(
spin
+ 7Tz)
FeN / Ni(001)
0.035
0.05
spin
0.045
/(
spin
orb/nh
+ 7Tz)
per Fe atom
per Fe atom
0.7
directly
from XAS
per Fe atom
0.04
0.8
0.03
(
orb
+ 7Tz)/nh
0.055
+ 7Tz) / nh
0.04
0.6
0.025
2
4
6
number of Fe atoms
8
2
4
6
number of Fe atoms
8
2
4
6
8
number of Fe atoms
◮
◮
sense
◮
0.045
(
spin
orb
/ nh
orb
/(
spin
+ 7Tz)
FeN / Ni(001)
0.035
0.05
spin
0.045
/(
spin
orb/nh
+ 7Tz)
per Fe atom
per Fe atom
0.7
directly
from XAS
per Fe atom
0.04
0.8
0.03
(
orb
+ 7Tz)/nh
0.055
+ 7Tz) / nh
0.04
0.6
0.025
2
4
6
number of Fe atoms
8
2
4
6
number of Fe atoms
8
2
4
6
8
number of Fe atoms
◮
◮
sense
◮
XMCD spectroscopy of clusters: Conclusions
◮
Sum rules can yield useful information about trends in
(µspin + 7Tz )/nh and µorb /nh
◮
However, the Tz term is a bad guy — it can completely
reverse the trends of (µspin + 7Tz )/nh and µspin
XMCD spectroscopy of clusters: Conclusions
◮
Sum rules can yield useful information about trends in
(µspin + 7Tz )/nh and µorb /nh
◮
However, the Tz term is a bad guy — it can completely
reverse the trends of (µspin + 7Tz )/nh and µspin
Praktický závěr (nejen pro magnetismus nanostruktur)
Pokud vı́te, co děláte, můžete si dovolit leccos

Ab-initio výpocty magnetismu clusteru a nanostruktur:

Transkript

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