Ab-initio výpocty magnetismu clusteru a nanostruktur:

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Ab-initio výpocty magnetismu clusteru a nanostruktur:
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
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
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
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
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
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
Where does magnetism come from?
◮
Classically: Magnetic field is something produced by moving
electric charges that affects other moving charges
◮
Special relativity: Magnetism is a fictitious force needed to
guarantee Lorentz invariance when charges move
◮
◮
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
Where does magnetism come from?
◮
Classically: Magnetic field is something produced by moving
electric charges that affects other moving charges
◮
Special relativity: Magnetism is a fictitious force needed to
guarantee Lorentz invariance when charges move
◮
◮
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
Where does magnetism come from?
◮
Classically: Magnetic field is something produced by moving
electric charges that affects other moving charges
◮
Special relativity: Magnetism is a fictitious force needed to
guarantee Lorentz invariance when charges move
◮
◮
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
Where does magnetism come from?
◮
Classically: Magnetic field is something produced by moving
electric charges that affects other moving charges
◮
Special relativity: Magnetism is a fictitious force needed to
guarantee Lorentz invariance when charges move
◮
◮
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
Magnetický moment
◮
Magnetický moment µ je mı́rou snahy zmagnetizovaného
objektu orientovat se v souhlau s vnějšı́m magnetickým polem
◮
Moment sı́ly τ působı́cı́ na magnetický moment
v magnetickém poli:
τ = µ×H
◮
Potenciálnı́ energie magnetického momentu v magnetickém
poli:
U = −µ · H
◮
Přı́klad: Pro uzavřenou smyčku
µ = µ0 I S
Magnetický moment
◮
Magnetický moment µ je mı́rou snahy zmagnetizovaného
objektu orientovat se v souhlau s vnějšı́m magnetickým polem
◮
Moment sı́ly τ působı́cı́ na magnetický moment
v magnetickém poli:
τ = µ×H
◮
Potenciálnı́ energie magnetického momentu v magnetickém
poli:
U = −µ · H
◮
Přı́klad: Pro uzavřenou smyčku
µ = µ0 I S
Magnetický moment
◮
Magnetický moment µ je mı́rou snahy zmagnetizovaného
objektu orientovat se v souhlau s vnějšı́m magnetickým polem
◮
Moment sı́ly τ působı́cı́ na magnetický moment
v magnetickém poli:
τ = µ×H
◮
Potenciálnı́ energie magnetického momentu v magnetickém
poli:
U = −µ · H
◮
Přı́klad: Pro uzavřenou smyčku
µ = µ0 I S
Magnetický moment
◮
Magnetický moment µ je mı́rou snahy zmagnetizovaného
objektu orientovat se v souhlau s vnějšı́m magnetickým polem
◮
Moment sı́ly τ působı́cı́ na magnetický moment
v magnetickém poli:
τ = µ×H
◮
Potenciálnı́ energie magnetického momentu v magnetickém
poli:
U = −µ · H
◮
Přı́klad: Pro uzavřenou smyčku
µ = µ0 I S
Two ways of moving an electron
(A quick and dirty introduction to magnetism)
◮
Orbiting
◮
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
◮
Magnetické vlastnosti materiálů závisı́ na směru (orientaci)
Energie systému závisı́ na směru spontánnı́ magnetizace
◮
Různé zdroje (druhy) magnetické anizotropie
Magnetická anizotropie
◮
Magnetické vlastnosti materiálů závisı́ na směru (orientaci)
Energie systému závisı́ na směru spontánnı́ magnetizace
◮
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.
#
Magnetokrystalická anizotropie
Orientace magnetizace ve směru preferovaném geometrickou
strukturou krystalu
◮
U normálnı́ch (3D) látek obvykle malá
◮
U povrchů, vrstev, clusterů může být vysoká
Magnetokrystalická anizotropie
Orientace magnetizace ve směru preferovaném geometrickou
strukturou krystalu
◮
U normálnı́ch (3D) látek obvykle malá
◮
U povrchů, vrstev, clusterů může být vysoká
Magnetokrystalická anizotropie
Orientace magnetizace ve směru preferovaném geometrickou
strukturou krystalu
◮
U normálnı́ch (3D) látek obvykle malá
◮
U povrchů, vrstev, clusterů může být vysoká
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
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
Magnetism of Fe atom
Magnetic properties of atoms are governed by Hund rules
Electron configuration: 3d 6 4s 2
◮
Spin magnetic moment: µspin = 4 µB
◮
◮
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
◮
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)
Magnetism of Fe atom
Magnetic properties of atoms are governed by Hund rules
Electron configuration: 3d 6 4s 2
◮
Spin magnetic moment: µspin = 4 µB
◮
◮
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
◮
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)
Magnetism of Fe atom
Magnetic properties of atoms are governed by Hund rules
Electron configuration: 3d 6 4s 2
◮
Spin magnetic moment: µspin = 4 µB
◮
◮
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
◮
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)
Magnetism of bulk Fe crystal
◮
Generally: Magnetism is suppressed in the bulk
(with respect to atomic case)
◮
Intuitively: Electron are not free to orbit around atoms
◮
Spin magnetic moment is µspin ≈ 2.2 µB per atom
◮
Orbital magnetic moment is quenched (outright zero in
non-relativistic case)
Magnetism of bulk Fe crystal
◮
Generally: Magnetism is suppressed in the bulk
(with respect to atomic case)
◮
Intuitively: Electron are not free to orbit around atoms
◮
Spin magnetic moment is µspin ≈ 2.2 µB per atom
◮
Orbital magnetic moment is quenched (outright zero in
non-relativistic case)
Magnetism of bulk Fe crystal
◮
Generally: Magnetism is suppressed in the bulk
(with respect to atomic case)
◮
Intuitively: Electron are not free to orbit around atoms
◮
Spin magnetic moment is µspin ≈ 2.2 µB per atom
◮
Orbital magnetic moment is quenched (outright zero in
non-relativistic case)
Magnetism of bulk Fe crystal
◮
Generally: Magnetism is suppressed in the bulk
(with respect to atomic case)
◮
Intuitively: Electron are not free to orbit around atoms
◮
Spin magnetic moment is µspin ≈ 2.2 µB per atom
◮
Orbital magnetic moment is quenched (outright zero in
non-relativistic case)
Surfaces are magnetism-friendly
◮
Atoms at surfaces exhibit some atomic-like
characteristics
◮
Spin magnetic moment is larger than in bulk; for Fe it is
µspin ≈ 2.5–3.0 µB per atom
◮
The orbital magnetic moment is increased by an even larger
percentage, µorb ≈ 0.07–0.12 µB per atom
Surfaces are magnetism-friendly
◮
Atoms at surfaces exhibit some atomic-like
characteristics
◮
Spin magnetic moment is larger than in bulk; for Fe it is
µspin ≈ 2.5–3.0 µB per atom
◮
The orbital magnetic moment is increased by an even larger
percentage, µorb ≈ 0.07–0.12 µB per atom
Surfaces are magnetism-friendly
◮
Atoms at surfaces exhibit some atomic-like
characteristics
◮
Spin magnetic moment is larger than in bulk; for Fe it is
µspin ≈ 2.5–3.0 µB per atom
◮
The orbital magnetic moment is increased by an even larger
percentage, µorb ≈ 0.07–0.12 µB per atom
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 ?
◮
Magnetická anizotropie vrstev je řádově většı́ než anizotropie
krystalů
◮
Magnetická anizotropie clusterů je (až) řádově většı́ než
anizotropie vrstev.
◮
⇒ Kdož máš zájem na vysoké anizotropii, vrhni se na
nanostruktury
A co anizotropie malých systémů ?
◮
Magnetická anizotropie vrstev je řádově většı́ než anizotropie
krystalů
◮
Magnetická anizotropie clusterů je (až) řádově většı́ než
anizotropie vrstev.
◮
⇒ Kdož máš zájem na vysoké anizotropii, vrhni se na
nanostruktury
A co anizotropie malých systémů ?
◮
Magnetická anizotropie vrstev je řádově většı́ než anizotropie
krystalů
◮
Magnetická anizotropie clusterů je (až) řádově většı́ než
anizotropie vrstev.
◮
⇒ Kdož máš zájem na vysoké anizotropii, vrhni se na
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 ?
◮
µorb is small but important !
◮
It is a manifestation of spin-orbit coupling, which is the
mechanism behind the magnetocrystalline anisotropy
◮
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
Why all the fuss with µorb ?
◮
µorb is small but important !
◮
It is a manifestation of spin-orbit coupling, which is the
mechanism behind the magnetocrystalline anisotropy
◮
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
Why all the fuss with µorb ?
◮
µorb is small but important !
◮
It is a manifestation of spin-orbit coupling, which is the
mechanism behind the magnetocrystalline anisotropy
◮
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
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
Clusters: Who they are?
◮
Free clusters — giant molecules, surrounded by vacuum
◮
Supported clusters — adsorbed on a surface
Clusters: Who they are?
◮
Free clusters — giant molecules, surrounded by vacuum
◮
Supported clusters — adsorbed on a surface
Comparing free and supported clusters
◮
How do the magnetic properties change if clusters are
deposited on a substrate ?
◮
Take analogous systems (identical sizes, identical geometries)
and have a look
◮
Focus rather on the trends than on particular values
Comparing free and supported clusters
◮
How do the magnetic properties change if clusters are
deposited on a substrate ?
◮
Take analogous systems (identical sizes, identical geometries)
and have a look
◮
Focus rather on the trends than on particular values
Comparing free and supported clusters
◮
How do the magnetic properties change if clusters are
deposited on a substrate ?
◮
Take analogous systems (identical sizes, identical geometries)
and have a look
◮
Focus rather on the trends than on particular values
Calculational procedure for supported clusters
Impurity Green function method
◮
Calculate electronic structure of the “host” system (clean
surface)
◮
Supported clusters are treated as a perturbation to the clean
surface and the
◮
◮
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)
Calculational procedure for supported clusters
Impurity Green function method
◮
Calculate electronic structure of the “host” system (clean
surface)
◮
Supported clusters are treated as a perturbation to the clean
surface and the
◮
◮
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)
Calculational procedure for supported clusters
Impurity Green function method
◮
Calculate electronic structure of the “host” system (clean
surface)
◮
Supported clusters are treated as a perturbation to the clean
surface and the
◮
◮
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)
Calculational procedure for supported clusters
Impurity Green function method
◮
Calculate electronic structure of the “host” system (clean
surface)
◮
Supported clusters are treated as a perturbation to the clean
surface and the
◮
◮
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)
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
◮
Supported
clusters: nearly
monotonous decay
of µspin and µorb
with N
◮
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
Number of atoms in cluster
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
Number of atoms in cluster
10
2
4
6
Number of atoms in cluster
8
Average magnetic moments
2.3
Co
free
supported
3.1
◮
Supported
clusters: nearly
monotonous decay
of µspin and µorb
with N
◮
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
Number of atoms in cluster
4
6
8
Number of atoms in cluster
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
Number of atoms in cluster
10
2
4
6
Number of atoms in cluster
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
◮
µspin decreases if coordination number increases
◮
Estimates of µspin possible for large clusters
◮
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]
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
◮
µspin decreases if coordination number increases
◮
Estimates of µspin possible for large clusters
◮
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]
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
◮
µspin decreases if coordination number increases
◮
Estimates of µspin possible for large clusters
◮
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]
Effect of coordination on µspin
1.6
2.0
0
2
4
0
3.0
2.8
2.6
2.4
2
4
6
B]
Number of neighboring Co atoms
2.2
Co
free
2.0
1.8
spin
in Co spheres [
Fe
free
3.2
spin
in Fe spheres [
B]
Number of neighboring Fe atoms
2.2
1.6
2.0
0
2
4
Number of neighboring Fe atoms
0
2
4
Number of neighboring Co atoms
◮
µspin decreases if coordination number increases
◮
Estimates of µspin possible for large clusters
◮
For free clusters, big scatter of data
6
Comparison between free and supported clusters: summary
◮
Substrate acts as an adult supervisor for the free clusters
◮
◮
It suppresses the tendency of magnetic moments to oscillate
with cluster size
It makes µspin to depend linearly on the coordination number
◮
For free clusters, this trend appears as well but only for
spherical and/or larger clusters
Comparison between free and supported clusters: summary
◮
Substrate acts as an adult supervisor for the free clusters
◮
◮
It suppresses the tendency of magnetic moments to oscillate
with cluster size
It makes µspin to depend linearly on the coordination number
◮
For free clusters, this trend appears as well but only for
spherical and/or larger clusters
Comparison between free and supported clusters: summary
◮
Substrate acts as an adult supervisor for the free clusters
◮
◮
It suppresses the tendency of magnetic moments to oscillate
with cluster size
It makes µspin to depend linearly on the coordination number
◮
For free clusters, this trend appears as well but only for
spherical and/or larger clusters
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
Clusters and magnetism: Problems . . .
◮
Magnetic properties of large assemblies of clusters are
macroscopic: no principal problems with measuring them
◮
To understand nanomagnetism, one needs to study individual
small systems
◮
Magnetization of individual clusters (of just few atoms)
cannot be measured by macroscopic methods
◮
Recent progress in studying magnetism of clusters is, to a
large extent, associated with spectroscopy
Clusters and magnetism: Problems . . .
◮
Magnetic properties of large assemblies of clusters are
macroscopic: no principal problems with measuring them
◮
To understand nanomagnetism, one needs to study individual
small systems
◮
Magnetization of individual clusters (of just few atoms)
cannot be measured by macroscopic methods
◮
Recent progress in studying magnetism of clusters is, to a
large extent, associated with spectroscopy
Clusters and magnetism: Problems . . .
◮
Magnetic properties of large assemblies of clusters are
macroscopic: no principal problems with measuring them
◮
To understand nanomagnetism, one needs to study individual
small systems
◮
Magnetization of individual clusters (of just few atoms)
cannot be measured by macroscopic methods
◮
Recent progress in studying magnetism of clusters is, to a
large extent, associated with spectroscopy
Clusters and magnetism: Problems . . .
◮
Magnetic properties of large assemblies of clusters are
macroscopic: no principal problems with measuring them
◮
To understand nanomagnetism, one needs to study individual
small systems
◮
Magnetization of individual clusters (of just few atoms)
cannot be measured by macroscopic methods
◮
Recent progress in studying magnetism of clusters is, to a
large extent, associated with spectroscopy
X-ray absorption spectroscopy howto
◮
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
◮
Most of the absorption goes on account of the photoelectric
effect on core electrons
X-ray absorption spectroscopy howto
◮
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
◮
Most of the absorption goes on account of the photoelectric
effect on core electrons
Absorption via core electron excitation
Absorption via core electron excitation
◮
By tuning the energy of incoming x-rays,
electrons from one core level only
participate
◮
◮
Chemical selectivity
Dipole selection rule
◮
Angular-momentum selectivity
(whether they are s, p, d states. . . )
Absorption via core electron excitation
◮
By tuning the energy of incoming x-rays,
electrons from one core level only
participate
◮
◮
Chemical selectivity
Dipole selection rule
◮
Angular-momentum selectivity
(whether they are s, p, d states. . . )
Absorption via core electron excitation
◮
By tuning the energy of incoming x-rays,
electrons from one core level only
participate
◮
◮
Chemical selectivity
Dipole selection rule
◮
Angular-momentum selectivity
(whether they are s, p, d states. . . )
Absorption via core electron excitation
◮
By tuning the energy of incoming x-rays,
electrons from one core level only
participate
◮
◮
Chemical selectivity
Dipole selection rule
◮
Angular-momentum selectivity
(whether they are s, p, d states. . . )
Absorption edges (Absorpčnı́ hrany)
hrana
excitovaný elektron
K
L1
L2
L3
1s
2s
2p1/2
2p3/2
◮
Zvyšuje-li se energii fotonů, absorpčnı́ koeficient klesá
◮
Vzroste-li energie tak, že může dojı́t k excitovánı́ dalšı́ho
vnitřnı́ho elektronu, absorpčnı́ koeficient se skokem zvýšı́
Absorption edges (Absorpčnı́ hrany)
hrana
excitovaný elektron
K
L1
L2
L3
1s
2s
2p1/2
2p3/2
◮
Zvyšuje-li se energii fotonů, absorpčnı́ koeficient klesá
◮
Vzroste-li energie tak, že může dojı́t k excitovánı́ dalšı́ho
vnitřnı́ho elektronu, absorpčnı́ koeficient se skokem zvýšı́
Absorption edges (Absorpčnı́ hrany)
hrana
excitovaný elektron
K
L1
L2
L3
1s
2s
2p1/2
2p3/2
◮
Zvyšuje-li se energii fotonů, absorpčnı́ koeficient klesá
◮
Vzroste-li energie tak, že může dojı́t k excitovánı́ dalšı́ho
vnitřnı́ho elektronu, absorpčnı́ koeficient se skokem zvýšı́
Jemná struktura absorpčnı́ hrany: EXAFS a ti druzı́
◮
Nı́zké energie fotoelektronu (do ∼50 eV)
◮
◮
◮
XANES (X-ray Absorption Near Edge Structure)
NEXAFS (Near Edge X-ray Absorption Fine Structure)
Vysoké energie fotoelektronu (∼100–1000 eV)
◮
EXAFS (Extended X-ray Absorption Fine Structure)
◮
Určovánı́ struktury, zejména nekrystalických látek
Jemná struktura absorpčnı́ hrany: EXAFS a ti druzı́
◮
Nı́zké energie fotoelektronu (do ∼50 eV)
◮
◮
◮
XANES (X-ray Absorption Near Edge Structure)
NEXAFS (Near Edge X-ray Absorption Fine Structure)
Vysoké energie fotoelektronu (∼100–1000 eV)
◮
EXAFS (Extended X-ray Absorption Fine Structure)
◮
Určovánı́ struktury, zejména nekrystalických látek
Jemná struktura absorpčnı́ hrany: EXAFS a ti druzı́
◮
Nı́zké energie fotoelektronu (do ∼50 eV)
◮
◮
◮
XANES (X-ray Absorption Near Edge Structure)
NEXAFS (Near Edge X-ray Absorption Fine Structure)
Vysoké energie fotoelektronu (∼100–1000 eV)
◮
EXAFS (Extended X-ray Absorption Fine Structure)
◮
Určovánı́ struktury, zejména nekrystalických látek
Jemná struktura absorpčnı́ hrany: EXAFS a ti druzı́
◮
Nı́zké energie fotoelektronu (do ∼50 eV)
◮
◮
◮
XANES (X-ray Absorption Near Edge Structure)
NEXAFS (Near Edge X-ray Absorption Fine Structure)
Vysoké energie fotoelektronu (∼100–1000 eV)
◮
EXAFS (Extended X-ray Absorption Fine Structure)
◮
Určovánı́ struktury, zejména nekrystalických látek
Jemná struktura absorpčnı́ hrany: EXAFS a ti druzı́
◮
Nı́zké energie fotoelektronu (do ∼50 eV)
◮
◮
◮
XANES (X-ray Absorption Near Edge Structure)
NEXAFS (Near Edge X-ray Absorption Fine Structure)
Vysoké energie fotoelektronu (∼100–1000 eV)
◮
EXAFS (Extended X-ray Absorption Fine Structure)
◮
Určovánı́ struktury, zejména nekrystalických látek
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
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
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
What can XMCD do for us?
◮
Through the sum rules, XMCD can inform about µspin and
µorb separately
◮
For compounds, magnetic state of each element can be
explored separately
◮
Employing sum rules on experimental data may require
substantial theoretical input
What can XMCD do for us?
◮
Through the sum rules, XMCD can inform about µspin and
µorb separately
◮
For compounds, magnetic state of each element can be
explored separately
◮
Employing sum rules on experimental data may require
substantial theoretical input
What can XMCD do for us?
◮
Through the sum rules, XMCD can inform about µspin and
µorb separately
◮
For compounds, magnetic state of each element can be
explored separately
◮
Employing sum rules on experimental data may require
substantial theoretical input
Problems with sum rules
Approximations involved in its derivation:
◮
Transition to a well-defined single band
◮
Core hole neglected
◮
...
◮
Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
◮
Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
Problems with sum rules
Approximations involved in its derivation:
◮
Transition to a well-defined single band
◮
Core hole neglected
◮
...
◮
Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
◮
Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
Problems with sum rules
Approximations involved in its derivation:
◮
Transition to a well-defined single band
◮
Core hole neglected
◮
...
◮
Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
◮
Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
Problems with sum rules
Approximations involved in its derivation:
◮
Transition to a well-defined single band
◮
Core hole neglected
◮
...
◮
Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
◮
Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
Problems with sum rules
Approximations involved in its derivation:
◮
Transition to a well-defined single band
◮
Core hole neglected
◮
...
◮
Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
◮
Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
Problems with sum rules
Approximations involved in its derivation:
◮
Transition to a well-defined single band
◮
Core hole neglected
◮
...
◮
Could be at least partly corrected for by renormalization,
scaling and/or varying the L2,3 edge integration ranges
◮
Justified when studying series of related systems:
One can assume that the corrections will be similar for each
member of the series
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 !
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 !
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 !
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
Does Tz term really matter ?
◮
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
◮
If variations in Tz are small, neglect of Tz causes just an
overall shift of the deduced µspin
◮
Could Tz vary in such a way that the overall trends
of µspin +7Tz and µspin would be quite different ?
Does Tz term really matter ?
◮
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
◮
If variations in Tz are small, neglect of Tz causes just an
overall shift of the deduced µspin
◮
Could Tz vary in such a way that the overall trends
of µspin +7Tz and µspin would be quite different ?
Does Tz term really matter ?
◮
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
◮
If variations in Tz are small, neglect of Tz causes just an
overall shift of the deduced µspin
◮
Could Tz vary in such a way that the overall trends
of µspin +7Tz and µspin would be quite different ?
Does Tz term really matter ?
◮
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
◮
If variations in Tz are small, neglect of Tz causes just an
overall shift of the deduced µspin
◮
Could Tz vary in such a way that the overall trends
of µspin +7Tz and µspin would be quite different ?
Does Tz term really matter ?
◮
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
◮
If variations in Tz are small, neglect of Tz causes just an
overall shift of the deduced µspin
◮
Could Tz vary in such a way that the overall trends
of µspin +7Tz and µspin would be quite different ?
To find out wheter Tz may turn nasty or not
◮
Take a series of supported clusters of different sizes
◮
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
To find out wheter Tz may turn nasty or not
◮
Take a series of supported clusters of different sizes
◮
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
To find out wheter Tz may turn nasty or not
◮
Take a series of supported clusters of different sizes
◮
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
To find out wheter Tz may turn nasty or not
◮
Take a series of supported clusters of different sizes
◮
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
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)
Results: µspin and [µspin + 7Tz ]/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
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)
Results: µspin and [µspin + 7Tz ]/nh
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)
Results: µspin and [µspin + 7Tz ]/nh
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)
Results: µspin and [µspin + 7Tz ]/nh
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
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
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
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
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
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
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
-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)
Validity of sum rules
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
◮
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)
Validity of sum rules
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
◮
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)
Validity of sum rules
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
◮
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)
Validity of sum rules
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
◮
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)
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)
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