Outlook of the lecture Magnetism in nutshell Xray absorption - - PowerPoint PPT Presentation

Outlook of the lecture

• Magnetism in nutshell
• X‐ray absorption spectroscopy XAS
• Magnetic XAS = XMCD (X‐ray Magnetic Circular

Dichroism)

Eberhard Goering, MPI‐IS, Stuttgart

Magnetism in a nutshell

• „Rotating“ charges produce magnetic field (angular momentum)
• There are two types spin (S) and orbital (L) magnetic moments

s

z B

 

        866 . 2 3 1 s s s 2   2  

macroscopic atomistic

L s

L is often quenched (3d) = close to zero  super important, but hard to quantify! interacts with the lattice

Magneton s Bohr' factor G g J/T 10 274 . 9 2

24

            

 B B B z B z z S B z z L

S S g m L m     

Magnetism is related to angular momenta of charges L and S

• 2
• 1

• 1,0
• 0,5

7 ML Fe

[110] [100] [110]

Feld [kOe]

• rbital moment
• orbital moment has preferred axis in anisotropic crystal field
• LS‐coupling in 3d‐shell orients the spin
• The small L is important for almost all properties, especially for technology
• remnant field, easy and hard axis, coercivity ….

magnetic easy axis

L S



Anisotropy

• P. Bruno, Physical Review B 39 (1989) 865

Some examples for “modern” magnetism applications!

• Supermagnets

www.helbling.ch

2x2cm Magnet

C- W- Co- FeNiAl AlNiCol SmCo5 Nd Fe B

Stähle 1880 1900 1920 1932 1936 1949 1967 1984-1997 Ticonal II Ticonal GG

Low weight and high field = forces Optimizing interaction strength between lattice and magnetic moments  orbital moments Important to know: What is the magnetism of each element? Nd? Fe? Co? Sm?....

Some examples for “modern” magnetism applications!

• Data storage

Optimizing interaction strength between lattice and magnetic moments  orbital moments permanent magnets, magnetostriction, spin wave damping, etc. etc.

10 TB

„Perpendicular Recording“ NdFeB‐Servo‐Motor

Why X‐rays and magnetism?

• It is important to know spin and orbital moments
• for each element in the system separately
• contact areas are important  probing single

atomic layers and separating them from others

• We know: X‐rays provide significant spatial

resolution on the atomic scale

• Your will see here how this is transferred to

magnetism using X‐ray Magnetic Circular Dichroism (XMCD)

• Or in other words: XMCD is able to transfer ANY

X‐ray technique in it’s magnetic counterpart!

Now XAS

• X‐ray absorption spectroscopy XAS
• Dipole selection rules provide “wanted projections”
• symmetry selective
• Electric field vector can provide orbital occupation and
• rientation
• Further Examples:
• Gas on a surface  Chemistry and binding orientation
• Valence and Band structure determination (unoccupied of

cause)

Why XAS!

• X‐ray absorption

spectroscopy (XAS)

• dipole selection rules
• probing 3d magnetism

2p  3d

• probing 4f magnetism

3d  4f

One famous example (also for magnetism): 2p  3d

p 2

2 / 1 1 2 2 2 / 1 1 2 2

2 / 1 2 / 3

          S L J p p S L J p p

J J 2 / 1 2 / 3

2 2 p p

Spin‐Orbit‐Splitting Energy

l l q m m 1      

p 2

Spin‐Orbit‐Splitting

2 / 1 2 / 3

2 2 p p

energy position of the resonant spectra (binding energy ) depends strongly on the nuclear charge element specific! probes the unoccupied (here) 3d electrons  holes

XAS: In resonance very strong effects

One famous example (also for magnetism): 2p  3d Energy

All is based on Fermi’s Golden Rule!

• It provides the probability to excite an electron from

the initial state to the final state Based on time dependent pertbation theory Time integral  “Energy‐Conserving‐ Deltafunction”

i



f



2 ) 1 ( (

dt d t) c W

b ba 

) ( H : is n Hamiltonia total The ) ( 2 : Rule Golden s Fermi'

tot 2

t H H E E H W

phot i f i phot f fi

            

What have we learned so far? XAS because ..

• it probes unoccupied states
• element specific due to energy position
• symmetry selective due to selection rules p  d

What else?

Good for chemistry and band structure determination

• Example: Mn L2,3 2p3d
• different oxidization states
• shape provides important

information about the unoccupied density of states

• some less clear chemical shift
• bservable
• reason: also the initial (here 2p)

and the final states (here 3d) are shifted

• details often complicated, due to

electron‐electron‐interaction and so called “multiplet effects”

(not discussed here)

source: PHYSICAL REVIEW B Volume: 75 Issue: 4 Article Number: 045102

“nano”‐complex

Hexadecane on a Cu surface

• Molecular orientation on the surface

Source: D.A.Fischer Tribology Letter 3 (1997) 41

C16H34

Tilt angle determined by the angular dependency of the XAS spectra

C C  *  H C 



C 1s  2p

parallel

E

C H

lar perpendicu

E

C C

This also works nicely in anisotropic single crystals

XAS: How to measure X‐ray Absorption Spectroscopy

I0

d

I1

intensity 1/e for length the i.e. length, n attenuatio ) ( 1 ) ( ln 1 ) ( ) (

) (

      

 

E E I I d E e I E I

phot d E phot

  



Lambert‐Beer‐Law:

Example: Fe metal (calculation without resonances and spin –orbit‐splitting)

source: http://henke.lbl.gov/optical_constants/

Hard to measure below 3‐5keV, due to the very short attenuation length  Other techniques to measure the absorption

1s or K edge 2p 3/2 and 1/2 or L2,3 edges 2s or

L1 edge

3p or

M23 edges

The absorption coefficient is often measured indirectly

• Example: Soft X‐rays  50‐2000eV

I0

conventional transmission Idea: Every additionally absorbed photon, for example due to the 2p3d transition, produce additional electrons (Photo el., AUGER and secondaries) and fluorescence photons higher absorption  more electrons (fluorescence photons)

e‐

GND Total Electron Yield (TEY) Total Fluorescence Yield (TFY) Typical sampling depth: Transmission: like  TEY: 0.5‐3nm TFY: 30‐200nm

Helical Undulator

108 x more brilliance than x-ray tubes

20 ps t ~ 2 ns

ca. 10 mm

104 * more brilliance than x-ray tubes

You need tunable polarized soft X-rays Synchrotron radiation

Global Synchrotron Density

multi-bunch mode: 348 buckets (~ 0.75 mA) + “camshaft” (~ 10 mA)

I = 200-300 mA

standard operation mode 2 ns

…

t

I = <25 mA Single Bunch Mode

available only for 2 x 2 weeks/a

T = 800 ns t

For dynamic investigations  time structure of synchrotron radiation

Pulse width down to 10 psec

Now we go for Magnetism

• As magnetism is related to angular motion, why not

using an “angular” probe?

• We will use circular polarized X‐rays!

XMCD: X‐ray Magnetic Circular Dichroism

• In other words: Sample magnetization changes the

absorption of X‐rays

• Sometimes a rather dramatic effect
• Pathway
• What is XMCD?
• How does it look like? Example: Fe Metal
• How is it used? Quantitative!  sum rules
• Can we understand this? Somehow!

Actually: First observed by Gisela Schütz in 1987 Director MPI for Intelligent Systems

Again: How to get polarized X‐rays?

x y z



• 1. bending magnet
• 2. Undulator
• ca. 30m

relativistic electrons

We also need „optical“ components

• approx. 1000 times higher brilliance

How does it look exactly for soft x‐rays

• typical setup for soft x‐rays (100‐2000eV)

planar grating (approx 1000 lines/mm) for about 0.5-10 nm wave length focusing mirror

sample top view side view

Ultra-High-Vacuum! 10-10 mBar

Measurement of the absorption coefficient µ  now depending on the sample magnetization

Measured quantity:

I±(x) = I0 exp( -d µ± )

I0

Magnetization Polarization

d

I1

X-ray magnetic circular dichroism: XMCD

=+‐‐  (PM)

XMCD: element specific, as XAS is!

1 2 3 4 5 6

2p1/2 2p3/2

Fe 2p  3d absorption

-  + 

absorption [edge normalized]

690 700 710 720 730 740 750 760

• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5

+--

Dichroism (edge normalized) Photon energy [eV]

E2p 2p3/2 2p1/2

Fe 3d

E2p

Energy

F

• Element specific, due to the defined

energy of the absorption edges!

• Magnetism has a strong impact on

the absorption coefficient!

 

XMCD strongly modifies the X-ray optical properties

Magneto‐Optic‐Effects: Origin (also for XMCD :=)

Start: Hunds rules Groundstate: Simplest example 3d1 L = 2 ; S = ½ and J = L - S = 3/2 For T 0 and B   only mJ = -2 +1/2 = -3/2 is occupied (saturated) Dipole-Selection-Rules: l = ±1  circular Pol.: mJ = ±1

• This is a very general approach!
• Could be done in resonance or off resonance

3/2 1/2 ‐1/2 ‐3/2 mJ= 5/2 3/2 1/2 ‐1/2 ‐3/2 ‐5/2

J = 5/2 J = 3/2

mJ = ‐1

mJ = +1

 mJ = 0

right circ. left circ. lin pol. Take home message: For circular polarization absorption is modified by magnetism!

N S

This is how the L2 and L3 edge excitations are using right circular polarized light!

• Schematics of the excitation:S

Flipping the magnetization gives different excitation probabilities

• H. Ebert, Rep. Prog. Phys. 59, 1996

N S N S N S

One example: SmCo5 doped with some Fe

• The magnetic moment of each

element could be extracted separately

• Good for the understanding of

magnetism in complex systems

• Sample has been modified to

change the coercive behavior  Sm is responsible for that!

• 4
• 2

Fe L2,3

XMCD@2T Hc=0.00T Hc=0.15T Hc=0.90T

Absorption (normalized)

Photon Energy (eV)

• 2

XMCD@2T Hc=0.00T Hc=0.15T Hc=0.90T

Absorption (normalized)

Photon Energy (eV)

Co L2,3

1060 1080 1100 1120 1140

• 2
• 1

1 2 3 4

XMCD (normalized) Photon Energy (eV)

Hc= 0.00T Hc= 0.15T Hc= 0.90T

1060 1080 1100 1120 1140 2 4 6 8 10 12 14 16

Absorption (normalized) Photon Energy (eV)

Schütz, Goering, Stoll, Int. J. Mat. Sci. 102 (2011) 773

B

XMCD in 3d Transition Elements

Spin orbit splitting of 2p shell decreases from Cu to Ti Width increase  more unoccupied electrons

Now it happens: Sum rules

• T. Thole, P. Carra et al. : PRL 86 (1992) 1943 ; PRL 70 (1993) 694

We cant do this here in detail! This would take at least 3‐4 times a 1.5h lecture!

Orbital L and Spin S XMCD

700 710 720 730 740

• 2
• 1

1 Reales XMCD Spektrum Photonenenergie [eV]



+ - 

• “Nur Bahn”

“Nur Spin”

(

+ + 

• )/2

XMCD XAS

„Real“ Spectra (Fe) A(L3) A(L2)

(µ++µ‐)/2

µ+ ‐ µ‐

pure S pure L

XMCD is famous because its quantitative: Sum‐Rules

• quantitative determination of

projected magnetic moments

• S, L and Tz separable
• in projected Bohr‐magnetons!
• one needs the “areas” and the

number of holes

• (10‐n3d)

Theoretical prediction: T. Thole, P. Carra et al. : PRL 86 (1992) 1943 ; PRL 70 (1993) 694

700 710 720 730 740

‐2 ‐1 1

XMCD (normalized) Photon Energy (eV) 1 2 3 4 5 Absorption (normalized)

   

d z z d z

n T S n L

3 3

10 2 2 7 10 2 3 4                

We will see Tzlater more!

“Spin” averaged

• r non magnetic

spectrum! magnetic or difference spectrum!

    

h

n

2 South 2 North 

South

• North
• Exp. verification and rough procedure: C.T. Chen et al, PRL 75 (1995) 152

Data measurement and analysis: Co thin film!

Measure sample current I1 and incoming intensity I0 for north and south field Step 1: Divide them I1/I0

770 780 790 800 810 820 10 20 30 40 50 60 70 80 90 100 110 120 130 140

I0,I1 current (pA) Energy (eV) I1 I0

Co 2p > 3d L2,3

740 750 760 770 780 790 800 810 820 830 2,0 2,5 3,0 3,5 4,0 4,5

I1/I0

Energy (eV) South North

Co 2p > 3d L2,3

• nly north

north and south means field orientation with respect to the photon beam!

Data measurement and analysis

Step 2: Remove „offset“ by a simple factor Important: Make sure that pre‐ and Post‐Edge region (without XMCD) are equal

740 750 760 770 780 790 800 810 820 830 2,0 2,5 3,0 3,5 4,0 4,5

I1/I0

Energy (eV) South North

Co 2p > 3d L2,3

Here the factor is 1.04

760 770 780 790 800 810 820 2,0 2,5 3,0 3,5 4,0 4,5

I1/I0 (factor applied)

Energy (eV)

South North

Co 2p > 3d L2,3

Data measurement and analysis

Step 3: Subtract background by a linear approximation Important: Exactly the same for north and south spectra

760 770 780 790 800 810 820 2,0 2,5 3,0 3,5 4,0 4,5

I1/I0 (factor applied)

Energy (eV)

South North

Co 2p > 3d L2,3

760 770 780 790 800 810 820 0,0 0,5 1,0 1,5 2,0 2,5

I1/I0 (line subtr.)

Energy (eV)

South North

Co 2p > 3d L2,3

Data measurement and analysis

Step 4: Devide by post edge value to normalize Important: Exactly the same value for north and south spectra

760 770 780 790 800 810 820 0,0 0,5 1,0 1,5 2,0 2,5

I1/I0 (line subtr.)

Energy (eV)

South North

Co 2p > 3d L2,3

760 770 780 790 800 810 820

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

I1/I0 (edge norm

Energy (eV)

South North

Co 2p > 3d L2,3

Now the data is so called edge normalized! Here 0.425

Data measurement and analysis

Step 5: Plot together with difference XMCD= North‐South

770 780 790 800 810

• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

I1/I0 (edge norm

Energy (eV)

South North XMCD

Co 2p > 3d L2,3

Data measurement and analysis

Step 6: For sum rule analysis remove non resonant background and calculate the “non magnetic” average. This does not change XMCD signal

760 770 780 790 800 810 820

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

I1/I0 (edge norm

Energy (eV)

South North backgroundB

Co 2p > 3d L2,3

770 780 790 800 810

• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

XAS (edge norm)

Energy (eV)

(N/2-S/2)-Back

Co 2p > 3d L2,3

Data measurement and analysis

Step 7: Calculate the integrals for XAS (= nonmagnetic) and XMCD

770 780 790 800 810

• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

XAS (edge norm)

Energy (eV)

(N/2-S/2)-Back

Co 2p > 3d L2,3

760 770 780 790 800 810 820

• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0

I1/I0 (edge norm

Energy (eV)

XMCD

Co 2p > 3d L2,3

760 770 780 790 800 810 820

• 4,0
• 3,5
• 3,0
• 2,5
• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5

Integral (XMCD)

Energy (eV)

Integral XMCD

Co 2p > 3d L2,3

760 770 780 790 800 810 820

• 2

2 4 6 8 10 12 14

XAS (edge norm)

Energy (eV)

XAS Integral

Co 2p > 3d L2,3

XAS = 13.77 ‐3.684 ‐1.169 = XMCD (L3) XMCD (L2)=‐1.169‐(‐3.684) =2.515

Data measurement and analysis

Step 8: Sum Rules Calculation: Use values in formula

785 . 49 . 2 77 . 13 2 515 . 2 2 64 . 3 7 14 . 49 . 2 77 . 13 2 515 . 2 64 . 3 3 4                  

z z z

T S L

XAS = 13.77= XMCD (L3)= ‐3.684 = XMCD (L2)= 2.515 = 49 . 2 ) Co ( 1

3

 

d

n

   

d z z d z

n T S n L

3 3

10 2 2 7 10 2 3 4                

Data measurement and analysis

Step 9: Correct for finite degree of circular polarization

Depends on Energy, setup, beamline, source as bending or undulator etc.

• etc.  usually ask the beamline responsible

In our case here 84%! Using the g‐factor of 2 for the spin and transfer from angular momenta to magnetic moments

B B B z z S B B B z z L

S m L m       87 . 1 84 . 785 . 2 84 . 2 17 . 84 . 14 . 84 .           

Element

• exp. (XMCD)

theo. ms (µB) ml (µB) ms (µB) ml (µB) Fe Chen PRL 75 1.98 0.085 2.19  0.059 Co Chen PRL 75 1.55 0.153 1.57  0.087 Ni

Dhesi PRB 60

0.58 0.07 0.58  0.06 The deviation here is because of Tz!

770 780 790 800 810

• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5

I1/I0 (edge norm

Energy (eV)

XMCD N/2+S/2

Co 2p > 3d L2,3

Sum‐Rules Hands On

• Try to estimate the areas using a rule and a pen.

Estimating area by FWHM x Height or as you want

B z z B z

T S L   57 . 1 7 14 .     XMCD N/2+S/2

Data measurement and analysis

Typical pitfall: Offset corrected with wrong factor

Best visible in a finite slope in the XMCD integral If present  better factor

I1/I0

Energy (eV) South North

Co 2p > 3d L2,3

740 750 760 770 780 790 800 810 820 830

• 1,0
• 0,5

0,0 0,5

XMCD

Energy (eV) XMCD

Co 2p > 3d L2,3

740 750 760 770 780 790 800 810 820 830

• 2,5
• 2,0
• 1,5
• 1,0
• 0,5

0,0

Integral(XMCD)

Energy (eV) XMCD

Co 2p > 3d L2,3

Why using a single factor for Offset correction?

Electron current depends on B‐field dependent proportionality. Could be asymmetric

• E. Goering et al., J.Sync.Rad. 8 (2001) 434‐436 and J. Appl. Phys. 88 (2000) 5920

) , ( ) ( ) , ( B E B f B E I

phot phot

  

) , ( ) ( ) , ( ) , ( ) ( ) , ( B E E B E B E E B E

phot c phot phot phot c phot phot

         

 

   

) , ( ) ( ) ( ) , ( ) ( ) ( ) ; ( B E E B f B E E B f B E I

phot c phot phot c phot phot

          

 

) , ( ) ( 2 ) ; ( : ) ( ) ( ) ( if B E B f B E I B f B f B f

phot c phot

      

 

) ( ) ( as choose ) ( ) ( if

   

    B f k B f k B f B f

As µ0 is not a straight line, a line offset subtraction is wrong!



   

) , ( ) ( ) ( ) ( ) ( ) ( B E B f B f E B f B f

phot c phot

       

   

Sum Rules: In general for all edges!

From Schütz, Stoll, and Goering Handbook of Magnetism (Wiley) based on T. Thole, P. Carra et al. : PRL 86 (1992) 1943 ; PRL 70 (1993) 694

J+ is L+S and J‐ is L‐S: Example L3 edge: l=1 s=1/2 J=J+= 1+1/2 = 3/2 and J=J‐= 1‐1/2 = 1/2

this is the absorption sum for all absorption channels: µ‐= left, µ+= right, and µ0= z‐polarized light angular momenta for the i=initial and f=final states

What is this Tz?

• G. van der Laan, J. Phys.:
• Condens. Matter 10 (1998) 3239

S Q Tz ˆ 7 2    

perturbation theory provides:

Q: quadrupolar charge distribution traceless tensor 2nd order

+ +

• 

z

T



z

T

Is important in less than cubic systems, with oriented crystals, in 4f metals, and in ultra thin films and interfaces Something more about Tz: König and Stöhr, PRL 75 (1995) 3748; Buck and Fähnle, JMMM 166 (1997) 297

Further “Problems”

• For the light 3d transition metals, its hard to

separate P3/2 and P1/2 excitations  excitations “mix”

• In 4f systems, as supermagnets, the spin‐sum‐rule

is not „simply“ valid anymore (orbital works fine)

• Actually, we are working on this at the moment, and it looks to be solvable, at least

in a practical way.

see: E. Goering, Phil. Mag. 85 (2005) 2897‐2911 and references therein see: Y. Teramura et al, J.Phys.Soc 65 (1996) 3056 and T. Jo, J.El.Spec.Rel.Phenom, 86 (1997) 73

Scienta‐ PES FOCUS‐ PEEM PLD

Neue 7T XMCD‐System 7T magnet 5‐450K Kryomanipulator

2013 we could inaugurate our “new” 7T XMCD system!

• ANKA‐Karlsruhe

@ WERA‐Beamline

• Unique superconducting magnet system
• 7T ramped with 1.5T/s! (‐5T  +5T in 6,6s)

– low temperatures, portable, “load lock” – TEY, FY, Transmission  parallel – No L‐He refill  two “cryo‐coolers” – Gives anough signal to detect paramgnetism of diluted systems  now 0.0002µB sensitivity – Fast XMCD measurements with highest quality  2‐5 min/spectra

500 600 700 800 900 1000 1100 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95

II0 (a.u.) Energy (eV)

• rel. BG: 5%
• rel. Ni L3: 1.5 %

In‐situ prepared Ni nanostructures (3nm height) : 0.2 ML nominal (@ 200 K) on Graphen/Ir Moiré‐template Cooperation with group of

• M. Fonin, Univ.‐ Konstanz

Sicot et. al.: APPLIED PHYSICS LETTERS 96, 093115 2010

STM

XMCD at the „recent“ limit: 0.2ML paramagnetic Ni on Graphen

1 2 3 XAS

 

15 K, 7 T

850 860 870 880 890

• 1.0
• 0.5

0.0

 integrated 

XMCD Energy (eV)

The oscillations are the so called EXAFS, which are usually not recognized, because they are so tiny! (for those who are interested)

Questions:

Remember: 1: Can we distinguish between pinned and rotatable moments? 2: Do we get a XMCD signal for a sample with permanent magnetic moments but disordered? 3: What do we get, if we have the same magnetic atoms, but half the amount? As Fe‐XMCD for Fe  FeCo alloy