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  • Synchrotron Radiation for

    Materials Science Applications

    Polarized X-rays from a Bending

    Magnet and X-ray Magnetic Circular

    Dichroism (XMCD)

    Brooke L. Mesler

    AS&T UC Berkeley

  • X-ray Magnetic Circular Dichroism

    Magnetization dependent absorption of circularly polarized light

    XMCD

    tioncrossAbsorptionrayX abs

    where abs

    x eIInotationAnother

    sec

    : 0

    −−==

    − =

    σρσµ

    µ

    ρ

    ρ

    )(),(),,(

    )3.1:(

    :

    0

    σµωµσωµµ

    ρµ

    ⋅+=⋅=

    −=

    MZMZ

    where

    aeqntext x

    e I

    I

    lecturespreviousfromrecall

    hh

    µ−

    µ+

    xright circ.

    left circ.

    I0 I

    I0 I

  • Circularly Polarized Light

    k̂σ σ=Photon angular momentum:

    Where σ=photon helicity =±1

    Right circularly polarized

    σ=+1

    Left circularly polarized

    σ=-1

  • Polarized Radiation at a Synchrotron

    Source

    Polarized light from an

    EPU or from off-axis

    bending magnet radiation

  • ultrarelativistic electrons

    ca. 30 m

    mm

    5

    -5

    1-1 010

    0

    Gain in polarization

    ⇔ Loss in intensity

    Polarization properties of SR

    e-

    TOP VIEW

    e- e-

    SIDE VIEW

  • Bending Magnet Radiation On-axis

    0=ψ

  • Power per Solid Angle

    observeremitter

    n v

    β& v

    a v

    Θ=××−=

    =

    ∝⇒

    Θ =

    =

    sin)(

    :

    )34.2:( 16

    sin :

    )32.2:( 16

    ),(:

    :

    2

    3

    0

    2

    222

    023

    0

    2

    22

    aaandanna

    onacceleratitransverseanote

    a SolidAngle

    power

    eqntext c

    ae

    d

    dP

    SolidAngle

    power and

    eqntextk rc

    ae trS

    area

    power

    lecturespreviousfromrecall

    TT

    T

    T

    T

    vvvvvv

    v

    v

    v

    v v

    vv

    επ

    επ

  • Flux per Solid Angle

    bandwidth

    electronsofbeamelectroncurrentI

    dtetaA

    SolidAngle

    Flux A

    e

    I

    dd

    Fd

    KimJeKwangfollowingNow

    tti

    B

    = ∆

    →=

    =

    =

    ∆ =

    ω ω

    α π

    ω ω

    ω ω ω

    α ψθ

    ω

    )(

    137/1

    ')'( 2

    )(

    )()(

    :,

    )'(

    2 2

    v

    K.-J. Kim,“Characteristics of Synchrotron Radiation,”pp565-632 in Physics of Particle Accelerators, AIP Conference Proceedings 184

    (American Inst. of Physics, New York 1989)

  • Horizontal and Vertical Components

      

      

    +

    −+ 

      

     =

      

     

      

    ∆ =

        

        

    )( 1

    )(

    ))(1( 2

    3

    :asAwritecanwefunctionsBesselifiedmodthegsinunow

    componentsverticalandhorizontalointupfluxbreak

    radiationtheofonpolarizatitheinerestedintareWe

    3/1 2

    3/2 2

    2

    h,

    2

    ,

    2

    ,

    2

    η

    η

    ω ω

    γ π

    ω ω

    α

    ψθ

    ψθ

    ν

    K X

    iX

    K

    iX A

    A

    A

    A

    e

    I

    dd

    Fd

    dd

    Fd

    cv

    h

    v

    h

    vB

    hB

    γψ

    ω ω

    η

    γ ω

    =

    +=

    =

    X

    X

    c

    m

    eB

    c

    2/3)21( 2

    1

    2

    23

    (We’ll see that this simplifies greatly for ψ� 0)

    K.-J. Kim,“Characteristics of Synchrotron Radiation,”pp565-632 in Physics of Particle Accelerators, AIP Conference Proceedings 184

    (American Inst. of Physics, New York 1989)

  • Flux as a function of angle

    ) 2

    1 ()/(

    )%1.0( )/()()(1033.1

    2

    1 0,00

    )( 1

    )(

    )1( 4

    3

    2

    3/2

    2

    2

    22

    213

    0

    2

    2

    ,

    2

    2

    3/12

    2

    2

    3/2 22

    2

    2

    2 ,

    2

    ,

    2

    )6.5:(

    cc

    c

    c

    B

    c

    vB

    cvB

    hB

    KEEHwhere

    BWmrad

    photons EEHAIGeVEe

    dddd

    Fd

    dd

    Fd XLet

    K X

    X

    K

    X e

    I

    dd

    Fd

    dd

    Fd

    eqntext

    ω ω

    ω ω

    ωωψθ

    ω ω

    η ψθ

    ψ

    η

    η

    ω ω

    ω ω

    γ π α

    ψθ

    ψθ

    ψ

     

      

     =

    ⋅ ×=

     

      

     ===⇒=

      

      

    +

    + 

      

    ∆ =

       

       

    =

    γψ

    ω ω

    η

    γ ω

    =

    +=

    =

    X

    X

    c

    m

    eB

    c

    2/3)21( 2

    1

    2

    23

    K.-J. Kim,“Characteristics of Synchrotron Radiation,”pp565-632 in Physics of Particle Accelerators, AIP Conference Proceedings 184

    (American Inst. of Physics, New York 1989)

  • Behavior at Critical Energy

    Horizontal (on axis) radiation as a

    function of energy

    Moving off axis

    Photon Flux

  • Behavior at 700eV

    L adsorption

    edges of Fe are

    ~707eV, ~720eV

    Bending magnet radiation is naturally polarized at small angles off-axis

    ALS:

    Ee=1.9GeV, I=400mA, B=1.27T

    Ec=0.6650*(Ee)2[GeV]B[T]

    EcALS=3.05keV

    700eV/3.05keV =0.2

    γ=1957Ee[GeV]

    γALS=3718.3

    γ*ψ=1 � ψ~2.7*10-4 radians

    Moving off axis

    Photon Flux

  • X-ray Magnetic Circular Dichroism

    (XMCD)

    0

    1

    2

    3

    4

    5

    700 710 720 730

    -2

    -1

    0

    µ (

    a. u .)

    ∆ µ

    ( a.

    u .)

    energy (eV)

    M↑↑σPhoton M σPhoton↑↓

    ∆µ/µ ≈ 50%

    L3

    L2

    706eV 719eV Fe

    � element specific

    � huge magnetic contrast

    � M·σPhoton � Quantitative probe of

    spin and orbital

    moments

    A typical XMCD result

    @ Fe L3,2 absorption

    edges

    M=magnetization

    = magnetic moment per volume

  • XMCD Measurement

    dichroic signal µ +− =µ − ∆µ

    transmission mode absorber

    µ −

    µ +

    x right circ.

    left circ.

    I0 I

    I0

    I

    x e

    I

    I ± ±

    −= 

      

     ρµ

    0

  • Dichroic signal

    dichroic signal µ +− =µ − ∆µ

    absorber

    µ−

    µ+ xright circ.

    left circ.

    I0 I

    I0

    I µ−

    µ+ I0

    I absorber

    right circ. x

    I0 I

  • X-ray Absorption

    Conservation laws

    • energy Eph=Ef-Ei

    • linear momentum (for

    small e-energies) in

    direction of E-vector

    • orbital momentum

    (symmetry)

    L2

    L3

    1s1/2 2s1/2

    2p1/2

    2p3/2

    d- d- continuum

    k k

    electron transitions

    E E (L )γ≥ B 3

    E E (L )γ≥ B 2

    0

    0

    1,0

    1

    :RulesSelection

    =∆

    =∆

    ±==∆

    ±=∆

    s

    l

    m

    s

    m

    l

    σ

  • Absorption of Circularly Polarized

    X-rays

    L2

    L3

    1s1/2 2s1/2

    2p1/2

    2p3/2

    d- d- continuum

    k k

    electron transitions

    E E (L )γ≥ B 3

    E E (L )γ≥ B 2

    2-step description:

    Photon “polarizes” electron through the transfer of angular momentum to electron spin through spin-orbit coupling

    Valence band only takes electrons of appropriate spin

  • | , >| , > | , > | , >

    Origin of Spin and Orbital Polarisation

    L L

    l

    z

    z

    2 3

    σ -1/2 +1/4

    +3/4 +3/4

    m=1m = +1/2j p1/2

    m = -1/2j

    2/3| >, l

    2/3| >,m=-1l ↑ 1/3| >,m=0l ↓

    1/3| , >m=0l ↑

    |m m>: l s 2 ↓ 1 ↑ 1 ↓0 ↑

    L absorption of a right pol. photon2